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Description of Statistical Computation

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationTue, 16 Nov 2010 17:40:38 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2010/Nov/16/t1289929174giqcuv2644o6h9u.htm/, Retrieved Fri, 19 Sep 2025 04:29:22 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=96122, Retrieved Fri, 19 Sep 2025 04:29:22 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact280

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Central Tendency] [Arabica Price in ...] [2008-01-06 21:28:17] [74be16979710d4c4e7c6647856088456]
- RM D  [Central Tendency] [WS6 - Mini Tutori...] [2010-11-11 14:21:40] [1f5baf2b24e732d76900bb8178fc04e7]
- R  D    [Central Tendency] [WS6 - Mini Tutori...] [2010-11-11 15:32:39] [1f5baf2b24e732d76900bb8178fc04e7]
- R  D        [Central Tendency] [WS6 - Mini Tutori...] [2010-11-16 17:40:38] [ee4a783fb13f41eb2e9bc8a0c4f26279] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
10,47
10,44
10,41
10,37
10,38
10,38
10,37
10,41
10,44
10,43
10,47
10,49
10,53
10,63
10,66
10,66
10,64
10,65
10,61
10,6
10,61
10,63
10,63
10,61
10,7
10,69
10,62
10,62
10,63
10,62
10,53
10,51
10,5
10,52
10,47
10,43
10,35
10,31
10,25
10,26
10,2
10,13
10,06
10,01
9,95
9,92
9,87
9,83
9,7
9,63
9,56
9,53
9,47
9,4
9,32
9,26
9,19
9,1
9,03
8,95
8,85
8,78
8,71
8,61
8,54
8,49
8,42
8,36
8,3
8,19
8,15
8,1
8,04
8,05
8,04
8
8,02
8
8
8,01
8,04
8,1
8,14
8,17
8,17
8,22
8,21
8,29
8,37
8,43
8,47
8,51
8,55
8,59
8,66
8,71
8,78
8,81
8,84
8,81
8,82
8,84
8,83
8,83
8,88
8,88
8,89
8,93
8,95
8,92
8,97
8,99
9,01
8,99
9,03
9,04
9,07
9,04
9,07
9,09
9,04
9,08
9,13
9,09
9,05
9,06
8,99
8,98
8,99
8,94
8,87
8,83
8,8
8,79
8,71
8,6
8,5
8,38
8,26
8,23
8,17
8,1
8,02
7,9
7,82
7,72
7,63
7,53
7,56
7,49
7,53
7,47
7,39
7,37
7,34
7,39
7,32
7,24
7,18
7,31
7,39
7,48
7,51
7,61
7,69
7,86
8,05
8,24
8,55
8,81
9,13
9,24
9,36
9,48
9,61
9,7
9,82
9,86
9,87
9,87

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 3 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=96122&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=96122&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=96122&T=0

As an alternative you can also use a QR Code:  
QR Code


The GUIDs for individual cells are displayed in the table below:

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24






Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean9.050944444444450.075564611659224119.777555203509
Geometric Mean8.9945324766582
Harmonic Mean8.93835329244322
Quadratic Mean9.10723268738766
Winsorized Mean ( 1 / 60 )9.051222222222220.0755124703714475119.863940057835
Winsorized Mean ( 2 / 60 )9.051666666666670.0753700780510754120.096288881812
Winsorized Mean ( 3 / 60 )9.051833333333330.0753486197226136120.132702717800
Winsorized Mean ( 4 / 60 )9.052055555555550.0752654189190105120.268453767540
Winsorized Mean ( 5 / 60 )9.052611111111110.075127467260575120.496689708874
Winsorized Mean ( 6 / 60 )9.052944444444440.0750052221323781120.697521946762
Winsorized Mean ( 7 / 60 )9.052944444444450.0750052221323781120.697521946762
Winsorized Mean ( 8 / 60 )9.052944444444440.0750052221323781120.697521946762
Winsorized Mean ( 9 / 60 )9.056944444444440.0745195285259724121.537865625221
Winsorized Mean ( 10 / 60 )9.056944444444440.0743882185504366121.752404089415
Winsorized Mean ( 11 / 60 )9.057555555555560.074316025501371121.878901548475
Winsorized Mean ( 12 / 60 )9.058888888888890.0741596784475357122.153831819775
Winsorized Mean ( 13 / 60 )9.059611111111110.0739071155231115122.581040363807
Winsorized Mean ( 14 / 60 )9.059611111111110.0739071155231115122.581040363807
Winsorized Mean ( 15 / 60 )9.062111111111110.0736201007592992123.092891990731
Winsorized Mean ( 16 / 60 )9.065666666666670.073014887557881124.16189314104
Winsorized Mean ( 17 / 60 )9.060944444444440.0720401767871385125.776266085762
Winsorized Mean ( 18 / 60 )9.066944444444440.0713839470111385127.016574791384
Winsorized Mean ( 19 / 60 )9.069055555555550.0709243176082438127.869479205274
Winsorized Mean ( 20 / 60 )9.079055555555560.0696453593899662130.361242085335
Winsorized Mean ( 21 / 60 )9.082555555555550.0690450119118555131.545426730472
Winsorized Mean ( 22 / 60 )9.086222222222220.0684263188733664132.788412000325
Winsorized Mean ( 23 / 60 )9.096444444444440.0669295386379263135.910759726795
Winsorized Mean ( 24 / 60 )9.096444444444440.0669295386379263135.910759726795
Winsorized Mean ( 25 / 60 )9.096444444444440.0669295386379263135.910759726795
Winsorized Mean ( 26 / 60 )9.093555555555560.0663032750656663137.150925750641
Winsorized Mean ( 27 / 60 )9.095055555555560.0661667239970961137.456639926056
Winsorized Mean ( 28 / 60 )9.09350.0659904002856266137.800346120656
Winsorized Mean ( 29 / 60 )9.096722222222220.0656992106897872138.460144752337
Winsorized Mean ( 30 / 60 )9.093388888888890.0653225850947189139.207425359901
Winsorized Mean ( 31 / 60 )9.093388888888890.0653225850947189139.207425359901
Winsorized Mean ( 32 / 60 )9.089833333333330.064564552744799140.786746703911
Winsorized Mean ( 33 / 60 )9.089833333333330.064564552744799140.786746703911
Winsorized Mean ( 34 / 60 )9.097388888888890.0635141671947586143.234010468764
Winsorized Mean ( 35 / 60 )9.097388888888890.0635141671947586143.234010468764
Winsorized Mean ( 36 / 60 )9.093388888888890.0630676660587943144.184642577571
Winsorized Mean ( 37 / 60 )9.093388888888890.0614369703653897148.011674970412
Winsorized Mean ( 38 / 60 )9.084944444444440.060093218359073151.180860212204
Winsorized Mean ( 39 / 60 )9.087111111111110.0594815949860019152.771813083520
Winsorized Mean ( 40 / 60 )9.0760.0582761145283291155.741337140588
Winsorized Mean ( 41 / 60 )9.060055555555560.0565745497976418160.143661557395
Winsorized Mean ( 42 / 60 )9.048388888888890.054453276339353166.167942448482
Winsorized Mean ( 43 / 60 )9.041222222222220.0528006837156626171.233052036034
Winsorized Mean ( 44 / 60 )9.0290.0510947258706211176.710997977809
Winsorized Mean ( 45 / 60 )9.0240.0501213672870293180.042973455261
Winsorized Mean ( 46 / 60 )9.013777777777780.0486280525590873185.361685352817
Winsorized Mean ( 47 / 60 )9.0190.048166062576354187.248023142910
Winsorized Mean ( 48 / 60 )9.0270.0474669279489806190.174514973933
Winsorized Mean ( 49 / 60 )9.0270.0469612212408761192.222428665094
Winsorized Mean ( 50 / 60 )9.035333333333330.0447102819381288202.086252684263
Winsorized Mean ( 51 / 60 )9.035333333333330.0441903787231406204.463813038151
Winsorized Mean ( 52 / 60 )9.003555555555550.0405603689226294221.979133689100
Winsorized Mean ( 53 / 60 )9.015333333333330.0395593669482431227.893771534019
Winsorized Mean ( 54 / 60 )8.997333333333330.0372949057351360241.248319468384
Winsorized Mean ( 55 / 60 )9.003444444444450.0356853031091261252.301190126137
Winsorized Mean ( 56 / 60 )8.994111111111110.0336969726318149266.911547496684
Winsorized Mean ( 57 / 60 )8.987777777777780.0325442501179397276.170990119799
Winsorized Mean ( 58 / 60 )8.974888888888890.0307849400177871291.535045502876
Winsorized Mean ( 59 / 60 )8.981444444444450.0296602029053869302.811294753929
Winsorized Mean ( 60 / 60 )8.961444444444440.0272578922360291328.765128530347
Trimmed Mean ( 1 / 60 )9.052191011235950.0751131619483163120.514045427412
Trimmed Mean ( 2 / 60 )9.053181818181820.0746832745627137121.221007932366
