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of Irreproducible Research!

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationMon, 15 Nov 2010 17:29:21 +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/15/t1289842101qcwgq9vlyv6l2ma.htm/, Retrieved Sat, 27 Apr 2024 17:28:08 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=94947, Retrieved Sat, 27 Apr 2024 17:28:08 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact129
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Central Tendency] [Arabica Price in ...] [2008-01-19 12:03:37] [74be16979710d4c4e7c6647856088456]
-  M D    [Central Tendency] [Mini tutorial mean Y] [2010-11-15 17:29:21] [628a2d48b4bd249e4129ba023c5511b0] [Current]
-    D      [Central Tendency] [W6] [2010-11-16 14:16:44] [5ddc7dfb25e070b079c4c8fcccc4d42e]
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Dataseries X:
10
20
40
67
38
61
29
0
30
39
70
65
5
30
50
90
45
75
76
15
10
60
67
60
80
70
70
87
27
65
56
82
30
38
56
70
80
71
50
31
40
71
71
10
20
40
55
80
80
72
60
29
70
60
63
70
38
40
80
24
40
47
70
75
60
65
91
68
90
20
61
13
80
40
70
39
93
10
25
56
18
60
74
35
71
100
64
50
40
35
60
70
55
65
30
25
80
26
78
10
70
65
80
60
74
49
70
66
65
40
40
20
90
48
25
35
40
77
70
82
80
52
71
70
50
80
72
80
91
18
70
76
65
35
62
76
50
68
80
90
79
30
60
100




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 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 & 2 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=94947&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]2 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=94947&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=94947&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 time2 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean55.68055555555561.9323155823739528.8154564727720
Geometric Mean0
Harmonic Mean0
Quadratic Mean60.2848562152129
Winsorized Mean ( 1 / 48 )55.71527777777781.9256191850336528.9336947880503
Winsorized Mean ( 2 / 48 )55.68751.8988727269254729.3266100515149
Winsorized Mean ( 3 / 48 )55.64583333333331.8932892969348629.3910885269467
Winsorized Mean ( 4 / 48 )55.64583333333331.8932892969348629.3910885269467
Winsorized Mean ( 5 / 48 )55.61111111111111.8888117585605329.4423787119435
Winsorized Mean ( 6 / 48 )55.61111111111111.8888117585605329.4423787119435
Winsorized Mean ( 7 / 48 )55.75694444444441.8648031857280129.8996402790234
Winsorized Mean ( 8 / 48 )55.86805555555561.8472991721766830.2431010618199
Winsorized Mean ( 9 / 48 )55.86805555555561.7954673605257931.116163280849
Winsorized Mean ( 10 / 48 )55.52083333333331.7560797031056631.6163516013217
Winsorized Mean ( 11 / 48 )55.67361111111111.7336714599015432.1131266210455
Winsorized Mean ( 12 / 48 )55.50694444444441.7165041826768232.3372031391636
Winsorized Mean ( 13 / 48 )55.50694444444441.7165041826768232.3372031391636
Winsorized Mean ( 14 / 48 )55.50694444444441.7165041826768232.3372031391636
Winsorized Mean ( 15 / 48 )55.92361111111111.6582854493183833.7237543355989
Winsorized Mean ( 16 / 48 )56.03472222222221.6434694878525734.095383356
Winsorized Mean ( 17 / 48 )56.03472222222221.6434694878525734.095383356
