Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationThu, 03 Mar 2016 16:43:59 +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/2016/Mar/03/t1457023535qng6nf308a7ba32.htm/, Retrieved Fri, 03 May 2024 11:30:35 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=293306, Retrieved Fri, 03 May 2024 11:30:35 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact113
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [] [2016-03-03 16:43:59] [70e23d918d09c907c02097a361cd6415] [Current]
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Dataseries X:



81,83
82,58
82,6
82,71
82,98
83,11
83,22
83,32
83,39
83,45
83,52
83,59
83,97
84,48
84,8
84,93
85,14
85,22
85,54
85,5
85,61
85,75
85,89
85,94
86,08
86,3
86,97
87,3
87,62
87,59
87,78
87,87
88,17
88,67
88,84
88,9
88,98
89,27
89,69
89,72
89,79
89,82
89,98
90,09
90,31
90,3
90,48
90,52
90,53
91,38
91,87
91,9
92,08
92,14
92,09
92,32
92,67
92,78
92,96
93,12
93,32
94,12
94,34
94,52
94,81
94,95
94,99
95,03
95,16
95,41
95,46
95,62
95,66
95,96
96,18
96,24
97,03
97,11
97,28
97,74
97,83
98,14
98,18
98,21
98,43
98,67
99,51
99,64
99,83
99,84
99,94
100,17
100,56
101,05
101,17
101,21
101,01
101,92
102,33
102,41
102,5
102,69
102,98
103,11
103,36
103,8
104,07
104,15
104,19
104,64
104,98
105,25
105,43
105,59
105,84
105,87
106
106,14
106,24
106,31




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Herman Ole Andreas Wold' @ wold.wessa.net
R Framework error message
Warning: there are blank lines in the 'Data' field.
Please, use NA for missing data - blank lines are simply
 deleted and are NOT treated as missing values.

\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 & 1 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
R Framework error message & 
Warning: there are blank lines in the 'Data' field.
Please, use NA for missing data - blank lines are simply
 deleted and are NOT treated as missing values.
\tabularnewline \hline \end{tabular} %Source: https://freestatistics.org/blog/index.php?pk=293306&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]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[ROW][C]R Framework error message[/C][C]
Warning: there are blank lines in the 'Data' field.
Please, use NA for missing data - blank lines are simply
 deleted and are NOT treated as missing values.
[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=293306&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=293306&T=0

As an alternative you can also use a 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 time1 seconds
R Server'Herman Ole Andreas Wold' @ wold.wessa.net
R Framework error message
Warning: there are blank lines in the 'Data' field.
Please, use NA for missing data - blank lines are simply
 deleted and are NOT treated as missing values.







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean93.83391666666670.661347377921301141.882949565172
Geometric Mean93.5571452952419
Harmonic Mean93.2815086353283
Quadratic Mean94.1108504858322
Winsorized Mean ( 1 / 40 )93.83958333333330.660330665785663142.109988518681
Winsorized Mean ( 2 / 40 )93.838250.660020908998439142.174662530611
Winsorized Mean ( 3 / 40 )93.83750.659083612285417142.375714174734
Winsorized Mean ( 4 / 40 )93.84216666666670.657150852897607142.801559570202
Winsorized Mean ( 5 / 40 )93.84633333333330.656210173483603143.012615661129
Winsorized Mean ( 6 / 40 )93.83933333333330.653552302812614143.583509582153
Winsorized Mean ( 7 / 40 )93.83583333333330.651355208476689144.062459487789
Winsorized Mean ( 8 / 40 )93.82850.648938334115495144.587698194604
Winsorized Mean ( 9 / 40 )93.812750.645360732974409145.364824983425
Winsorized Mean ( 10 / 40 )93.790250.64049739362428146.433460828442
Winsorized Mean ( 11 / 40 )93.75541666666670.633843052614609147.915822820688
Winsorized Mean ( 12 / 40 )93.78941666666670.628232685128952149.290889962873
Winsorized Mean ( 13 / 40 )93.8360.619898015015057151.373286778021
Winsorized Mean ( 14 / 40 )93.84183333333340.610865528937789153.621098077856
Winsorized Mean ( 15 / 40 )93.80308333333330.601407310766209155.972635606683
Winsorized Mean ( 16 / 40 )93.797750.593532114230771158.033150609826
Winsorized Mean ( 17 / 40 )93.79066666666670.589725553760535159.041211744322
Winsorized Mean ( 18 / 40 )93.78916666666670.57897573984546161.991531271588
Winsorized Mean ( 19 / 40 )93.76541666666670.57434808855989163.255382118137
Winsorized Mean ( 20 / 40 )93.76208333333330.57103328987803164.197228069419