Trimmed Mean ( 3 / 60 )9.053965517241380.0742980715413166121.86003390689
Trimmed Mean ( 4 / 60 )9.054709302325580.0738903324364164122.542543845195
Trimmed Mean ( 5 / 60 )9.055411764705880.0734742286488751123.246095008097
Trimmed Mean ( 6 / 60 )9.05601190476190.0730575441761911123.957245030325
Trimmed Mean ( 7 / 60 )9.056566265060240.0726319330014893124.691246546812
Trimmed Mean ( 8 / 60 )9.057134146341460.0721715791297777125.494471030696
Trimmed Mean ( 9 / 60 )9.057716049382720.0716737829397029126.374187016230
Trimmed Mean ( 10 / 60 )9.05781250.0712075026011322127.203063850409
Trimmed Mean ( 11 / 60 )9.057911392405060.0707203153790799128.080755068077
Trimmed Mean ( 12 / 60 )9.057948717948720.0702015718795877129.027719400432
Trimmed Mean ( 13 / 60 )9.057948717948720.0696582392977329130.034132491252
Trimmed Mean ( 14 / 60 )9.057697368421050.0690981887839837131.084439806916
Trimmed Mean ( 15 / 60 )9.057533333333330.0684903322210909132.245428509458
Trimmed Mean ( 16 / 60 )9.057162162162160.067861175829523133.466036381613
Trimmed Mean ( 17 / 60 )9.056506849315070.0672401903447488134.688893694102
Trimmed Mean ( 18 / 60 )9.056180555555550.0666625141865114135.851170122653
Trimmed Mean ( 19 / 60 )9.055422535211270.0660960715372286137.003944782267
Trimmed Mean ( 20 / 60 )9.05450.0655208654777212138.192619007433
Trimmed Mean ( 21 / 60 )9.052898550724640.0650084585386182139.257240584266
Trimmed Mean ( 22 / 60 )9.05102941176470.0644995211523801140.327079179110
Trimmed Mean ( 23 / 60 )9.048880597014930.0639938714353092141.402299846203
Trimmed Mean ( 24 / 60 )9.04606060606060.0635630284730241142.31638773945
Trimmed Mean ( 25 / 60 )9.043153846153850.0630856375875814143.347268759855
Trimmed Mean ( 26 / 60 )9.043153846153850.0625570590304159144.558487664149
Trimmed Mean ( 27 / 60 )9.037222222222220.0620261735730399145.700140789441
Trimmed Mean ( 28 / 60 )9.03411290322580.0614485526887943147.019132394851
Trimmed Mean ( 29 / 60 )9.030983606557380.0608236616276352148.478131123467
Trimmed Mean ( 30 / 60 )9.027583333333330.0601536310242102150.075451466928
Trimmed Mean ( 31 / 60 )9.02423728813560.0594434819811709151.812057224274
Trimmed Mean ( 32 / 60 )9.020775862068970.0586539608157143153.796533714261
Trimmed Mean ( 33 / 60 )9.017368421052630.0578439743016645155.891232058603
Trimmed Mean ( 34 / 60 )9.013839285714290.056941180439589158.300885512505
Trimmed Mean ( 35 / 60 )9.009818181818180.0560234940914215160.822139495898
Trimmed Mean ( 36 / 60 )9.005648148148150.0549965027913829163.749469349153
Trimmed Mean ( 37 / 60 )9.001509433962260.0538901402288706167.034440729473
Trimmed Mean ( 38 / 60 )8.997211538461540.0528031375538039170.391608439817
Trimmed Mean ( 39 / 60 )8.993137254901960.0517156593621377173.895825090960
Trimmed Mean ( 40 / 60 )8.98880.0505461645179409177.833473335242
Trimmed Mean ( 41 / 60 )8.984795918367350.0493537511631925182.048896114468
Trimmed Mean ( 42 / 60 )8.981354166666670.0481888235458133186.378365475722
Trimmed Mean ( 43 / 60 )8.978297872340430.0470929410790076190.650608490932
Trimmed Mean ( 44 / 60 )8.97543478260870.0460219761594354195.024975709752
Trimmed Mean ( 45 / 60 )8.9730.0449872918662945199.456327059393
Trimmed Mean ( 46 / 60 )8.970681818181820.0439104708792284204.29482168057
Trimmed Mean ( 47 / 60 )8.968720930232560.0428447381505062209.330744389824
Trimmed Mean ( 48 / 60 )8.966428571428570.0416659126232893215.198180164587
Trimmed Mean ( 49 / 60 )8.966428571428570.0403781851728593222.061207878542
Trimmed Mean ( 50 / 60 )8.960750.038942823634891230.100161303444
Trimmed Mean ( 51 / 60 )8.95730769230770.0375470281545805238.562361192225
Trimmed Mean ( 52 / 60 )8.95730769230770.0359750606135637248.986590697515
Trimmed Mean ( 53 / 60 )8.951351351351350.0346625581940016258.242663488709
Trimmed Mean ( 54 / 60 )8.948333333333330.033236361293771269.233242900461
Trimmed Mean ( 55 / 60 )8.9460.0318942351534700280.489560478665
Trimmed Mean ( 56 / 60 )8.943235294117650.0305254259917616292.976592579946
Trimmed Mean ( 57 / 60 )8.940757575757580.0292049350860908306.13858751618
Trimmed Mean ( 58 / 60 )8.93843750.0278051421513993321.467067182397
Trimmed Mean ( 59 / 60 )8.93661290322580.0264214545416127338.233191861221
Trimmed Mean ( 60 / 60 )8.934333333333330.0249183601072210358.544193714589
Median8.945
Midrange8.94
Midmean - Weighted Average at Xnp8.96472527472528
Midmean - Weighted Average at X(n+1)p8.973
Midmean - Empirical Distribution Function8.96472527472528
Midmean - Empirical Distribution Function - Averaging8.973
Midmean - Empirical Distribution Function - Interpolation8.973
Midmean - Closest Observation8.96472527472528
Midmean - True Basic - Statistics Graphics Toolkit8.973
Midmean - MS Excel (old versions)8.9754347826087
Number of observations180

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 9.05094444444445 & 0.075564611659224 & 119.777555203509 \tabularnewline
Geometric Mean & 8.9945324766582 &  &  \tabularnewline
Harmonic Mean & 8.93835329244322 &  &  \tabularnewline
Quadratic Mean & 9.10723268738766 &  &  \tabularnewline
Winsorized Mean ( 1 / 60 ) & 9.05122222222222 & 0.0755124703714475 & 119.863940057835 \tabularnewline
Winsorized Mean ( 2 / 60 ) & 9.05166666666667 & 0.0753700780510754 & 120.096288881812 \tabularnewline
Winsorized Mean ( 3 / 60 ) & 9.05183333333333 & 0.0753486197226136 & 120.132702717800 \tabularnewline
Winsorized Mean ( 4 / 60 ) & 9.05205555555555 & 0.0752654189190105 & 120.268453767540 \tabularnewline
Winsorized Mean ( 5 / 60 ) & 9.05261111111111 & 0.075127467260575 & 120.496689708874 \tabularnewline
Winsorized Mean ( 6 / 60 ) & 9.05294444444444 & 0.0750052221323781 & 120.697521946762 \tabularnewline
Winsorized Mean ( 7 / 60 ) & 9.05294444444445 & 0.0750052221323781 & 120.697521946762 \tabularnewline
Winsorized Mean ( 8 / 60 ) & 9.05294444444444 & 0.0750052221323781 & 120.697521946762 \tabularnewline
Winsorized Mean ( 9 / 60 ) & 9.05694444444444 & 0.0745195285259724 & 121.537865625221 \tabularnewline
Winsorized Mean ( 10 / 60 ) & 9.05694444444444 & 0.0743882185504366 & 121.752404089415 \tabularnewline
Winsorized Mean ( 11 / 60 ) & 9.05755555555556 & 0.074316025501371 & 121.878901548475 \tabularnewline
Winsorized Mean ( 12 / 60 ) & 9.05888888888889 & 0.0741596784475357 & 122.153831819775 \tabularnewline
Winsorized Mean ( 13 / 60 ) & 9.05961111111111 & 0.0739071155231115 & 122.581040363807 \tabularnewline
Winsorized Mean ( 14 / 60 ) & 9.05961111111111 & 0.0739071155231115 & 122.581040363807 \tabularnewline
Winsorized Mean ( 15 / 60 ) & 9.06211111111111 & 0.0736201007592992 & 123.092891990731 \tabularnewline
Winsorized Mean ( 16 / 60 ) & 9.06566666666667 & 0.073014887557881 & 124.16189314104 \tabularnewline
Winsorized Mean ( 17 / 60 ) & 9.06094444444444 & 0.0720401767871385 & 125.776266085762 \tabularnewline
Winsorized Mean ( 18 / 60 ) & 9.06694444444444 & 0.0713839470111385 & 127.016574791384 \tabularnewline
Winsorized Mean ( 19 / 60 ) & 9.06905555555555 & 0.0709243176082438 & 127.869479205274 \tabularnewline
Winsorized Mean ( 20 / 60 ) & 9.07905555555556 & 0.0696453593899662 & 130.361242085335 \tabularnewline
Winsorized Mean ( 21 / 60 ) & 9.08255555555555 & 0.0690450119118555 & 131.545426730472 \tabularnewline
Winsorized Mean ( 22 / 60 ) & 9.08622222222222 & 0.0684263188733664 & 132.788412000325 \tabularnewline