Winsorized Mean ( 18 / 48 )56.03472222222221.6434694878525734.095383356
Winsorized Mean ( 19 / 48 )56.16666666666671.6261986792892634.5386251889065
Winsorized Mean ( 20 / 48 )56.30555555555561.6083406638291435.0084760162087
Winsorized Mean ( 21 / 48 )56.59722222222221.5718458088314236.0068537920389
Winsorized Mean ( 22 / 48 )56.59722222222221.5718458088314236.0068537920389
Winsorized Mean ( 23 / 48 )56.75694444444441.5524139199966636.5604454542424
Winsorized Mean ( 24 / 48 )56.59027777777781.5351809708601236.8622845462133
Winsorized Mean ( 25 / 48 )56.41666666666671.5176858175756437.1728232637681
Winsorized Mean ( 26 / 48 )56.23611111111111.4999671749552437.4915611821901
Winsorized Mean ( 27 / 48 )56.04861111111111.4820648127786237.8179217452909
Winsorized Mean ( 28 / 48 )56.24305555555561.4583457051682338.5663394874315
Winsorized Mean ( 29 / 48 )57.04861111111111.3639523995090841.8259545799725
Winsorized Mean ( 30 / 48 )56.84027777777781.3439865490622542.2922966137104
Winsorized Mean ( 31 / 48 )56.84027777777781.3439865490622542.2922966137104
Winsorized Mean ( 32 / 48 )56.61805555555561.3232792746916542.7861726835771
Winsorized Mean ( 33 / 48 )57.30555555555561.2467236696584345.9649214579009
Winsorized Mean ( 34 / 48 )56.83333333333331.2037883738873947.2120636535154
Winsorized Mean ( 35 / 48 )56.83333333333331.2037883738873947.2120636535154
Winsorized Mean ( 36 / 48 )56.83333333333331.1548687517297549.2119413987165
Winsorized Mean ( 37 / 48 )56.83333333333331.1548687517297549.2119413987165
Winsorized Mean ( 38 / 48 )57.09722222222221.1266151939786150.680323261561
Winsorized Mean ( 39 / 48 )57.09722222222221.1266151939786150.680323261561
Winsorized Mean ( 40 / 48 )57.09722222222221.1266151939786150.680323261561
Winsorized Mean ( 41 / 48 )56.81251.1024170286996951.5344905974564
Winsorized Mean ( 42 / 48 )56.81251.1024170286996951.5344905974564
Winsorized Mean ( 43 / 48 )56.81251.1024170286996951.5344905974564
Winsorized Mean ( 44 / 48 )56.81251.1024170286996951.5344905974564
Winsorized Mean ( 45 / 48 )56.81251.1024170286996951.5344905974564
Winsorized Mean ( 46 / 48 )56.81251.1024170286996951.5344905974564
Winsorized Mean ( 47 / 48 )56.81251.1024170286996951.5344905974564
Winsorized Mean ( 48 / 48 )58.47916666666670.92858687106663762.9765167791933
Trimmed Mean ( 1 / 48 )55.76056338028171.8939765299340329.4410001913931
Trimmed Mean ( 2 / 48 )55.80714285714291.8595023157110630.0118705879657
Trimmed Mean ( 3 / 48 )55.86956521739131.8370871071172530.4120392554829
Trimmed Mean ( 4 / 48 )55.94852941176471.8147699474572630.829543706163
Trimmed Mean ( 5 / 48 )56.02985074626871.7903512104914031.2954522095640
Trimmed Mean ( 6 / 48 )56.12121212121211.7647311412260931.8015650147255
Trimmed Mean ( 7 / 48 )56.21538461538461.7366231090665332.3705151232276
Trimmed Mean ( 8 / 48 )56.28906251.7105779181158732.9064592170113
Trimmed Mean ( 9 / 48 )56.34920634920631.6851288852904733.4391077389272
Trimmed Mean ( 10 / 48 )56.41129032258061.6656308909794033.8678218734348
Trimmed Mean ( 11 / 48 )56.5163934426231.6498547027271034.2553761547638