Winsorized Mean ( 21 / 40 )93.77258333333330.566325686204333165.58066430259
Winsorized Mean ( 22 / 40 )93.72308333333330.553824894661883169.228729579866
Winsorized Mean ( 23 / 40 )93.59658333333330.536091944325574174.59054239489
Winsorized Mean ( 24 / 40 )93.61658333333330.531789517551877176.040670685467
Winsorized Mean ( 25 / 40 )93.63741666666670.523380542070866178.908861029052
Winsorized Mean ( 26 / 40 )93.77391666666670.505578381600364185.478493700291
Winsorized Mean ( 27 / 40 )93.74691666666670.485168064037413193.225654398055
Winsorized Mean ( 28 / 40 )93.72358333333330.46700622594104200.690222372252
Winsorized Mean ( 29 / 40 )93.675250.459798868500989203.730927623626
Winsorized Mean ( 30 / 40 )93.690250.452531650200042207.035795084353
Winsorized Mean ( 31 / 40 )93.71091666666670.449691708834913208.389247178824
Winsorized Mean ( 32 / 40 )93.740250.435240161375567215.375919592843
Winsorized Mean ( 33 / 40 )93.8420.416589184952764225.262688974128
Winsorized Mean ( 34 / 40 )93.65216666666670.384881373978374243.327354864226
Winsorized Mean ( 35 / 40 )93.59966666666670.375422207388144249.318406915378
Winsorized Mean ( 36 / 40 )93.55766666666670.365802516201037255.760041342224
Winsorized Mean ( 37 / 40 )93.63783333333330.355492796858269263.402899189166
Winsorized Mean ( 38 / 40 )93.75816666666670.340582977367419275.287295305781
Winsorized Mean ( 39 / 40 )93.66716666666670.328794466022501284.88060580757
Winsorized Mean ( 40 / 40 )93.66050.323256903886621289.740138180778
Trimmed Mean ( 1 / 40 )93.82991525423730.656266271662268142.975373420569
Trimmed Mean ( 2 / 40 )93.81991379310350.651687953579721143.964474527649
Trimmed Mean ( 3 / 40 )93.81026315789470.64671544775884145.056474965906
Trimmed Mean ( 4 / 40 )93.80053571428570.641494868767612146.221802045724
Trimmed Mean ( 5 / 40 )93.78918181818180.636215393730498147.417341269034
Trimmed Mean ( 6 / 40 )93.77648148148150.630503327851287148.732730406143
Trimmed Mean ( 7 / 40 )93.76462264150940.624657651783939150.105617651093
Trimmed Mean ( 8 / 40 )93.75288461538460.618493702405733151.582601812625
Trimmed Mean ( 9 / 40 )93.74176470588230.611965992899949153.181329997872
Trimmed Mean ( 10 / 40 )93.73230.605187688642828154.881372769166
Trimmed Mean ( 11 / 40 )93.72520408163270.598284792048243156.656504272425
Trimmed Mean ( 12 / 40 )93.72177083333330.591458463394404158.458753460827
Trimmed Mean ( 13 / 40 )93.71457446808510.584491963021114160.335095086157
Trimmed Mean ( 14 / 40 )93.70239130434780.577696121362683162.20013920696
Trimmed Mean ( 15 / 40 )93.68911111111110.57113035181354164.041555160946
Trimmed Mean ( 16 / 40 )93.678750.564830839300189165.852753571433
Trimmed Mean ( 17 / 40 )93.66837209302330.558561687706071167.695662188549
Trimmed Mean ( 18 / 40 )93.65809523809520.55176204149593169.743636195362
Trimmed Mean ( 19 / 40 )93.64743902439020.545219011296655171.761140173149
Trimmed Mean ( 20 / 40 )93.6381250.538152109389334173.999364429242
Trimmed Mean ( 21 / 40 )93.62858974358970.530287613023448176.561902341569
Trimmed Mean ( 22 / 40 )93.61776315789470.521657500015339179.462124392235
Trimmed Mean ( 23 / 40 )93.610.513150175440494182.422231308104
Trimmed Mean ( 24 / 40 )93.61097222222220.505424880519635185.212433796253
Trimmed Mean ( 25 / 40 )93.61057142857140.496786355124889188.432251536052
Trimmed Mean ( 26 / 40 )93.60867647058820.487607213595428191.975577597292
Trimmed Mean ( 27 / 40 )93.59712121212120.479018458610988195.393558493602
Trimmed Mean ( 28 / 40 )93.586718750.47146644405663198.501335417964
Trimmed Mean ( 29 / 40 )93.57725806451610.464763017653359201.344028053261
Trimmed Mean ( 30 / 40 )93.57050.457502889682455204.524391233782
Trimmed Mean ( 31 / 40 )93.56224137931040.449545380567481208.126354810281
Trimmed Mean ( 32 / 40 )93.55196428571430.440048950910678212.594449076879
Trimmed Mean ( 33 / 40 )93.53888888888890.430486428480604217.286498947326
Trimmed Mean ( 34 / 40 )93.51769230769230.421427457833533221.906974900132
Trimmed Mean ( 35 / 40 )93.50820.415302465630995225.156862138844
Trimmed Mean ( 36 / 40 )93.50166666666670.408847664209484228.695611719965
Trimmed Mean ( 37 / 40 )93.49760869565220.401981947918592232.591560839411
Trimmed Mean ( 38 / 40 )93.48727272727270.394657820536218236.881845139297
Trimmed Mean ( 39 / 40 )93.46690476190480.387525801935217241.188855800445
Trimmed Mean ( 40 / 40 )93.45150.380214269886916245.786408878852
Median93.22
Midrange94.07
Midmean - Weighted Average at Xnp93.4729508196721
Midmean - Weighted Average at X(n+1)p93.5705