Winsorized Mean ( 23 / 60 ) & 9.09644444444444 & 0.0669295386379263 & 135.910759726795 \tabularnewline
Winsorized Mean ( 24 / 60 ) & 9.09644444444444 & 0.0669295386379263 & 135.910759726795 \tabularnewline
Winsorized Mean ( 25 / 60 ) & 9.09644444444444 & 0.0669295386379263 & 135.910759726795 \tabularnewline
Winsorized Mean ( 26 / 60 ) & 9.09355555555556 & 0.0663032750656663 & 137.150925750641 \tabularnewline
Winsorized Mean ( 27 / 60 ) & 9.09505555555556 & 0.0661667239970961 & 137.456639926056 \tabularnewline
Winsorized Mean ( 28 / 60 ) & 9.0935 & 0.0659904002856266 & 137.800346120656 \tabularnewline
Winsorized Mean ( 29 / 60 ) & 9.09672222222222 & 0.0656992106897872 & 138.460144752337 \tabularnewline
Winsorized Mean ( 30 / 60 ) & 9.09338888888889 & 0.0653225850947189 & 139.207425359901 \tabularnewline
Winsorized Mean ( 31 / 60 ) & 9.09338888888889 & 0.0653225850947189 & 139.207425359901 \tabularnewline
Winsorized Mean ( 32 / 60 ) & 9.08983333333333 & 0.064564552744799 & 140.786746703911 \tabularnewline
Winsorized Mean ( 33 / 60 ) & 9.08983333333333 & 0.064564552744799 & 140.786746703911 \tabularnewline
Winsorized Mean ( 34 / 60 ) & 9.09738888888889 & 0.0635141671947586 & 143.234010468764 \tabularnewline
Winsorized Mean ( 35 / 60 ) & 9.09738888888889 & 0.0635141671947586 & 143.234010468764 \tabularnewline
Winsorized Mean ( 36 / 60 ) & 9.09338888888889 & 0.0630676660587943 & 144.184642577571 \tabularnewline
Winsorized Mean ( 37 / 60 ) & 9.09338888888889 & 0.0614369703653897 & 148.011674970412 \tabularnewline
Winsorized Mean ( 38 / 60 ) & 9.08494444444444 & 0.060093218359073 & 151.180860212204 \tabularnewline
Winsorized Mean ( 39 / 60 ) & 9.08711111111111 & 0.0594815949860019 & 152.771813083520 \tabularnewline
Winsorized Mean ( 40 / 60 ) & 9.076 & 0.0582761145283291 & 155.741337140588 \tabularnewline
Winsorized Mean ( 41 / 60 ) & 9.06005555555556 & 0.0565745497976418 & 160.143661557395 \tabularnewline
Winsorized Mean ( 42 / 60 ) & 9.04838888888889 & 0.054453276339353 & 166.167942448482 \tabularnewline
Winsorized Mean ( 43 / 60 ) & 9.04122222222222 & 0.0528006837156626 & 171.233052036034 \tabularnewline
Winsorized Mean ( 44 / 60 ) & 9.029 & 0.0510947258706211 & 176.710997977809 \tabularnewline
Winsorized Mean ( 45 / 60 ) & 9.024 & 0.0501213672870293 & 180.042973455261 \tabularnewline
Winsorized Mean ( 46 / 60 ) & 9.01377777777778 & 0.0486280525590873 & 185.361685352817 \tabularnewline
Winsorized Mean ( 47 / 60 ) & 9.019 & 0.048166062576354 & 187.248023142910 \tabularnewline
Winsorized Mean ( 48 / 60 ) & 9.027 & 0.0474669279489806 & 190.174514973933 \tabularnewline
Winsorized Mean ( 49 / 60 ) & 9.027 & 0.0469612212408761 & 192.222428665094 \tabularnewline
Winsorized Mean ( 50 / 60 ) & 9.03533333333333 & 0.0447102819381288 & 202.086252684263 \tabularnewline
Winsorized Mean ( 51 / 60 ) & 9.03533333333333 & 0.0441903787231406 & 204.463813038151 \tabularnewline
Winsorized Mean ( 52 / 60 ) & 9.00355555555555 & 0.0405603689226294 & 221.979133689100 \tabularnewline
Winsorized Mean ( 53 / 60 ) & 9.01533333333333 & 0.0395593669482431 & 227.893771534019 \tabularnewline
Winsorized Mean ( 54 / 60 ) & 8.99733333333333 & 0.0372949057351360 & 241.248319468384 \tabularnewline
Winsorized Mean ( 55 / 60 ) & 9.00344444444445 & 0.0356853031091261 & 252.301190126137 \tabularnewline
Winsorized Mean ( 56 / 60 ) & 8.99411111111111 & 0.0336969726318149 & 266.911547496684 \tabularnewline
Winsorized Mean ( 57 / 60 ) & 8.98777777777778 & 0.0325442501179397 & 276.170990119799 \tabularnewline
Winsorized Mean ( 58 / 60 ) & 8.97488888888889 & 0.0307849400177871 & 291.535045502876 \tabularnewline
Winsorized Mean ( 59 / 60 ) & 8.98144444444445 & 0.0296602029053869 & 302.811294753929 \tabularnewline
Winsorized Mean ( 60 / 60 ) & 8.96144444444444 & 0.0272578922360291 & 328.765128530347 \tabularnewline
Trimmed Mean ( 1 / 60 ) & 9.05219101123595 & 0.0751131619483163 & 120.514045427412 \tabularnewline
Trimmed Mean ( 2 / 60 ) & 9.05318181818182 & 0.0746832745627137 & 121.221007932366 \tabularnewline
Trimmed Mean ( 3 / 60 ) & 9.05396551724138 & 0.0742980715413166 & 121.86003390689 \tabularnewline
Trimmed Mean ( 4 / 60 ) & 9.05470930232558 & 0.0738903324364164 & 122.542543845195 \tabularnewline
Trimmed Mean ( 5 / 60 ) & 9.05541176470588 & 0.0734742286488751 & 123.246095008097 \tabularnewline
Trimmed Mean ( 6 / 60 ) & 9.0560119047619 & 0.0730575441761911 & 123.957245030325 \tabularnewline
Trimmed Mean ( 7 / 60 ) & 9.05656626506024 & 0.0726319330014893 & 124.691246546812 \tabularnewline
Trimmed Mean ( 8 / 60 ) & 9.05713414634146 & 0.0721715791297777 & 125.494471030696 \tabularnewline
Trimmed Mean ( 9 / 60 ) & 9.05771604938272 & 0.0716737829397029 & 126.374187016230 \tabularnewline
Trimmed Mean ( 10 / 60 ) & 9.0578125 & 0.0712075026011322 & 127.203063850409 \tabularnewline
Trimmed Mean ( 11 / 60 ) & 9.05791139240506 & 0.0707203153790799 & 128.080755068077 \tabularnewline
Trimmed Mean ( 12 / 60 ) & 9.05794871794872 & 0.0702015718795877 & 129.027719400432 \tabularnewline
Trimmed Mean ( 13 / 60 ) & 9.05794871794872 & 0.0696582392977329 & 130.034132491252 \tabularnewline
Trimmed Mean ( 14 / 60 ) & 9.05769736842105 & 0.0690981887839837 & 131.084439806916 \tabularnewline
Trimmed Mean ( 15 / 60 ) & 9.05753333333333 & 0.0684903322210909 & 132.245428509458 \tabularnewline
Trimmed Mean ( 16 / 60 ) & 9.05716216216216 & 0.067861175829523 & 133.466036381613 \tabularnewline
Trimmed Mean ( 17 / 60 ) & 9.05650684931507 & 0.0672401903447488 & 134.688893694102 \tabularnewline
Trimmed Mean ( 18 / 60 ) & 9.05618055555555 & 0.0666625141865114 & 135.851170122653 \tabularnewline
Trimmed Mean ( 19 / 60 ) & 9.05542253521127 & 0.0660960715372286 & 137.003944782267 \tabularnewline
Trimmed Mean ( 20 / 60 ) & 9.0545 & 0.0655208654777212 & 138.192619007433 \tabularnewline
Trimmed Mean ( 21 / 60 ) & 9.05289855072464 & 0.0650084585386182 & 139.257240584266 \tabularnewline
Trimmed Mean ( 22 / 60 ) & 9.0510294117647 & 0.0644995211523801 & 140.327079179110 \tabularnewline
Trimmed Mean ( 23 / 60 ) & 9.04888059701493 & 0.0639938714353092 & 141.402299846203 \tabularnewline
Trimmed Mean ( 24 / 60 ) & 9.0460606060606 & 0.0635630284730241 & 142.31638773945 \tabularnewline
Trimmed Mean ( 25 / 60 ) & 9.04315384615385 & 0.0630856375875814 & 143.347268759855 \tabularnewline
Trimmed Mean ( 26 / 60 ) & 9.04315384615385 & 0.0625570590304159 & 144.558487664149 \tabularnewline
Trimmed Mean ( 27 / 60 ) & 9.03722222222222 & 0.0620261735730399 & 145.700140789441 \tabularnewline
Trimmed Mean ( 28 / 60 ) & 9.0341129032258 & 0.0614485526887943 & 147.019132394851 \tabularnewline
Trimmed Mean ( 29 / 60 ) & 9.03098360655738 & 0.0608236616276352 & 148.478131123467 \tabularnewline
Trimmed Mean ( 30 / 60 ) & 9.02758333333333 & 0.0601536310242102 & 150.075451466928 \tabularnewline
Trimmed Mean ( 31 / 60 ) & 9.0242372881356 & 0.0594434819811709 & 151.812057224274 \tabularnewline
Trimmed Mean ( 32 / 60 ) & 9.02077586206897 & 0.0586539608157143 & 153.796533714261 \tabularnewline
Trimmed Mean ( 33 / 60 ) & 9.01736842105263 & 0.0578439743016645 & 155.891232058603 \tabularnewline
Trimmed Mean ( 34 / 60 ) & 9.01383928571429 & 0.056941180439589 & 158.300885512505 \tabularnewline
Trimmed Mean ( 35 / 60 ) & 9.00981818181818 & 0.0560234940914215 & 160.822139495898 \tabularnewline