Trimmed Mean ( 12 / 48 )56.60833333333331.6355339816796134.6115299146518
Trimmed Mean ( 13 / 48 )56.72033898305081.6217272771997934.9752635850024
Trimmed Mean ( 14 / 48 )56.83620689655171.6062538930826235.3843232015304
Trimmed Mean ( 15 / 48 )56.95614035087721.5889205720258635.8458071181359
Trimmed Mean ( 16 / 48 )57.04464285714291.5766754480889136.1803330712651
Trimmed Mean ( 17 / 48 )57.12727272727271.5645738795825836.5129914750425
Trimmed Mean ( 18 / 48 )57.2129629629631.5508598607566436.8911236989844
Trimmed Mean ( 19 / 48 )57.30188679245281.5353381446984837.3219977568564
Trimmed Mean ( 20 / 48 )57.38461538461541.5197423534333737.7594368249152
Trimmed Mean ( 21 / 48 )57.46078431372551.5040662912225838.203624832931
Trimmed Mean ( 22 / 48 )57.521.4902701266901438.5970294712615
Trimmed Mean ( 23 / 48 )57.58163265306121.4745133648908339.0512788992756
Trimmed Mean ( 24 / 48 )57.63541666666671.4586493235352039.512866963103
Trimmed Mean ( 25 / 48 )57.70212765957451.4422323905713640.0088973433157
Trimmed Mean ( 26 / 48 )57.78260869565221.4251366089837740.545312169656
Trimmed Mean ( 27 / 48 )57.87777777777781.4072070405153141.1295396564982
Trimmed Mean ( 28 / 48 )57.98863636363641.3882525417560841.7709563782128
Trimmed Mean ( 29 / 48 )58.0930232558141.3690569019637042.4328770940702
Trimmed Mean ( 30 / 48 )58.15476190476191.3574441543334242.8413660474445
Trimmed Mean ( 31 / 48 )58.23170731707321.3456185135942643.2750491530706
Trimmed Mean ( 32 / 48 )58.31251.3315302120854043.7935988764931
Trimmed Mean ( 33 / 48 )58.41025641025641.3168439117541844.3562489744496
Trimmed Mean ( 34 / 48 )58.47368421052631.3082026888680544.6977251370138
Trimmed Mean ( 35 / 48 )58.56756756756761.3016210496664844.995866948045
Trimmed Mean ( 36 / 48 )58.66666666666671.2931140610792545.3685165388292
Trimmed Mean ( 37 / 48 )58.77142857142861.2876497968813045.6424011511309
Trimmed Mean ( 38 / 48 )58.88235294117651.2802150506225645.9941108429732
Trimmed Mean ( 39 / 48 )58.98484848484851.2739989761594046.298976363909
Trimmed Mean ( 40 / 48 )59.093751.2655224213770146.6951426555526
Trimmed Mean ( 41 / 48 )59.20967741935481.2543182095025547.2046702111076
Trimmed Mean ( 42 / 48 )59.351.2423381000364847.7728244817229
Trimmed Mean ( 43 / 48 )59.51.2266574278302248.5058001118102
Trimmed Mean ( 44 / 48 )59.66071428571431.2063890484326049.4539587898519
Trimmed Mean ( 45 / 48 )59.83333333333331.180362852690350.6906272058295
Trimmed Mean ( 46 / 48 )60.01923076923081.1469976496520152.3272482619649
Trimmed Mean ( 47 / 48 )60.221.1040888754525054.5427105905035
Trimmed Mean ( 48 / 48 )60.43751.0484310508754157.645660102814
Median60.5
Midrange50
Midmean - Weighted Average at Xnp57.84
Midmean - Weighted Average at X(n+1)p58.6666666666667
Midmean - Empirical Distribution Function57.84
Midmean - Empirical Distribution Function - Averaging58.6666666666667
Midmean - Empirical Distribution Function - Interpolation58.6666666666667
Midmean - Closest Observation57.84
Midmean - True Basic - Statistics Graphics Toolkit58.6666666666667
Midmean - MS Excel (old versions)58.2077922077922
Number of observations144