Midmean - Empirical Distribution Function93.4729508196721
Midmean - Empirical Distribution Function - Averaging93.5705
Midmean - Empirical Distribution Function - Interpolation93.5705
Midmean - Closest Observation93.4729508196721
Midmean - True Basic - Statistics Graphics Toolkit93.5705
Midmean - MS Excel (old versions)93.5772580645161
Number of observations120

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 93.8339166666667 & 0.661347377921301 & 141.882949565172 \tabularnewline
Geometric Mean & 93.5571452952419 &  &  \tabularnewline
Harmonic Mean & 93.2815086353283 &  &  \tabularnewline
Quadratic Mean & 94.1108504858322 &  &  \tabularnewline
Winsorized Mean ( 1 / 40 ) & 93.8395833333333 & 0.660330665785663 & 142.109988518681 \tabularnewline
Winsorized Mean ( 2 / 40 ) & 93.83825 & 0.660020908998439 & 142.174662530611 \tabularnewline
Winsorized Mean ( 3 / 40 ) & 93.8375 & 0.659083612285417 & 142.375714174734 \tabularnewline
Winsorized Mean ( 4 / 40 ) & 93.8421666666667 & 0.657150852897607 & 142.801559570202 \tabularnewline
Winsorized Mean ( 5 / 40 ) & 93.8463333333333 & 0.656210173483603 & 143.012615661129 \tabularnewline
Winsorized Mean ( 6 / 40 ) & 93.8393333333333 & 0.653552302812614 & 143.583509582153 \tabularnewline
Winsorized Mean ( 7 / 40 ) & 93.8358333333333 & 0.651355208476689 & 144.062459487789 \tabularnewline
Winsorized Mean ( 8 / 40 ) & 93.8285 & 0.648938334115495 & 144.587698194604 \tabularnewline
Winsorized Mean ( 9 / 40 ) & 93.81275 & 0.645360732974409 & 145.364824983425 \tabularnewline
Winsorized Mean ( 10 / 40 ) & 93.79025 & 0.64049739362428 & 146.433460828442 \tabularnewline
Winsorized Mean ( 11 / 40 ) & 93.7554166666667 & 0.633843052614609 & 147.915822820688 \tabularnewline
Winsorized Mean ( 12 / 40 ) & 93.7894166666667 & 0.628232685128952 & 149.290889962873 \tabularnewline
Winsorized Mean ( 13 / 40 ) & 93.836 & 0.619898015015057 & 151.373286778021 \tabularnewline
Winsorized Mean ( 14 / 40 ) & 93.8418333333334 & 0.610865528937789 & 153.621098077856 \tabularnewline
Winsorized Mean ( 15 / 40 ) & 93.8030833333333 & 0.601407310766209 & 155.972635606683 \tabularnewline
Winsorized Mean ( 16 / 40 ) & 93.79775 & 0.593532114230771 & 158.033150609826 \tabularnewline
Winsorized Mean ( 17 / 40 ) & 93.7906666666667 & 0.589725553760535 & 159.041211744322 \tabularnewline
Winsorized Mean ( 18 / 40 ) & 93.7891666666667 & 0.57897573984546 & 161.991531271588 \tabularnewline
Winsorized Mean ( 19 / 40 ) & 93.7654166666667 & 0.57434808855989 & 163.255382118137 \tabularnewline
Winsorized Mean ( 20 / 40 ) & 93.7620833333333 & 0.57103328987803 & 164.197228069419 \tabularnewline
Winsorized Mean ( 21 / 40 ) & 93.7725833333333 & 0.566325686204333 & 165.58066430259 \tabularnewline
Winsorized Mean ( 22 / 40 ) & 93.7230833333333 & 0.553824894661883 & 169.228729579866 \tabularnewline
Winsorized Mean ( 23 / 40 ) & 93.5965833333333 & 0.536091944325574 & 174.59054239489 \tabularnewline
Winsorized Mean ( 24 / 40 ) & 93.6165833333333 & 0.531789517551877 & 176.040670685467 \tabularnewline
Winsorized Mean ( 25 / 40 ) & 93.6374166666667 & 0.523380542070866 & 178.908861029052 \tabularnewline
Winsorized Mean ( 26 / 40 ) & 93.7739166666667 & 0.505578381600364 & 185.478493700291 \tabularnewline
Winsorized Mean ( 27 / 40 ) & 93.7469166666667 & 0.485168064037413 & 193.225654398055 \tabularnewline
Winsorized Mean ( 28 / 40 ) & 93.7235833333333 & 0.46700622594104 & 200.690222372252 \tabularnewline
Winsorized Mean ( 29 / 40 ) & 93.67525 & 0.459798868500989 & 203.730927623626 \tabularnewline
Winsorized Mean ( 30 / 40 ) & 93.69025 & 0.452531650200042 & 207.035795084353 \tabularnewline
Winsorized Mean ( 31 / 40 ) & 93.7109166666667 & 0.449691708834913 & 208.389247178824 \tabularnewline
Winsorized Mean ( 32 / 40 ) & 93.74025 & 0.435240161375567 & 215.375919592843 \tabularnewline
Winsorized Mean ( 33 / 40 ) & 93.842 & 0.416589184952764 & 225.262688974128 \tabularnewline
Winsorized Mean ( 34 / 40 ) & 93.6521666666667 & 0.384881373978374 & 243.327354864226 \tabularnewline
Winsorized Mean ( 35 / 40 ) & 93.5996666666667 & 0.375422207388144 & 249.318406915378 \tabularnewline
Winsorized Mean ( 36 / 40 ) & 93.5576666666667 & 0.365802516201037 & 255.760041342224 \tabularnewline
Winsorized Mean ( 37 / 40 ) & 93.6378333333333 & 0.355492796858269 & 263.402899189166 \tabularnewline
Winsorized Mean ( 38 / 40 ) & 93.7581666666667 & 0.340582977367419 & 275.287295305781 \tabularnewline