Trimmed Mean ( 36 / 60 ) & 9.00564814814815 & 0.0549965027913829 & 163.749469349153 \tabularnewline
Trimmed Mean ( 37 / 60 ) & 9.00150943396226 & 0.0538901402288706 & 167.034440729473 \tabularnewline
Trimmed Mean ( 38 / 60 ) & 8.99721153846154 & 0.0528031375538039 & 170.391608439817 \tabularnewline
Trimmed Mean ( 39 / 60 ) & 8.99313725490196 & 0.0517156593621377 & 173.895825090960 \tabularnewline
Trimmed Mean ( 40 / 60 ) & 8.9888 & 0.0505461645179409 & 177.833473335242 \tabularnewline
Trimmed Mean ( 41 / 60 ) & 8.98479591836735 & 0.0493537511631925 & 182.048896114468 \tabularnewline
Trimmed Mean ( 42 / 60 ) & 8.98135416666667 & 0.0481888235458133 & 186.378365475722 \tabularnewline
Trimmed Mean ( 43 / 60 ) & 8.97829787234043 & 0.0470929410790076 & 190.650608490932 \tabularnewline
Trimmed Mean ( 44 / 60 ) & 8.9754347826087 & 0.0460219761594354 & 195.024975709752 \tabularnewline
Trimmed Mean ( 45 / 60 ) & 8.973 & 0.0449872918662945 & 199.456327059393 \tabularnewline
Trimmed Mean ( 46 / 60 ) & 8.97068181818182 & 0.0439104708792284 & 204.29482168057 \tabularnewline
Trimmed Mean ( 47 / 60 ) & 8.96872093023256 & 0.0428447381505062 & 209.330744389824 \tabularnewline
Trimmed Mean ( 48 / 60 ) & 8.96642857142857 & 0.0416659126232893 & 215.198180164587 \tabularnewline
Trimmed Mean ( 49 / 60 ) & 8.96642857142857 & 0.0403781851728593 & 222.061207878542 \tabularnewline
Trimmed Mean ( 50 / 60 ) & 8.96075 & 0.038942823634891 & 230.100161303444 \tabularnewline
Trimmed Mean ( 51 / 60 ) & 8.9573076923077 & 0.0375470281545805 & 238.562361192225 \tabularnewline
Trimmed Mean ( 52 / 60 ) & 8.9573076923077 & 0.0359750606135637 & 248.986590697515 \tabularnewline
Trimmed Mean ( 53 / 60 ) & 8.95135135135135 & 0.0346625581940016 & 258.242663488709 \tabularnewline
Trimmed Mean ( 54 / 60 ) & 8.94833333333333 & 0.033236361293771 & 269.233242900461 \tabularnewline
Trimmed Mean ( 55 / 60 ) & 8.946 & 0.0318942351534700 & 280.489560478665 \tabularnewline
Trimmed Mean ( 56 / 60 ) & 8.94323529411765 & 0.0305254259917616 & 292.976592579946 \tabularnewline
Trimmed Mean ( 57 / 60 ) & 8.94075757575758 & 0.0292049350860908 & 306.13858751618 \tabularnewline
Trimmed Mean ( 58 / 60 ) & 8.9384375 & 0.0278051421513993 & 321.467067182397 \tabularnewline
Trimmed Mean ( 59 / 60 ) & 8.9366129032258 & 0.0264214545416127 & 338.233191861221 \tabularnewline
Trimmed Mean ( 60 / 60 ) & 8.93433333333333 & 0.0249183601072210 & 358.544193714589 \tabularnewline
Median & 8.945 &  &  \tabularnewline
Midrange & 8.94 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 8.96472527472528 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 8.973 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 8.96472527472528 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 8.973 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 8.973 &  &  \tabularnewline
Midmean - Closest Observation & 8.96472527472528 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 8.973 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 8.9754347826087 &  &  \tabularnewline
Number of observations & 180 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=96122&T=1

[TABLE]
[ROW][C]Central Tendency - Ungrouped Data[/C][/ROW]
[ROW][C]Measure[/C][C]Value[/C][C]S.E.[/C][C]Value/S.E.[/C][/ROW]
[ROW][C]Arithmetic Mean[/C][C]9.05094444444445[/C][C]0.075564611659224[/C][C]119.777555203509[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]8.9945324766582[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]8.93835329244322[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]9.10723268738766[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 60 )[/C][C]9.05122222222222[/C][C]0.0755124703714475[/C][C]119.863940057835[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 60 )[/C][C]9.05166666666667[/C][C]0.0753700780510754[/C][C]120.096288881812[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 60 )[/C][C]9.05183333333333[/C][C]0.0753486197226136[/C][C]120.132702717800[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 60 )[/C][C]9.05205555555555[/C][C]0.0752654189190105[/C][C]120.268453767540[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 60 )[/C][C]9.05261111111111[/C][C]0.075127467260575[/C][C]120.496689708874[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 60 )[/C][C]9.05294444444444[/C][C]0.0750052221323781[/C][C]120.697521946762[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 60 )[/C][C]9.05294444444445[/C][C]0.0750052221323781[/C][C]120.697521946762[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 60 )[/C][C]9.05294444444444[/C][C]0.0750052221323781[/C][C]120.697521946762[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 60 )[/C][C]9.05694444444444[/C][C]0.0745195285259724[/C][C]121.537865625221[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 60 )[/C][C]9.05694444444444[/C][C]0.0743882185504366[/C][C]121.752404089415[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 60 )[/C][C]9.05755555555556[/C][C]0.074316025501371[/C][C]121.878901548475[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 60 )[/C][C]9.05888888888889[/C][C]0.0741596784475357[/C][C]122.153831819775[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 60 )[/C][C]9.05961111111111[/C][C]0.0739071155231115[/C][C]122.581040363807[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 60 )[/C][C]9.05961111111111[/C][C]0.0739071155231115[/C][C]122.581040363807[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 60 )[/C][C]9.06211111111111[/C][C]0.0736201007592992[/C][C]123.092891990731[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 60 )[/C][C]9.06566666666667[/C][C]0.073014887557881[/C][C]124.16189314104[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 60 )[/C][C]9.06094444444444[/C][C]0.0720401767871385[/C][C]125.776266085762[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 60 )[/C][C]9.06694444444444[/C][C]0.0713839470111385[/C][C]127.016574791384[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 60 )[/C][C]9.06905555555555[/C][C]0.0709243176082438[/C][C]127.869479205274[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 60 )[/C][C]9.07905555555556[/C][C]0.0696453593899662[/C][C]130.361242085335[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 60 )[/C][C]9.08255555555555[/C][C]0.0690450119118555[/C][C]131.545426730472[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 60 )[/C][C]9.08622222222222[/C][C]0.0684263188733664[/C][C]132.788412000325[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 60 )[/C][C]9.09644444444444[/C][C]0.0669295386379263[/C][C]135.910759726795[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 60 )[/C][C]9.09644444444444[/C][C]0.0669295386379263[/C][C]135.910759726795[/C][/ROW]
[ROW][C]Winsorized Mean ( 25 / 60 )[/C][C]9.09644444444444[/C][C]0.0669295386379263[/C][C]135.910759726795[/C][/ROW]
[ROW][C]Winsorized Mean ( 26 / 60 )[/C][C]9.09355555555556[/C][C]0.0663032750656663[/C][C]137.150925750641[/C][/ROW]
[ROW][C]Winsorized Mean ( 27 / 60 )[/C][C]9.09505555555556[/C][C]0.0661667239970961[/C][C]137.456639926056[/C][/ROW]
[ROW][C]Winsorized Mean ( 28 / 60 )[/C][C]9.0935[/C][C]0.0659904002856266[/C][C]137.800346120656[/C][/ROW]
[ROW][C]Winsorized Mean ( 29 / 60 )[/C][C]9.09672222222222[/C][C]0.0656992106897872[/C][C]138.460144752337[/C][/ROW]