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 55.6805555555556 & 1.93231558237395 & 28.8154564727720 \tabularnewline
Geometric Mean & 0 &  &  \tabularnewline
Harmonic Mean & 0 &  &  \tabularnewline
Quadratic Mean & 60.2848562152129 &  &  \tabularnewline
Winsorized Mean ( 1 / 48 ) & 55.7152777777778 & 1.92561918503365 & 28.9336947880503 \tabularnewline
Winsorized Mean ( 2 / 48 ) & 55.6875 & 1.89887272692547 & 29.3266100515149 \tabularnewline
Winsorized Mean ( 3 / 48 ) & 55.6458333333333 & 1.89328929693486 & 29.3910885269467 \tabularnewline
Winsorized Mean ( 4 / 48 ) & 55.6458333333333 & 1.89328929693486 & 29.3910885269467 \tabularnewline
Winsorized Mean ( 5 / 48 ) & 55.6111111111111 & 1.88881175856053 & 29.4423787119435 \tabularnewline
Winsorized Mean ( 6 / 48 ) & 55.6111111111111 & 1.88881175856053 & 29.4423787119435 \tabularnewline
Winsorized Mean ( 7 / 48 ) & 55.7569444444444 & 1.86480318572801 & 29.8996402790234 \tabularnewline
Winsorized Mean ( 8 / 48 ) & 55.8680555555556 & 1.84729917217668 & 30.2431010618199 \tabularnewline
Winsorized Mean ( 9 / 48 ) & 55.8680555555556 & 1.79546736052579 & 31.116163280849 \tabularnewline
Winsorized Mean ( 10 / 48 ) & 55.5208333333333 & 1.75607970310566 & 31.6163516013217 \tabularnewline
Winsorized Mean ( 11 / 48 ) & 55.6736111111111 & 1.73367145990154 & 32.1131266210455 \tabularnewline
Winsorized Mean ( 12 / 48 ) & 55.5069444444444 & 1.71650418267682 & 32.3372031391636 \tabularnewline
Winsorized Mean ( 13 / 48 ) & 55.5069444444444 & 1.71650418267682 & 32.3372031391636 \tabularnewline
Winsorized Mean ( 14 / 48 ) & 55.5069444444444 & 1.71650418267682 & 32.3372031391636 \tabularnewline
Winsorized Mean ( 15 / 48 ) & 55.9236111111111 & 1.65828544931838 & 33.7237543355989 \tabularnewline
Winsorized Mean ( 16 / 48 ) & 56.0347222222222 & 1.64346948785257 & 34.095383356 \tabularnewline
Winsorized Mean ( 17 / 48 ) & 56.0347222222222 & 1.64346948785257 & 34.095383356 \tabularnewline
Winsorized Mean ( 18 / 48 ) & 56.0347222222222 & 1.64346948785257 & 34.095383356 \tabularnewline
Winsorized Mean ( 19 / 48 ) & 56.1666666666667 & 1.62619867928926 & 34.5386251889065 \tabularnewline
Winsorized Mean ( 20 / 48 ) & 56.3055555555556 & 1.60834066382914 & 35.0084760162087 \tabularnewline
Winsorized Mean ( 21 / 48 ) & 56.5972222222222 & 1.57184580883142 & 36.0068537920389 \tabularnewline
Winsorized Mean ( 22 / 48 ) & 56.5972222222222 & 1.57184580883142 & 36.0068537920389 \tabularnewline
Winsorized Mean ( 23 / 48 ) & 56.7569444444444 & 1.55241391999666 & 36.5604454542424 \tabularnewline
Winsorized Mean ( 24 / 48 ) & 56.5902777777778 & 1.53518097086012 & 36.8622845462133 \tabularnewline
Winsorized Mean ( 25 / 48 ) & 56.4166666666667 & 1.51768581757564 & 37.1728232637681 \tabularnewline
Winsorized Mean ( 26 / 48 ) & 56.2361111111111 & 1.49996717495524 & 37.4915611821901 \tabularnewline
Winsorized Mean ( 27 / 48 ) & 56.0486111111111 & 1.48206481277862 & 37.8179217452909 \tabularnewline
Winsorized Mean ( 28 / 48 ) & 56.2430555555556 & 1.45834570516823 & 38.5663394874315 \tabularnewline
Winsorized Mean ( 29 / 48 ) & 57.0486111111111 & 1.36395239950908 & 41.8259545799725 \tabularnewline