Winsorized Mean ( 39 / 40 ) & 93.6671666666667 & 0.328794466022501 & 284.88060580757 \tabularnewline
Winsorized Mean ( 40 / 40 ) & 93.6605 & 0.323256903886621 & 289.740138180778 \tabularnewline
Trimmed Mean ( 1 / 40 ) & 93.8299152542373 & 0.656266271662268 & 142.975373420569 \tabularnewline
Trimmed Mean ( 2 / 40 ) & 93.8199137931035 & 0.651687953579721 & 143.964474527649 \tabularnewline
Trimmed Mean ( 3 / 40 ) & 93.8102631578947 & 0.64671544775884 & 145.056474965906 \tabularnewline
Trimmed Mean ( 4 / 40 ) & 93.8005357142857 & 0.641494868767612 & 146.221802045724 \tabularnewline
Trimmed Mean ( 5 / 40 ) & 93.7891818181818 & 0.636215393730498 & 147.417341269034 \tabularnewline
Trimmed Mean ( 6 / 40 ) & 93.7764814814815 & 0.630503327851287 & 148.732730406143 \tabularnewline
Trimmed Mean ( 7 / 40 ) & 93.7646226415094 & 0.624657651783939 & 150.105617651093 \tabularnewline
Trimmed Mean ( 8 / 40 ) & 93.7528846153846 & 0.618493702405733 & 151.582601812625 \tabularnewline
Trimmed Mean ( 9 / 40 ) & 93.7417647058823 & 0.611965992899949 & 153.181329997872 \tabularnewline
Trimmed Mean ( 10 / 40 ) & 93.7323 & 0.605187688642828 & 154.881372769166 \tabularnewline
Trimmed Mean ( 11 / 40 ) & 93.7252040816327 & 0.598284792048243 & 156.656504272425 \tabularnewline
Trimmed Mean ( 12 / 40 ) & 93.7217708333333 & 0.591458463394404 & 158.458753460827 \tabularnewline
Trimmed Mean ( 13 / 40 ) & 93.7145744680851 & 0.584491963021114 & 160.335095086157 \tabularnewline
Trimmed Mean ( 14 / 40 ) & 93.7023913043478 & 0.577696121362683 & 162.20013920696 \tabularnewline
Trimmed Mean ( 15 / 40 ) & 93.6891111111111 & 0.57113035181354 & 164.041555160946 \tabularnewline
Trimmed Mean ( 16 / 40 ) & 93.67875 & 0.564830839300189 & 165.852753571433 \tabularnewline
Trimmed Mean ( 17 / 40 ) & 93.6683720930233 & 0.558561687706071 & 167.695662188549 \tabularnewline
Trimmed Mean ( 18 / 40 ) & 93.6580952380952 & 0.55176204149593 & 169.743636195362 \tabularnewline
Trimmed Mean ( 19 / 40 ) & 93.6474390243902 & 0.545219011296655 & 171.761140173149 \tabularnewline
Trimmed Mean ( 20 / 40 ) & 93.638125 & 0.538152109389334 & 173.999364429242 \tabularnewline
Trimmed Mean ( 21 / 40 ) & 93.6285897435897 & 0.530287613023448 & 176.561902341569 \tabularnewline
Trimmed Mean ( 22 / 40 ) & 93.6177631578947 & 0.521657500015339 & 179.462124392235 \tabularnewline
Trimmed Mean ( 23 / 40 ) & 93.61 & 0.513150175440494 & 182.422231308104 \tabularnewline
Trimmed Mean ( 24 / 40 ) & 93.6109722222222 & 0.505424880519635 & 185.212433796253 \tabularnewline
Trimmed Mean ( 25 / 40 ) & 93.6105714285714 & 0.496786355124889 & 188.432251536052 \tabularnewline
Trimmed Mean ( 26 / 40 ) & 93.6086764705882 & 0.487607213595428 & 191.975577597292 \tabularnewline
Trimmed Mean ( 27 / 40 ) & 93.5971212121212 & 0.479018458610988 & 195.393558493602 \tabularnewline
Trimmed Mean ( 28 / 40 ) & 93.58671875 & 0.47146644405663 & 198.501335417964 \tabularnewline
Trimmed Mean ( 29 / 40 ) & 93.5772580645161 & 0.464763017653359 & 201.344028053261 \tabularnewline
Trimmed Mean ( 30 / 40 ) & 93.5705 & 0.457502889682455 & 204.524391233782 \tabularnewline
Trimmed Mean ( 31 / 40 ) & 93.5622413793104 & 0.449545380567481 & 208.126354810281 \tabularnewline
Trimmed Mean ( 32 / 40 ) & 93.5519642857143 & 0.440048950910678 & 212.594449076879 \tabularnewline
Trimmed Mean ( 33 / 40 ) & 93.5388888888889 & 0.430486428480604 & 217.286498947326 \tabularnewline
Trimmed Mean ( 34 / 40 ) & 93.5176923076923 & 0.421427457833533 & 221.906974900132 \tabularnewline
Trimmed Mean ( 35 / 40 ) & 93.5082 & 0.415302465630995 & 225.156862138844 \tabularnewline
Trimmed Mean ( 36 / 40 ) & 93.5016666666667 & 0.408847664209484 & 228.695611719965 \tabularnewline
Trimmed Mean ( 37 / 40 ) & 93.4976086956522 & 0.401981947918592 & 232.591560839411 \tabularnewline
Trimmed Mean ( 38 / 40 ) & 93.4872727272727 & 0.394657820536218 & 236.881845139297 \tabularnewline
Trimmed Mean ( 39 / 40 ) & 93.4669047619048 & 0.387525801935217 & 241.188855800445 \tabularnewline
Trimmed Mean ( 40 / 40 ) & 93.4515 & 0.380214269886916 & 245.786408878852 \tabularnewline
Median & 93.22 &  &  \tabularnewline
Midrange & 94.07 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 93.4729508196721 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 93.5705 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 93.4729508196721 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 93.5705 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 93.5705 &  &  \tabularnewline