[ROW][C]Winsorized Mean ( 30 / 60 )[/C][C]9.09338888888889[/C][C]0.0653225850947189[/C][C]139.207425359901[/C][/ROW]
[ROW][C]Winsorized Mean ( 31 / 60 )[/C][C]9.09338888888889[/C][C]0.0653225850947189[/C][C]139.207425359901[/C][/ROW]
[ROW][C]Winsorized Mean ( 32 / 60 )[/C][C]9.08983333333333[/C][C]0.064564552744799[/C][C]140.786746703911[/C][/ROW]
[ROW][C]Winsorized Mean ( 33 / 60 )[/C][C]9.08983333333333[/C][C]0.064564552744799[/C][C]140.786746703911[/C][/ROW]
[ROW][C]Winsorized Mean ( 34 / 60 )[/C][C]9.09738888888889[/C][C]0.0635141671947586[/C][C]143.234010468764[/C][/ROW]
[ROW][C]Winsorized Mean ( 35 / 60 )[/C][C]9.09738888888889[/C][C]0.0635141671947586[/C][C]143.234010468764[/C][/ROW]
[ROW][C]Winsorized Mean ( 36 / 60 )[/C][C]9.09338888888889[/C][C]0.0630676660587943[/C][C]144.184642577571[/C][/ROW]
[ROW][C]Winsorized Mean ( 37 / 60 )[/C][C]9.09338888888889[/C][C]0.0614369703653897[/C][C]148.011674970412[/C][/ROW]
[ROW][C]Winsorized Mean ( 38 / 60 )[/C][C]9.08494444444444[/C][C]0.060093218359073[/C][C]151.180860212204[/C][/ROW]
[ROW][C]Winsorized Mean ( 39 / 60 )[/C][C]9.08711111111111[/C][C]0.0594815949860019[/C][C]152.771813083520[/C][/ROW]
[ROW][C]Winsorized Mean ( 40 / 60 )[/C][C]9.076[/C][C]0.0582761145283291[/C][C]155.741337140588[/C][/ROW]
[ROW][C]Winsorized Mean ( 41 / 60 )[/C][C]9.06005555555556[/C][C]0.0565745497976418[/C][C]160.143661557395[/C][/ROW]
[ROW][C]Winsorized Mean ( 42 / 60 )[/C][C]9.04838888888889[/C][C]0.054453276339353[/C][C]166.167942448482[/C][/ROW]
[ROW][C]Winsorized Mean ( 43 / 60 )[/C][C]9.04122222222222[/C][C]0.0528006837156626[/C][C]171.233052036034[/C][/ROW]
[ROW][C]Winsorized Mean ( 44 / 60 )[/C][C]9.029[/C][C]0.0510947258706211[/C][C]176.710997977809[/C][/ROW]
[ROW][C]Winsorized Mean ( 45 / 60 )[/C][C]9.024[/C][C]0.0501213672870293[/C][C]180.042973455261[/C][/ROW]
[ROW][C]Winsorized Mean ( 46 / 60 )[/C][C]9.01377777777778[/C][C]0.0486280525590873[/C][C]185.361685352817[/C][/ROW]
[ROW][C]Winsorized Mean ( 47 / 60 )[/C][C]9.019[/C][C]0.048166062576354[/C][C]187.248023142910[/C][/ROW]
[ROW][C]Winsorized Mean ( 48 / 60 )[/C][C]9.027[/C][C]0.0474669279489806[/C][C]190.174514973933[/C][/ROW]
[ROW][C]Winsorized Mean ( 49 / 60 )[/C][C]9.027[/C][C]0.0469612212408761[/C][C]192.222428665094[/C][/ROW]
[ROW][C]Winsorized Mean ( 50 / 60 )[/C][C]9.03533333333333[/C][C]0.0447102819381288[/C][C]202.086252684263[/C][/ROW]
[ROW][C]Winsorized Mean ( 51 / 60 )[/C][C]9.03533333333333[/C][C]0.0441903787231406[/C][C]204.463813038151[/C][/ROW]
[ROW][C]Winsorized Mean ( 52 / 60 )[/C][C]9.00355555555555[/C][C]0.0405603689226294[/C][C]221.979133689100[/C][/ROW]
[ROW][C]Winsorized Mean ( 53 / 60 )[/C][C]9.01533333333333[/C][C]0.0395593669482431[/C][C]227.893771534019[/C][/ROW]
[ROW][C]Winsorized Mean ( 54 / 60 )[/C][C]8.99733333333333[/C][C]0.0372949057351360[/C][C]241.248319468384[/C][/ROW]
[ROW][C]Winsorized Mean ( 55 / 60 )[/C][C]9.00344444444445[/C][C]0.0356853031091261[/C][C]252.301190126137[/C][/ROW]
[ROW][C]Winsorized Mean ( 56 / 60 )[/C][C]8.99411111111111[/C][C]0.0336969726318149[/C][C]266.911547496684[/C][/ROW]
[ROW][C]Winsorized Mean ( 57 / 60 )[/C][C]8.98777777777778[/C][C]0.0325442501179397[/C][C]276.170990119799[/C][/ROW]
[ROW][C]Winsorized Mean ( 58 / 60 )[/C][C]8.97488888888889[/C][C]0.0307849400177871[/C][C]291.535045502876[/C][/ROW]
[ROW][C]Winsorized Mean ( 59 / 60 )[/C][C]8.98144444444445[/C][C]0.0296602029053869[/C][C]302.811294753929[/C][/ROW]
[ROW][C]Winsorized Mean ( 60 / 60 )[/C][C]8.96144444444444[/C][C]0.0272578922360291[/C][C]328.765128530347[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 60 )[/C][C]9.05219101123595[/C][C]0.0751131619483163[/C][C]120.514045427412[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 60 )[/C][C]9.05318181818182[/C][C]0.0746832745627137[/C][C]121.221007932366[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 60 )[/C][C]9.05396551724138[/C][C]0.0742980715413166[/C][C]121.86003390689[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 60 )[/C][C]9.05470930232558[/C][C]0.0738903324364164[/C][C]122.542543845195[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 60 )[/C][C]9.05541176470588[/C][C]0.0734742286488751[/C][C]123.246095008097[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 60 )[/C][C]9.0560119047619[/C][C]0.0730575441761911[/C][C]123.957245030325[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 60 )[/C][C]9.05656626506024[/C][C]0.0726319330014893[/C][C]124.691246546812[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 60 )[/C][C]9.05713414634146[/C][C]0.0721715791297777[/C][C]125.494471030696[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 60 )[/C][C]9.05771604938272[/C][C]0.0716737829397029[/C][C]126.374187016230[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 60 )[/C][C]9.0578125[/C][C]0.0712075026011322[/C][C]127.203063850409[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 60 )[/C][C]9.05791139240506[/C][C]0.0707203153790799[/C][C]128.080755068077[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 60 )[/C][C]9.05794871794872[/C][C]0.0702015718795877[/C][C]129.027719400432[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 60 )[/C][C]9.05794871794872[/C][C]0.0696582392977329[/C][C]130.034132491252[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 60 )[/C][C]9.05769736842105[/C][C]0.0690981887839837[/C][C]131.084439806916[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 60 )[/C][C]9.05753333333333[/C][C]0.0684903322210909[/C][C]132.245428509458[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 60 )[/C][C]9.05716216216216[/C][C]0.067861175829523[/C][C]133.466036381613[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 60 )[/C][C]9.05650684931507[/C][C]0.0672401903447488[/C][C]134.688893694102[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 60 )[/C][C]9.05618055555555[/C][C]0.0666625141865114[/C][C]135.851170122653[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 60 )[/C][C]9.05542253521127[/C][C]0.0660960715372286[/C][C]137.003944782267[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 60 )[/C][C]9.0545[/C][C]0.0655208654777212[/C][C]138.192619007433[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 60 )[/C][C]9.05289855072464[/C][C]0.0650084585386182[/C][C]139.257240584266[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 60 )[/C][C]9.0510294117647[/C][C]0.0644995211523801[/C][C]140.327079179110[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 60 )[/C][C]9.04888059701493[/C][C]0.0639938714353092[/C][C]141.402299846203[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 60 )[/C][C]9.0460606060606[/C][C]0.0635630284730241[/C][C]142.31638773945[/C][/ROW]
[ROW][C]Trimmed Mean ( 25 / 60 )[/C][C]9.04315384615385[/C][C]0.0630856375875814[/C][C]143.347268759855[/C][/ROW]
[ROW][C]Trimmed Mean ( 26 / 60 )[/C][C]9.04315384615385[/C][C]0.0625570590304159[/C][C]144.558487664149[/C][/ROW]
[ROW][C]Trimmed Mean ( 27 / 60 )[/C][C]9.03722222222222[/C][C]0.0620261735730399[/C][C]145.700140789441[/C][/ROW]
[ROW][C]Trimmed Mean ( 28 / 60 )[/C][C]9.0341129032258[/C][C]0.0614485526887943[/C][C]147.019132394851[/C][/ROW]
[ROW][C]Trimmed Mean ( 29 / 60 )[/C][C]9.03098360655738[/C][C]0.0608236616276352[/C][C]148.478131123467[/C][/ROW]
[ROW][C]Trimmed Mean ( 30 / 60 )[/C][C]9.02758333333333[/C][C]0.0601536310242102[/C][C]150.075451466928[/C][/ROW]