Winsorized Mean ( 30 / 48 ) & 56.8402777777778 & 1.34398654906225 & 42.2922966137104 \tabularnewline
Winsorized Mean ( 31 / 48 ) & 56.8402777777778 & 1.34398654906225 & 42.2922966137104 \tabularnewline
Winsorized Mean ( 32 / 48 ) & 56.6180555555556 & 1.32327927469165 & 42.7861726835771 \tabularnewline
Winsorized Mean ( 33 / 48 ) & 57.3055555555556 & 1.24672366965843 & 45.9649214579009 \tabularnewline
Winsorized Mean ( 34 / 48 ) & 56.8333333333333 & 1.20378837388739 & 47.2120636535154 \tabularnewline
Winsorized Mean ( 35 / 48 ) & 56.8333333333333 & 1.20378837388739 & 47.2120636535154 \tabularnewline
Winsorized Mean ( 36 / 48 ) & 56.8333333333333 & 1.15486875172975 & 49.2119413987165 \tabularnewline
Winsorized Mean ( 37 / 48 ) & 56.8333333333333 & 1.15486875172975 & 49.2119413987165 \tabularnewline
Winsorized Mean ( 38 / 48 ) & 57.0972222222222 & 1.12661519397861 & 50.680323261561 \tabularnewline
Winsorized Mean ( 39 / 48 ) & 57.0972222222222 & 1.12661519397861 & 50.680323261561 \tabularnewline
Winsorized Mean ( 40 / 48 ) & 57.0972222222222 & 1.12661519397861 & 50.680323261561 \tabularnewline
Winsorized Mean ( 41 / 48 ) & 56.8125 & 1.10241702869969 & 51.5344905974564 \tabularnewline
Winsorized Mean ( 42 / 48 ) & 56.8125 & 1.10241702869969 & 51.5344905974564 \tabularnewline
Winsorized Mean ( 43 / 48 ) & 56.8125 & 1.10241702869969 & 51.5344905974564 \tabularnewline
Winsorized Mean ( 44 / 48 ) & 56.8125 & 1.10241702869969 & 51.5344905974564 \tabularnewline
Winsorized Mean ( 45 / 48 ) & 56.8125 & 1.10241702869969 & 51.5344905974564 \tabularnewline
Winsorized Mean ( 46 / 48 ) & 56.8125 & 1.10241702869969 & 51.5344905974564 \tabularnewline
Winsorized Mean ( 47 / 48 ) & 56.8125 & 1.10241702869969 & 51.5344905974564 \tabularnewline
Winsorized Mean ( 48 / 48 ) & 58.4791666666667 & 0.928586871066637 & 62.9765167791933 \tabularnewline
Trimmed Mean ( 1 / 48 ) & 55.7605633802817 & 1.89397652993403 & 29.4410001913931 \tabularnewline
Trimmed Mean ( 2 / 48 ) & 55.8071428571429 & 1.85950231571106 & 30.0118705879657 \tabularnewline
Trimmed Mean ( 3 / 48 ) & 55.8695652173913 & 1.83708710711725 & 30.4120392554829 \tabularnewline
Trimmed Mean ( 4 / 48 ) & 55.9485294117647 & 1.81476994745726 & 30.829543706163 \tabularnewline
Trimmed Mean ( 5 / 48 ) & 56.0298507462687 & 1.79035121049140 & 31.2954522095640 \tabularnewline
Trimmed Mean ( 6 / 48 ) & 56.1212121212121 & 1.76473114122609 & 31.8015650147255 \tabularnewline
Trimmed Mean ( 7 / 48 ) & 56.2153846153846 & 1.73662310906653 & 32.3705151232276 \tabularnewline
Trimmed Mean ( 8 / 48 ) & 56.2890625 & 1.71057791811587 & 32.9064592170113 \tabularnewline
Trimmed Mean ( 9 / 48 ) & 56.3492063492063 & 1.68512888529047 & 33.4391077389272 \tabularnewline
Trimmed Mean ( 10 / 48 ) & 56.4112903225806 & 1.66563089097940 & 33.8678218734348 \tabularnewline
Trimmed Mean ( 11 / 48 ) & 56.516393442623 & 1.64985470272710 & 34.2553761547638 \tabularnewline
Trimmed Mean ( 12 / 48 ) & 56.6083333333333 & 1.63553398167961 & 34.6115299146518 \tabularnewline
Trimmed Mean ( 13 / 48 ) & 56.7203389830508 & 1.62172727719979 & 34.9752635850024 \tabularnewline
Trimmed Mean ( 14 / 48 ) & 56.8362068965517 & 1.60625389308262 & 35.3843232015304 \tabularnewline