Midmean - Closest Observation & 93.4729508196721 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 93.5705 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 93.5772580645161 &  &  \tabularnewline
Number of observations & 120 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=293306&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]93.8339166666667[/C][C]0.661347377921301[/C][C]141.882949565172[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]93.5571452952419[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]93.2815086353283[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]94.1108504858322[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 40 )[/C][C]93.8395833333333[/C][C]0.660330665785663[/C][C]142.109988518681[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 40 )[/C][C]93.83825[/C][C]0.660020908998439[/C][C]142.174662530611[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 40 )[/C][C]93.8375[/C][C]0.659083612285417[/C][C]142.375714174734[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 40 )[/C][C]93.8421666666667[/C][C]0.657150852897607[/C][C]142.801559570202[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 40 )[/C][C]93.8463333333333[/C][C]0.656210173483603[/C][C]143.012615661129[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 40 )[/C][C]93.8393333333333[/C][C]0.653552302812614[/C][C]143.583509582153[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 40 )[/C][C]93.8358333333333[/C][C]0.651355208476689[/C][C]144.062459487789[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 40 )[/C][C]93.8285[/C][C]0.648938334115495[/C][C]144.587698194604[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 40 )[/C][C]93.81275[/C][C]0.645360732974409[/C][C]145.364824983425[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 40 )[/C][C]93.79025[/C][C]0.64049739362428[/C][C]146.433460828442[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 40 )[/C][C]93.7554166666667[/C][C]0.633843052614609[/C][C]147.915822820688[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 40 )[/C][C]93.7894166666667[/C][C]0.628232685128952[/C][C]149.290889962873[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 40 )[/C][C]93.836[/C][C]0.619898015015057[/C][C]151.373286778021[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 40 )[/C][C]93.8418333333334[/C][C]0.610865528937789[/C][C]153.621098077856[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 40 )[/C][C]93.8030833333333[/C][C]0.601407310766209[/C][C]155.972635606683[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 40 )[/C][C]93.79775[/C][C]0.593532114230771[/C][C]158.033150609826[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 40 )[/C][C]93.7906666666667[/C][C]0.589725553760535[/C][C]159.041211744322[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 40 )[/C][C]93.7891666666667[/C][C]0.57897573984546[/C][C]161.991531271588[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 40 )[/C][C]93.7654166666667[/C][C]0.57434808855989[/C][C]163.255382118137[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 40 )[/C][C]93.7620833333333[/C][C]0.57103328987803[/C][C]164.197228069419[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 40 )[/C][C]93.7725833333333[/C][C]0.566325686204333[/C][C]165.58066430259[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 40 )[/C][C]93.7230833333333[/C][C]0.553824894661883[/C][C]169.228729579866[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 40 )[/C][C]93.5965833333333[/C][C]0.536091944325574[/C][C]174.59054239489[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 40 )[/C][C]93.6165833333333[/C][C]0.531789517551877[/C][C]176.040670685467[/C][/ROW]
[ROW][C]Winsorized Mean ( 25 / 40 )[/C][C]93.6374166666667[/C][C]0.523380542070866[/C][C]178.908861029052[/C][/ROW]
[ROW][C]Winsorized Mean ( 26 / 40 )[/C][C]93.7739166666667[/C][C]0.505578381600364[/C][C]185.478493700291[/C][/ROW]
[ROW][C]Winsorized Mean ( 27 / 40 )[/C][C]93.7469166666667[/C][C]0.485168064037413[/C][C]193.225654398055[/C][/ROW]
[ROW][C]Winsorized Mean ( 28 / 40 )[/C][C]93.7235833333333[/C][C]0.46700622594104[/C][C]200.690222372252[/C][/ROW]
[ROW][C]Winsorized Mean ( 29 / 40 )[/C][C]93.67525[/C][C]0.459798868500989[/C][C]203.730927623626[/C][/ROW]
[ROW][C]Winsorized Mean ( 30 / 40 )[/C][C]93.69025[/C][C]0.452531650200042[/C][C]207.035795084353[/C][/ROW]
[ROW][C]Winsorized Mean ( 31 / 40 )[/C][C]93.7109166666667[/C][C]0.449691708834913[/C][C]208.389247178824[/C][/ROW]