[ROW][C]Trimmed Mean ( 31 / 60 )[/C][C]9.0242372881356[/C][C]0.0594434819811709[/C][C]151.812057224274[/C][/ROW]
[ROW][C]Trimmed Mean ( 32 / 60 )[/C][C]9.02077586206897[/C][C]0.0586539608157143[/C][C]153.796533714261[/C][/ROW]
[ROW][C]Trimmed Mean ( 33 / 60 )[/C][C]9.01736842105263[/C][C]0.0578439743016645[/C][C]155.891232058603[/C][/ROW]
[ROW][C]Trimmed Mean ( 34 / 60 )[/C][C]9.01383928571429[/C][C]0.056941180439589[/C][C]158.300885512505[/C][/ROW]
[ROW][C]Trimmed Mean ( 35 / 60 )[/C][C]9.00981818181818[/C][C]0.0560234940914215[/C][C]160.822139495898[/C][/ROW]
[ROW][C]Trimmed Mean ( 36 / 60 )[/C][C]9.00564814814815[/C][C]0.0549965027913829[/C][C]163.749469349153[/C][/ROW]
[ROW][C]Trimmed Mean ( 37 / 60 )[/C][C]9.00150943396226[/C][C]0.0538901402288706[/C][C]167.034440729473[/C][/ROW]
[ROW][C]Trimmed Mean ( 38 / 60 )[/C][C]8.99721153846154[/C][C]0.0528031375538039[/C][C]170.391608439817[/C][/ROW]
[ROW][C]Trimmed Mean ( 39 / 60 )[/C][C]8.99313725490196[/C][C]0.0517156593621377[/C][C]173.895825090960[/C][/ROW]
[ROW][C]Trimmed Mean ( 40 / 60 )[/C][C]8.9888[/C][C]0.0505461645179409[/C][C]177.833473335242[/C][/ROW]
[ROW][C]Trimmed Mean ( 41 / 60 )[/C][C]8.98479591836735[/C][C]0.0493537511631925[/C][C]182.048896114468[/C][/ROW]
[ROW][C]Trimmed Mean ( 42 / 60 )[/C][C]8.98135416666667[/C][C]0.0481888235458133[/C][C]186.378365475722[/C][/ROW]
[ROW][C]Trimmed Mean ( 43 / 60 )[/C][C]8.97829787234043[/C][C]0.0470929410790076[/C][C]190.650608490932[/C][/ROW]
[ROW][C]Trimmed Mean ( 44 / 60 )[/C][C]8.9754347826087[/C][C]0.0460219761594354[/C][C]195.024975709752[/C][/ROW]
[ROW][C]Trimmed Mean ( 45 / 60 )[/C][C]8.973[/C][C]0.0449872918662945[/C][C]199.456327059393[/C][/ROW]
[ROW][C]Trimmed Mean ( 46 / 60 )[/C][C]8.97068181818182[/C][C]0.0439104708792284[/C][C]204.29482168057[/C][/ROW]
[ROW][C]Trimmed Mean ( 47 / 60 )[/C][C]8.96872093023256[/C][C]0.0428447381505062[/C][C]209.330744389824[/C][/ROW]
[ROW][C]Trimmed Mean ( 48 / 60 )[/C][C]8.96642857142857[/C][C]0.0416659126232893[/C][C]215.198180164587[/C][/ROW]
[ROW][C]Trimmed Mean ( 49 / 60 )[/C][C]8.96642857142857[/C][C]0.0403781851728593[/C][C]222.061207878542[/C][/ROW]
[ROW][C]Trimmed Mean ( 50 / 60 )[/C][C]8.96075[/C][C]0.038942823634891[/C][C]230.100161303444[/C][/ROW]
[ROW][C]Trimmed Mean ( 51 / 60 )[/C][C]8.9573076923077[/C][C]0.0375470281545805[/C][C]238.562361192225[/C][/ROW]
[ROW][C]Trimmed Mean ( 52 / 60 )[/C][C]8.9573076923077[/C][C]0.0359750606135637[/C][C]248.986590697515[/C][/ROW]
[ROW][C]Trimmed Mean ( 53 / 60 )[/C][C]8.95135135135135[/C][C]0.0346625581940016[/C][C]258.242663488709[/C][/ROW]
[ROW][C]Trimmed Mean ( 54 / 60 )[/C][C]8.94833333333333[/C][C]0.033236361293771[/C][C]269.233242900461[/C][/ROW]
[ROW][C]Trimmed Mean ( 55 / 60 )[/C][C]8.946[/C][C]0.0318942351534700[/C][C]280.489560478665[/C][/ROW]
[ROW][C]Trimmed Mean ( 56 / 60 )[/C][C]8.94323529411765[/C][C]0.0305254259917616[/C][C]292.976592579946[/C][/ROW]
[ROW][C]Trimmed Mean ( 57 / 60 )[/C][C]8.94075757575758[/C][C]0.0292049350860908[/C][C]306.13858751618[/C][/ROW]
[ROW][C]Trimmed Mean ( 58 / 60 )[/C][C]8.9384375[/C][C]0.0278051421513993[/C][C]321.467067182397[/C][/ROW]
[ROW][C]Trimmed Mean ( 59 / 60 )[/C][C]8.9366129032258[/C][C]0.0264214545416127[/C][C]338.233191861221[/C][/ROW]
[ROW][C]Trimmed Mean ( 60 / 60 )[/C][C]8.93433333333333[/C][C]0.0249183601072210[/C][C]358.544193714589[/C][/ROW]
[ROW][C]Median[/C][C]8.945[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]8.94[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]8.96472527472528[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]8.973[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]8.96472527472528[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]8.973[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]8.973[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]8.96472527472528[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]8.973[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]8.9754347826087[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]180[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=96122&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=96122&T=1

As an alternative you can also use a QR Code:  
QR Code


The GUIDs for individual cells are displayed in the table below:

Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean9.050944444444450.075564611659224119.777555203509
Geometric Mean8.9945324766582
Harmonic Mean8.93835329244322
Quadratic Mean9.10723268738766
Winsorized Mean ( 1 / 60 )9.051222222222220.0755124703714475119.863940057835
Winsorized Mean ( 2 / 60 )9.051666666666670.0753700780510754120.096288881812
Winsorized Mean ( 3 / 60 )9.051833333333330.0753486197226136120.132702717800
Winsorized Mean ( 4 / 60 )9.052055555555550.0752654189190105120.268453767540
Winsorized Mean ( 5 / 60 )9.052611111111110.075127467260575120.496689708874
Winsorized Mean ( 6 / 60 )9.052944444444440.0750052221323781120.697521946762
Winsorized Mean ( 7 / 60 )9.052944444444450.0750052221323781120.697521946762
Winsorized Mean ( 8 / 60 )9.052944444444440.0750052221323781120.697521946762
Winsorized Mean ( 9 / 60 )9.056944444444440.0745195285259724121.537865625221
Winsorized Mean ( 10 / 60 )9.056944444444440.0743882185504366121.752404089415
Winsorized Mean ( 11 / 60 )9.057555555555560.074316025501371121.878901548475
Winsorized Mean ( 12 / 60 )9.058888888888890.0741596784475357122.153831819775
Winsorized Mean ( 13 / 60 )9.059611111111110.0739071155231115122.581040363807
Winsorized Mean ( 14 / 60 )9.059611111111110.0739071155231115122.581040363807
Winsorized Mean ( 15 / 60 )9.062111111111110.0736201007592992123.092891990731
Winsorized Mean ( 16 / 60 )9.065666666666670.073014887557881124.16189314104
Winsorized Mean ( 17 / 60 )9.060944444444440.0720401767871385125.776266085762
Winsorized Mean ( 18 / 60 )9.066944444444440.0713839470111385127.016574791384
Winsorized Mean ( 19 / 60 )9.069055555555550.0709243176082438127.869479205274
Winsorized Mean ( 20 / 60 )9.079055555555560.0696453593899662130.361242085335
Winsorized Mean ( 21 / 60 )9.082555555555550.0690450119118555131.545426730472
Winsorized Mean ( 22 / 60 )9.086222222222220.0684263188733664132.788412000325
Winsorized Mean ( 23 / 60 )9.096444444444440.0669295386379263135.910759726795
Winsorized Mean ( 24 / 60 )9.096444444444440.0669295386379263135.910759726795
Winsorized Mean ( 25 / 60 )9.096444444444440.0669295386379263135.910759726795
Winsorized Mean ( 26 / 60 )9.093555555555560.0663032750656663137.150925750641
Winsorized Mean ( 27 / 60 )9.095055555555560.0661667239970961137.456639926056
Winsorized Mean ( 28 / 60 )9.09350.0659904002856266137.800346120656
Winsorized Mean ( 29 / 60 )9.096722222222220.0656992106897872138.460144752337
Winsorized Mean ( 30 / 60 )9.093388888888890.0653225850947189139.207425359901
Winsorized Mean ( 31 / 60 )9.093388888888890.0653225850947189139.207425359901
Winsorized Mean ( 32 / 60 )9.089833333333330.064564552744799140.786746703911
Winsorized Mean ( 33 / 60 )9.089833333333330.064564552744799140.786746703911
Winsorized Mean ( 34 / 60 )9.097388888888890.0635141671947586143.234010468764
Winsorized Mean ( 35 / 60 )9.097388888888890.0635141671947586143.234010468764
Winsorized Mean ( 36 / 60 )9.093388888888890.0630676660587943144.184642577571