Trimmed Mean ( 15 / 48 ) & 56.9561403508772 & 1.58892057202586 & 35.8458071181359 \tabularnewline
Trimmed Mean ( 16 / 48 ) & 57.0446428571429 & 1.57667544808891 & 36.1803330712651 \tabularnewline
Trimmed Mean ( 17 / 48 ) & 57.1272727272727 & 1.56457387958258 & 36.5129914750425 \tabularnewline
Trimmed Mean ( 18 / 48 ) & 57.212962962963 & 1.55085986075664 & 36.8911236989844 \tabularnewline
Trimmed Mean ( 19 / 48 ) & 57.3018867924528 & 1.53533814469848 & 37.3219977568564 \tabularnewline
Trimmed Mean ( 20 / 48 ) & 57.3846153846154 & 1.51974235343337 & 37.7594368249152 \tabularnewline
Trimmed Mean ( 21 / 48 ) & 57.4607843137255 & 1.50406629122258 & 38.203624832931 \tabularnewline
Trimmed Mean ( 22 / 48 ) & 57.52 & 1.49027012669014 & 38.5970294712615 \tabularnewline
Trimmed Mean ( 23 / 48 ) & 57.5816326530612 & 1.47451336489083 & 39.0512788992756 \tabularnewline
Trimmed Mean ( 24 / 48 ) & 57.6354166666667 & 1.45864932353520 & 39.512866963103 \tabularnewline
Trimmed Mean ( 25 / 48 ) & 57.7021276595745 & 1.44223239057136 & 40.0088973433157 \tabularnewline
Trimmed Mean ( 26 / 48 ) & 57.7826086956522 & 1.42513660898377 & 40.545312169656 \tabularnewline
Trimmed Mean ( 27 / 48 ) & 57.8777777777778 & 1.40720704051531 & 41.1295396564982 \tabularnewline
Trimmed Mean ( 28 / 48 ) & 57.9886363636364 & 1.38825254175608 & 41.7709563782128 \tabularnewline
Trimmed Mean ( 29 / 48 ) & 58.093023255814 & 1.36905690196370 & 42.4328770940702 \tabularnewline
Trimmed Mean ( 30 / 48 ) & 58.1547619047619 & 1.35744415433342 & 42.8413660474445 \tabularnewline
Trimmed Mean ( 31 / 48 ) & 58.2317073170732 & 1.34561851359426 & 43.2750491530706 \tabularnewline
Trimmed Mean ( 32 / 48 ) & 58.3125 & 1.33153021208540 & 43.7935988764931 \tabularnewline
Trimmed Mean ( 33 / 48 ) & 58.4102564102564 & 1.31684391175418 & 44.3562489744496 \tabularnewline
Trimmed Mean ( 34 / 48 ) & 58.4736842105263 & 1.30820268886805 & 44.6977251370138 \tabularnewline
Trimmed Mean ( 35 / 48 ) & 58.5675675675676 & 1.30162104966648 & 44.995866948045 \tabularnewline
Trimmed Mean ( 36 / 48 ) & 58.6666666666667 & 1.29311406107925 & 45.3685165388292 \tabularnewline
Trimmed Mean ( 37 / 48 ) & 58.7714285714286 & 1.28764979688130 & 45.6424011511309 \tabularnewline
Trimmed Mean ( 38 / 48 ) & 58.8823529411765 & 1.28021505062256 & 45.9941108429732 \tabularnewline
Trimmed Mean ( 39 / 48 ) & 58.9848484848485 & 1.27399897615940 & 46.298976363909 \tabularnewline
Trimmed Mean ( 40 / 48 ) & 59.09375 & 1.26552242137701 & 46.6951426555526 \tabularnewline
Trimmed Mean ( 41 / 48 ) & 59.2096774193548 & 1.25431820950255 & 47.2046702111076 \tabularnewline
Trimmed Mean ( 42 / 48 ) & 59.35 & 1.24233810003648 & 47.7728244817229 \tabularnewline
Trimmed Mean ( 43 / 48 ) & 59.5 & 1.22665742783022 & 48.5058001118102 \tabularnewline
Trimmed Mean ( 44 / 48 ) & 59.6607142857143 & 1.20638904843260 & 49.4539587898519 \tabularnewline
Trimmed Mean ( 45 / 48 ) & 59.8333333333333 & 1.1803628526903 & 50.6906272058295 \tabularnewline
Trimmed Mean ( 46 / 48 ) & 60.0192307692308 & 1.14699764965201 & 52.3272482619649 \tabularnewline