[ROW][C]Winsorized Mean ( 32 / 40 )[/C][C]93.74025[/C][C]0.435240161375567[/C][C]215.375919592843[/C][/ROW]
[ROW][C]Winsorized Mean ( 33 / 40 )[/C][C]93.842[/C][C]0.416589184952764[/C][C]225.262688974128[/C][/ROW]
[ROW][C]Winsorized Mean ( 34 / 40 )[/C][C]93.6521666666667[/C][C]0.384881373978374[/C][C]243.327354864226[/C][/ROW]
[ROW][C]Winsorized Mean ( 35 / 40 )[/C][C]93.5996666666667[/C][C]0.375422207388144[/C][C]249.318406915378[/C][/ROW]
[ROW][C]Winsorized Mean ( 36 / 40 )[/C][C]93.5576666666667[/C][C]0.365802516201037[/C][C]255.760041342224[/C][/ROW]
[ROW][C]Winsorized Mean ( 37 / 40 )[/C][C]93.6378333333333[/C][C]0.355492796858269[/C][C]263.402899189166[/C][/ROW]
[ROW][C]Winsorized Mean ( 38 / 40 )[/C][C]93.7581666666667[/C][C]0.340582977367419[/C][C]275.287295305781[/C][/ROW]
[ROW][C]Winsorized Mean ( 39 / 40 )[/C][C]93.6671666666667[/C][C]0.328794466022501[/C][C]284.88060580757[/C][/ROW]
[ROW][C]Winsorized Mean ( 40 / 40 )[/C][C]93.6605[/C][C]0.323256903886621[/C][C]289.740138180778[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 40 )[/C][C]93.8299152542373[/C][C]0.656266271662268[/C][C]142.975373420569[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 40 )[/C][C]93.8199137931035[/C][C]0.651687953579721[/C][C]143.964474527649[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 40 )[/C][C]93.8102631578947[/C][C]0.64671544775884[/C][C]145.056474965906[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 40 )[/C][C]93.8005357142857[/C][C]0.641494868767612[/C][C]146.221802045724[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 40 )[/C][C]93.7891818181818[/C][C]0.636215393730498[/C][C]147.417341269034[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 40 )[/C][C]93.7764814814815[/C][C]0.630503327851287[/C][C]148.732730406143[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 40 )[/C][C]93.7646226415094[/C][C]0.624657651783939[/C][C]150.105617651093[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 40 )[/C][C]93.7528846153846[/C][C]0.618493702405733[/C][C]151.582601812625[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 40 )[/C][C]93.7417647058823[/C][C]0.611965992899949[/C][C]153.181329997872[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 40 )[/C][C]93.7323[/C][C]0.605187688642828[/C][C]154.881372769166[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 40 )[/C][C]93.7252040816327[/C][C]0.598284792048243[/C][C]156.656504272425[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 40 )[/C][C]93.7217708333333[/C][C]0.591458463394404[/C][C]158.458753460827[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 40 )[/C][C]93.7145744680851[/C][C]0.584491963021114[/C][C]160.335095086157[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 40 )[/C][C]93.7023913043478[/C][C]0.577696121362683[/C][C]162.20013920696[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 40 )[/C][C]93.6891111111111[/C][C]0.57113035181354[/C][C]164.041555160946[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 40 )[/C][C]93.67875[/C][C]0.564830839300189[/C][C]165.852753571433[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 40 )[/C][C]93.6683720930233[/C][C]0.558561687706071[/C][C]167.695662188549[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 40 )[/C][C]93.6580952380952[/C][C]0.55176204149593[/C][C]169.743636195362[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 40 )[/C][C]93.6474390243902[/C][C]0.545219011296655[/C][C]171.761140173149[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 40 )[/C][C]93.638125[/C][C]0.538152109389334[/C][C]173.999364429242[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 40 )[/C][C]93.6285897435897[/C][C]0.530287613023448[/C][C]176.561902341569[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 40 )[/C][C]93.6177631578947[/C][C]0.521657500015339[/C][C]179.462124392235[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 40 )[/C][C]93.61[/C][C]0.513150175440494[/C][C]182.422231308104[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 40 )[/C][C]93.6109722222222[/C][C]0.505424880519635[/C][C]185.212433796253[/C][/ROW]
[ROW][C]Trimmed Mean ( 25 / 40 )[/C][C]93.6105714285714[/C][C]0.496786355124889[/C][C]188.432251536052[/C][/ROW]
[ROW][C]Trimmed Mean ( 26 / 40 )[/C][C]93.6086764705882[/C][C]0.487607213595428[/C][C]191.975577597292[/C][/ROW]
[ROW][C]Trimmed Mean ( 27 / 40 )[/C][C]93.5971212121212[/C][C]0.479018458610988[/C][C]195.393558493602[/C][/ROW]