Winsorized Mean ( 37 / 60 )9.093388888888890.0614369703653897148.011674970412
Winsorized Mean ( 38 / 60 )9.084944444444440.060093218359073151.180860212204
Winsorized Mean ( 39 / 60 )9.087111111111110.0594815949860019152.771813083520
Winsorized Mean ( 40 / 60 )9.0760.0582761145283291155.741337140588
Winsorized Mean ( 41 / 60 )9.060055555555560.0565745497976418160.143661557395
Winsorized Mean ( 42 / 60 )9.048388888888890.054453276339353166.167942448482
Winsorized Mean ( 43 / 60 )9.041222222222220.0528006837156626171.233052036034
Winsorized Mean ( 44 / 60 )9.0290.0510947258706211176.710997977809
Winsorized Mean ( 45 / 60 )9.0240.0501213672870293180.042973455261
Winsorized Mean ( 46 / 60 )9.013777777777780.0486280525590873185.361685352817
Winsorized Mean ( 47 / 60 )9.0190.048166062576354187.248023142910
Winsorized Mean ( 48 / 60 )9.0270.0474669279489806190.174514973933
Winsorized Mean ( 49 / 60 )9.0270.0469612212408761192.222428665094
Winsorized Mean ( 50 / 60 )9.035333333333330.0447102819381288202.086252684263
Winsorized Mean ( 51 / 60 )9.035333333333330.0441903787231406204.463813038151
Winsorized Mean ( 52 / 60 )9.003555555555550.0405603689226294221.979133689100
Winsorized Mean ( 53 / 60 )9.015333333333330.0395593669482431227.893771534019
Winsorized Mean ( 54 / 60 )8.997333333333330.0372949057351360241.248319468384
Winsorized Mean ( 55 / 60 )9.003444444444450.0356853031091261252.301190126137
Winsorized Mean ( 56 / 60 )8.994111111111110.0336969726318149266.911547496684
Winsorized Mean ( 57 / 60 )8.987777777777780.0325442501179397276.170990119799
Winsorized Mean ( 58 / 60 )8.974888888888890.0307849400177871291.535045502876
Winsorized Mean ( 59 / 60 )8.981444444444450.0296602029053869302.811294753929
Winsorized Mean ( 60 / 60 )8.961444444444440.0272578922360291328.765128530347
Trimmed Mean ( 1 / 60 )9.052191011235950.0751131619483163120.514045427412
Trimmed Mean ( 2 / 60 )9.053181818181820.0746832745627137121.221007932366
Trimmed Mean ( 3 / 60 )9.053965517241380.0742980715413166121.86003390689
Trimmed Mean ( 4 / 60 )9.054709302325580.0738903324364164122.542543845195
Trimmed Mean ( 5 / 60 )9.055411764705880.0734742286488751123.246095008097
Trimmed Mean ( 6 / 60 )9.05601190476190.0730575441761911123.957245030325
Trimmed Mean ( 7 / 60 )9.056566265060240.0726319330014893124.691246546812
Trimmed Mean ( 8 / 60 )9.057134146341460.0721715791297777125.494471030696
Trimmed Mean ( 9 / 60 )9.057716049382720.0716737829397029126.374187016230
Trimmed Mean ( 10 / 60 )9.05781250.0712075026011322127.203063850409
Trimmed Mean ( 11 / 60 )9.057911392405060.0707203153790799128.080755068077
Trimmed Mean ( 12 / 60 )9.057948717948720.0702015718795877129.027719400432
Trimmed Mean ( 13 / 60 )9.057948717948720.0696582392977329130.034132491252
Trimmed Mean ( 14 / 60 )9.057697368421050.0690981887839837131.084439806916
Trimmed Mean ( 15 / 60 )9.057533333333330.0684903322210909132.245428509458
Trimmed Mean ( 16 / 60 )9.057162162162160.067861175829523133.466036381613
Trimmed Mean ( 17 / 60 )9.056506849315070.0672401903447488134.688893694102
Trimmed Mean ( 18 / 60 )9.056180555555550.0666625141865114135.851170122653
Trimmed Mean ( 19 / 60 )9.055422535211270.0660960715372286137.003944782267
Trimmed Mean ( 20 / 60 )9.05450.0655208654777212138.192619007433
Trimmed Mean ( 21 / 60 )9.052898550724640.0650084585386182139.257240584266
Trimmed Mean ( 22 / 60 )9.05102941176470.0644995211523801140.327079179110
Trimmed Mean ( 23 / 60 )9.048880597014930.0639938714353092141.402299846203
Trimmed Mean ( 24 / 60 )9.04606060606060.0635630284730241142.31638773945
Trimmed Mean ( 25 / 60 )9.043153846153850.0630856375875814143.347268759855
Trimmed Mean ( 26 / 60 )9.043153846153850.0625570590304159144.558487664149
Trimmed Mean ( 27 / 60 )9.037222222222220.0620261735730399145.700140789441
Trimmed Mean ( 28 / 60 )9.03411290322580.0614485526887943147.019132394851
Trimmed Mean ( 29 / 60 )9.030983606557380.0608236616276352148.478131123467
Trimmed Mean ( 30 / 60 )9.027583333333330.0601536310242102150.075451466928
Trimmed Mean ( 31 / 60 )9.02423728813560.0594434819811709151.812057224274
Trimmed Mean ( 32 / 60 )9.020775862068970.0586539608157143153.796533714261
Trimmed Mean ( 33 / 60 )9.017368421052630.0578439743016645155.891232058603
Trimmed Mean ( 34 / 60 )9.013839285714290.056941180439589158.300885512505
Trimmed Mean ( 35 / 60 )9.009818181818180.0560234940914215160.822139495898
Trimmed Mean ( 36 / 60 )9.005648148148150.0549965027913829163.749469349153
Trimmed Mean ( 37 / 60 )9.001509433962260.0538901402288706167.034440729473
Trimmed Mean ( 38 / 60 )8.997211538461540.0528031375538039170.391608439817
Trimmed Mean ( 39 / 60 )8.993137254901960.0517156593621377173.895825090960
Trimmed Mean ( 40 / 60 )8.98880.0505461645179409177.833473335242
Trimmed Mean ( 41 / 60 )8.984795918367350.0493537511631925182.048896114468
Trimmed Mean ( 42 / 60 )8.981354166666670.0481888235458133186.378365475722
Trimmed Mean ( 43 / 60 )8.978297872340430.0470929410790076190.650608490932
Trimmed Mean ( 44 / 60 )8.97543478260870.0460219761594354195.024975709752
Trimmed Mean ( 45 / 60 )8.9730.0449872918662945199.456327059393
Trimmed Mean ( 46 / 60 )8.970681818181820.0439104708792284204.29482168057
Trimmed Mean ( 47 / 60 )8.968720930232560.0428447381505062209.330744389824
Trimmed Mean ( 48 / 60 )8.966428571428570.0416659126232893215.198180164587
Trimmed Mean ( 49 / 60 )8.966428571428570.0403781851728593222.061207878542
Trimmed Mean ( 50 / 60 )8.960750.038942823634891230.100161303444
Trimmed Mean ( 51 / 60 )8.95730769230770.0375470281545805238.562361192225
Trimmed Mean ( 52 / 60 )8.95730769230770.0359750606135637248.986590697515
Trimmed Mean ( 53 / 60 )8.951351351351350.0346625581940016258.242663488709
Trimmed Mean ( 54 / 60 )8.948333333333330.033236361293771269.233242900461
Trimmed Mean ( 55 / 60 )8.9460.0318942351534700280.489560478665
Trimmed Mean ( 56 / 60 )8.943235294117650.0305254259917616292.976592579946
Trimmed Mean ( 57 / 60 )8.940757575757580.0292049350860908306.13858751618
Trimmed Mean ( 58 / 60 )8.93843750.0278051421513993321.467067182397
Trimmed Mean ( 59 / 60 )8.93661290322580.0264214545416127338.233191861221
Trimmed Mean ( 60 / 60 )8.934333333333330.0249183601072210358.544193714589
Median8.945
Midrange8.94
Midmean - Weighted Average at Xnp8.96472527472528
Midmean - Weighted Average at X(n+1)p8.973
Midmean - Empirical Distribution Function8.96472527472528
Midmean - Empirical Distribution Function - Averaging8.973
Midmean - Empirical Distribution Function - Interpolation8.973
Midmean - Closest Observation8.96472527472528
Midmean - True Basic - Statistics Graphics Toolkit8.973
Midmean - MS Excel (old versions)8.9754347826087
Number of observations180


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
Parameters (R input):
R code (references can be found in the software module):
geomean <- function(x) {
return(exp(mean(log(x))))
}
harmean <- function(x) {
return(1/mean(1/x))
}
quamean <- function(x) {
return(sqrt(mean(x*x)))
}
winmean <- function(x) {
x <-sort(x[!is.na(x)])
n<-length(x)
denom <- 3
nodenom <- n/denom
if (nodenom>40) denom <- n/40
sqrtn = sqrt(n)
roundnodenom = floor(nodenom)
win <- array(NA,dim=c(roundnodenom,2))
for (j in 1:roundnodenom) {
win[j,1] <- (j*x[j+1]+sum(x[(j+1):(n-j)])+j*x[n-j])/n