[ROW][C]Trimmed Mean ( 28 / 40 )[/C][C]93.58671875[/C][C]0.47146644405663[/C][C]198.501335417964[/C][/ROW]
[ROW][C]Trimmed Mean ( 29 / 40 )[/C][C]93.5772580645161[/C][C]0.464763017653359[/C][C]201.344028053261[/C][/ROW]
[ROW][C]Trimmed Mean ( 30 / 40 )[/C][C]93.5705[/C][C]0.457502889682455[/C][C]204.524391233782[/C][/ROW]
[ROW][C]Trimmed Mean ( 31 / 40 )[/C][C]93.5622413793104[/C][C]0.449545380567481[/C][C]208.126354810281[/C][/ROW]
[ROW][C]Trimmed Mean ( 32 / 40 )[/C][C]93.5519642857143[/C][C]0.440048950910678[/C][C]212.594449076879[/C][/ROW]
[ROW][C]Trimmed Mean ( 33 / 40 )[/C][C]93.5388888888889[/C][C]0.430486428480604[/C][C]217.286498947326[/C][/ROW]
[ROW][C]Trimmed Mean ( 34 / 40 )[/C][C]93.5176923076923[/C][C]0.421427457833533[/C][C]221.906974900132[/C][/ROW]
[ROW][C]Trimmed Mean ( 35 / 40 )[/C][C]93.5082[/C][C]0.415302465630995[/C][C]225.156862138844[/C][/ROW]
[ROW][C]Trimmed Mean ( 36 / 40 )[/C][C]93.5016666666667[/C][C]0.408847664209484[/C][C]228.695611719965[/C][/ROW]
[ROW][C]Trimmed Mean ( 37 / 40 )[/C][C]93.4976086956522[/C][C]0.401981947918592[/C][C]232.591560839411[/C][/ROW]
[ROW][C]Trimmed Mean ( 38 / 40 )[/C][C]93.4872727272727[/C][C]0.394657820536218[/C][C]236.881845139297[/C][/ROW]
[ROW][C]Trimmed Mean ( 39 / 40 )[/C][C]93.4669047619048[/C][C]0.387525801935217[/C][C]241.188855800445[/C][/ROW]
[ROW][C]Trimmed Mean ( 40 / 40 )[/C][C]93.4515[/C][C]0.380214269886916[/C][C]245.786408878852[/C][/ROW]
[ROW][C]Median[/C][C]93.22[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]94.07[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]93.4729508196721[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]93.5705[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]93.4729508196721[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]93.5705[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]93.5705[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]93.4729508196721[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]93.5705[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]93.5772580645161[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]120[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=293306&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=293306&T=1

As an alternative you can also use a QR Code:  

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

Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean93.83391666666670.661347377921301141.882949565172
Geometric Mean93.5571452952419
Harmonic Mean93.2815086353283
Quadratic Mean94.1108504858322
Winsorized Mean ( 1 / 40 )93.83958333333330.660330665785663142.109988518681
Winsorized Mean ( 2 / 40 )93.838250.660020908998439142.174662530611
Winsorized Mean ( 3 / 40 )93.83750.659083612285417142.375714174734
Winsorized Mean ( 4 / 40 )93.84216666666670.657150852897607142.801559570202
Winsorized Mean ( 5 / 40 )93.84633333333330.656210173483603143.012615661129
Winsorized Mean ( 6 / 40 )93.83933333333330.653552302812614143.583509582153
Winsorized Mean ( 7 / 40 )93.83583333333330.651355208476689144.062459487789
Winsorized Mean ( 8 / 40 )93.82850.648938334115495144.587698194604
Winsorized Mean ( 9 / 40 )93.812750.645360732974409145.364824983425
Winsorized Mean ( 10 / 40 )93.790250.64049739362428146.433460828442
Winsorized Mean ( 11 / 40 )93.75541666666670.633843052614609147.915822820688
Winsorized Mean ( 12 / 40 )93.78941666666670.628232685128952149.290889962873
Winsorized Mean ( 13 / 40 )93.8360.619898015015057151.373286778021
Winsorized Mean ( 14 / 40 )93.84183333333340.610865528937789153.621098077856
Winsorized Mean ( 15 / 40 )93.80308333333330.601407310766209155.972635606683
Winsorized Mean ( 16 / 40 )93.797750.593532114230771158.033150609826
Winsorized Mean ( 17 / 40 )93.79066666666670.589725553760535159.041211744322
Winsorized Mean ( 18 / 40 )93.78916666666670.57897573984546161.991531271588
Winsorized Mean ( 19 / 40 )93.76541666666670.57434808855989163.255382118137
Winsorized Mean ( 20 / 40 )93.76208333333330.57103328987803164.197228069419
Winsorized Mean ( 21 / 40 )93.77258333333330.566325686204333165.58066430259
Winsorized Mean ( 22 / 40 )93.72308333333330.553824894661883169.228729579866
Winsorized Mean ( 23 / 40 )93.59658333333330.536091944325574174.59054239489
Winsorized Mean ( 24 / 40 )93.61658333333330.531789517551877176.040670685467
Winsorized Mean ( 25 / 40 )93.63741666666670.523380542070866178.908861029052
Winsorized Mean ( 26 / 40 )93.77391666666670.505578381600364185.478493700291
Winsorized Mean ( 27 / 40 )93.74691666666670.485168064037413193.225654398055
Winsorized Mean ( 28 / 40 )93.72358333333330.46700622594104200.690222372252
Winsorized Mean ( 29 / 40 )93.675250.459798868500989203.730927623626
Winsorized Mean ( 30 / 40 )93.690250.452531650200042207.035795084353
Winsorized Mean ( 31 / 40 )93.71091666666670.449691708834913208.389247178824
Winsorized Mean ( 32 / 40 )93.740250.435240161375567215.375919592843
Winsorized Mean ( 33 / 40 )93.8420.416589184952764225.262688974128
Winsorized Mean ( 34 / 40 )93.65216666666670.384881373978374243.327354864226
Winsorized Mean ( 35 / 40 )93.59966666666670.375422207388144249.318406915378
Winsorized Mean ( 36 / 40 )93.55766666666670.365802516201037255.760041342224
Winsorized Mean ( 37 / 40 )93.63783333333330.355492796858269263.402899189166
Winsorized Mean ( 38 / 40 )93.75816666666670.340582977367419275.287295305781
Winsorized Mean ( 39 / 40 )93.66716666666670.328794466022501284.88060580757
Winsorized Mean ( 40 / 40 )93.66050.323256903886621289.740138180778
Trimmed Mean ( 1 / 40 )93.82991525423730.656266271662268142.975373420569
Trimmed Mean ( 2 / 40 )93.81991379310350.651687953579721143.964474527649
Trimmed Mean ( 3 / 40 )93.81026315789470.64671544775884145.056474965906
Trimmed Mean ( 4 / 40 )93.80053571428570.641494868767612146.221802045724
Trimmed Mean ( 5 / 40 )93.78918181818180.636215393730498147.417341269034
Trimmed Mean ( 6 / 40 )93.77648148148150.630503327851287148.732730406143
Trimmed Mean ( 7 / 40 )93.76462264150940.624657651783939150.105617651093
Trimmed Mean ( 8 / 40 )93.75288461538460.618493702405733151.582601812625
Trimmed Mean ( 9 / 40 )93.74176470588230.611965992899949153.181329997872
Trimmed Mean ( 10 / 40 )93.73230.605187688642828154.881372769166
Trimmed Mean ( 11 / 40 )93.72520408163270.598284792048243156.656504272425
Trimmed Mean ( 12 / 40 )93.72177083333330.591458463394404158.458753460827
Trimmed Mean ( 13 / 40 )93.71457446808510.584491963021114160.335095086157
Trimmed Mean ( 14 / 40 )93.70239130434780.577696121362683162.20013920696
Trimmed Mean ( 15 / 40 )93.68911111111110.57113035181354164.041555160946
Trimmed Mean ( 16 / 40 )93.678750.564830839300189165.852753571433
Trimmed Mean ( 17 / 40 )93.66837209302330.558561687706071167.695662188549
Trimmed Mean ( 18 / 40 )93.65809523809520.55176204149593169.743636195362
Trimmed Mean ( 19 / 40 )93.64743902439020.545219011296655171.761140173149
Trimmed Mean ( 20 / 40 )93.6381250.538152109389334173.999364429242
Trimmed Mean ( 21 / 40 )93.62858974358970.530287613023448176.561902341569
Trimmed Mean ( 22 / 40 )93.61776315789470.521657500015339179.462124392235
Trimmed Mean ( 23 / 40 )93.610.513150175440494182.422231308104
Trimmed Mean ( 24 / 40 )93.61097222222220.505424880519635185.212433796253
Trimmed Mean ( 25 / 40 )93.61057142857140.496786355124889188.432251536052
Trimmed Mean ( 26 / 40 )93.60867647058820.487607213595428191.975577597292
Trimmed Mean ( 27 / 40 )93.59712121212120.479018458610988195.393558493602
Trimmed Mean ( 28 / 40 )93.586718750.47146644405663198.501335417964
Trimmed Mean ( 29 / 40 )93.57725806451610.464763017653359201.344028053261
Trimmed Mean ( 30 / 40 )93.57050.457502889682455204.524391233782
Trimmed Mean ( 31 / 40 )93.56224137931040.449545380567481208.126354810281
Trimmed Mean ( 32 / 40 )93.55196428571430.440048950910678212.594449076879
Trimmed Mean ( 33 / 40 )93.53888888888890.430486428480604217.286498947326
Trimmed Mean ( 34 / 40 )93.51769230769230.421427457833533221.906974900132
Trimmed Mean ( 35 / 40 )93.50820.415302465630995225.156862138844
Trimmed Mean ( 36 / 40 )93.50166666666670.408847664209484228.695611719965
Trimmed Mean ( 37 / 40 )93.49760869565220.401981947918592232.591560839411
Trimmed Mean ( 38 / 40 )93.48727272727270.394657820536218236.881845139297
Trimmed Mean ( 39 / 40 )93.46690476190480.387525801935217241.188855800445
Trimmed Mean ( 40 / 40 )93.45150.380214269886916245.786408878852
Median93.22
Midrange94.07
Midmean - Weighted Average at Xnp93.4729508196721
Midmean - Weighted Average at X(n+1)p93.5705
Midmean - Empirical Distribution Function93.4729508196721
Midmean - Empirical Distribution Function - Averaging93.5705
Midmean - Empirical Distribution Function - Interpolation93.5705
Midmean - Closest Observation93.4729508196721
Midmean - True Basic - Statistics Graphics Toolkit93.5705
Midmean - MS Excel (old versions)93.5772580645161
Number of observations120



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')