win[j,2] <- sd(c(rep(x[j+1],j),x[(j+1):(n-j)],rep(x[n-j],j)))/sqrtn
}
return(win)
}
trimean <- function(x) {
x <-sort(x[!is.na(x)])
n<-length(x)
denom <- 3
nodenom <- n/denom
if (nodenom>40) denom <- n/40
sqrtn = sqrt(n)
roundnodenom = floor(nodenom)
tri <- array(NA,dim=c(roundnodenom,2))
for (j in 1:roundnodenom) {
tri[j,1] <- mean(x,trim=j/n)
tri[j,2] <- sd(x[(j+1):(n-j)]) / sqrt(n-j*2)
}
return(tri)
}
midrange <- function(x) {
return((max(x)+min(x))/2)
}
q1 <- function(data,n,p,i,f) {
np <- n*p;
i <<- floor(np)
f <<- np - i
qvalue <- (1-f)*data[i] + f*data[i+1]
}
q2 <- function(data,n,p,i,f) {
np <- (n+1)*p
i <<- floor(np)
f <<- np - i
qvalue <- (1-f)*data[i] + f*data[i+1]
}
q3 <- function(data,n,p,i,f) {
np <- n*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i]
} else {
qvalue <- data[i+1]
}
}
q4 <- function(data,n,p,i,f) {
np <- n*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- (data[i]+data[i+1])/2
} else {
qvalue <- data[i+1]
}
}
q5 <- function(data,n,p,i,f) {
np <- (n-1)*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i+1]
} else {
qvalue <- data[i+1] + f*(data[i+2]-data[i+1])
}
}
q6 <- function(data,n,p,i,f) {
np <- n*p+0.5
i <<- floor(np)
f <<- np - i
qvalue <- data[i]
}
q7 <- function(data,n,p,i,f) {
np <- (n+1)*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i]
} else {
qvalue <- f*data[i] + (1-f)*data[i+1]
}
}
q8 <- function(data,n,p,i,f) {
np <- (n+1)*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i]
} else {
if (f == 0.5) {
qvalue <- (data[i]+data[i+1])/2
} else {
if (f < 0.5) {
qvalue <- data[i]
} else {
qvalue <- data[i+1]
}
}
}
}
midmean <- function(x,def) {
x <-sort(x[!is.na(x)])
n<-length(x)
if (def==1) {
qvalue1 <- q1(x,n,0.25,i,f)
qvalue3 <- q1(x,n,0.75,i,f)
}
if (def==2) {
qvalue1 <- q2(x,n,0.25,i,f)
qvalue3 <- q2(x,n,0.75,i,f)
}
if (def==3) {
qvalue1 <- q3(x,n,0.25,i,f)
qvalue3 <- q3(x,n,0.75,i,f)
}
if (def==4) {
qvalue1 <- q4(x,n,0.25,i,f)
qvalue3 <- q4(x,n,0.75,i,f)
}
if (def==5) {
qvalue1 <- q5(x,n,0.25,i,f)
qvalue3 <- q5(x,n,0.75,i,f)
}
if (def==6) {
qvalue1 <- q6(x,n,0.25,i,f)
qvalue3 <- q6(x,n,0.75,i,f)
}
if (def==7) {
qvalue1 <- q7(x,n,0.25,i,f)
qvalue3 <- q7(x,n,0.75,i,f)
}
if (def==8) {
qvalue1 <- q8(x,n,0.25,i,f)
qvalue3 <- q8(x,n,0.75,i,f)
}
midm <- 0
myn <- 0
roundno4 <- round(n/4)
round3no4 <- round(3*n/4)
for (i in 1:n) {
if ((x[i]>=qvalue1) & (x[i]<=qvalue3)){
midm = midm + x[i]
myn = myn + 1
}
}
midm = midm / myn
return(midm)
}
(arm <- mean(x))
sqrtn <- sqrt(length(x))
(armse <- sd(x) / sqrtn)
(armose <- arm / armse)
(geo <- geomean(x))
(har <- harmean(x))
(qua <- quamean(x))
(win <- winmean(x))
(tri <- trimean(x))
(midr <- midrange(x))
midm <- array(NA,dim=8)
for (j in 1:8) midm[j] <- midmean(x,j)
midm
bitmap(file='test1.png')
lb <- win[,1] - 2*win[,2]
ub <- win[,1] + 2*win[,2]
if ((ylimmin == '') | (ylimmax == '')) plot(win[,1],type='b',main=main, xlab='j', pch=19, ylab='Winsorized Mean(j/n)', ylim=c(min(lb),max(ub))) else plot(win[,1],type='l',main=main, xlab='j', pch=19, ylab='Winsorized Mean(j/n)', ylim=c(ylimmin,ylimmax))
lines(ub,lty=3)
lines(lb,lty=3)
grid()
dev.off()
bitmap(file='test2.png')
lb <- tri[,1] - 2*tri[,2]
ub <- tri[,1] + 2*tri[,2]
if ((ylimmin == '') | (ylimmax == '')) plot(tri[,1],type='b',main=main, xlab='j', pch=19, ylab='Trimmed Mean(j/n)', ylim=c(min(lb),max(ub))) else plot(tri[,1],type='l',main=main, xlab='j', pch=19, ylab='Trimmed Mean(j/n)', ylim=c(ylimmin,ylimmax))
lines(ub,lty=3)
lines(lb,lty=3)
grid()
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Central Tendency - Ungrouped Data',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Measure',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.element(a,'S.E.',header=TRUE)
a<-table.element(a,'Value/S.E.',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('arithmetic_mean.htm', 'Arithmetic Mean', 'click to view the definition of the Arithmetic Mean'),header=TRUE)
a<-table.element(a,arm)
a<-table.element(a,hyperlink('arithmetic_mean_standard_error.htm', armse, 'click to view the definition of the Standard Error of the Arithmetic Mean'))
a<-table.element(a,armose)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('geometric_mean.htm', 'Geometric Mean', 'click to view the definition of the Geometric Mean'),header=TRUE)
a<-table.element(a,geo)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('harmonic_mean.htm', 'Harmonic Mean', 'click to view the definition of the Harmonic Mean'),header=TRUE)
a<-table.element(a,har)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('quadratic_mean.htm', 'Quadratic Mean', 'click to view the definition of the Quadratic Mean'),header=TRUE)
a<-table.element(a,qua)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
for (j in 1:length(win[,1])) {
a<-table.row.start(a)
mylabel <- paste('Winsorized Mean (',j)
mylabel <- paste(mylabel,'/')
mylabel <- paste(mylabel,length(win[,1]))
mylabel <- paste(mylabel,')')
a<-table.element(a,hyperlink('winsorized_mean.htm', mylabel, 'click to view the definition of the Winsorized Mean'),header=TRUE)
a<-table.element(a,win[j,1])
a<-table.element(a,win[j,2])
a<-table.element(a,win[j,1]/win[j,2])
a<-table.row.end(a)
}
for (j in 1:length(tri[,1])) {
a<-table.row.start(a)
mylabel <- paste('Trimmed Mean (',j)
mylabel <- paste(mylabel,'/')
mylabel <- paste(mylabel,length(tri[,1]))
mylabel <- paste(mylabel,')')
a<-table.element(a,hyperlink('arithmetic_mean.htm', mylabel, 'click to view the definition of the Trimmed Mean'),header=TRUE)
a<-table.element(a,tri[j,1])
a<-table.element(a,tri[j,2])
a<-table.element(a,tri[j,1]/tri[j,2])
a<-table.row.end(a)
}
a<-table.row.start(a)
a<-table.element(a,hyperlink('median_1.htm', 'Median', 'click to view the definition of the Median'),header=TRUE)
a<-table.element(a,median(x))
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('midrange.htm', 'Midrange', 'click to view the definition of the Midrange'),header=TRUE)
a<-table.element(a,midr)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_1.htm','Weighted Average at Xnp',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[1])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_2.htm','Weighted Average at X(n+1)p',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[2])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_3.htm','Empirical Distribution Function',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[3])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_4.htm','Empirical Distribution Function - Averaging',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[4])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_5.htm','Empirical Distribution Function - Interpolation',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[5])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_6.htm','Closest Observation',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[6])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_7.htm','True Basic - Statistics Graphics Toolkit',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[7])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_8.htm','MS Excel (old versions)',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[8])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Number of observations',header=TRUE)
a<-table.element(a,length(x))
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')