Trimmed Mean ( 47 / 48 ) & 60.22 & 1.10408887545250 & 54.5427105905035 \tabularnewline
Trimmed Mean ( 48 / 48 ) & 60.4375 & 1.04843105087541 & 57.645660102814 \tabularnewline
Median & 60.5 &  &  \tabularnewline
Midrange & 50 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 57.84 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 58.6666666666667 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 57.84 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 58.6666666666667 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 58.6666666666667 &  &  \tabularnewline
Midmean - Closest Observation & 57.84 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 58.6666666666667 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 58.2077922077922 &  &  \tabularnewline
Number of observations & 144 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=94947&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]55.6805555555556[/C][C]1.93231558237395[/C][C]28.8154564727720[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]0[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]0[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]60.2848562152129[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 48 )[/C][C]55.7152777777778[/C][C]1.92561918503365[/C][C]28.9336947880503[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 48 )[/C][C]55.6875[/C][C]1.89887272692547[/C][C]29.3266100515149[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 48 )[/C][C]55.6458333333333[/C][C]1.89328929693486[/C][C]29.3910885269467[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 48 )[/C][C]55.6458333333333[/C][C]1.89328929693486[/C][C]29.3910885269467[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 48 )[/C][C]55.6111111111111[/C][C]1.88881175856053[/C][C]29.4423787119435[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 48 )[/C][C]55.6111111111111[/C][C]1.88881175856053[/C][C]29.4423787119435[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 48 )[/C][C]55.7569444444444[/C][C]1.86480318572801[/C][C]29.8996402790234[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 48 )[/C][C]55.8680555555556[/C][C]1.84729917217668[/C][C]30.2431010618199[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 48 )[/C][C]55.8680555555556[/C][C]1.79546736052579[/C][C]31.116163280849[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 48 )[/C][C]55.5208333333333[/C][C]1.75607970310566[/C][C]31.6163516013217[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 48 )[/C][C]55.6736111111111[/C][C]1.73367145990154[/C][C]32.1131266210455[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 48 )[/C][C]55.5069444444444[/C][C]1.71650418267682[/C][C]32.3372031391636[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 48 )[/C][C]55.5069444444444[/C][C]1.71650418267682[/C][C]32.3372031391636[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 48 )[/C][C]55.5069444444444[/C][C]1.71650418267682[/C][C]32.3372031391636[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 48 )[/C][C]55.9236111111111[/C][C]1.65828544931838[/C][C]33.7237543355989[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 48 )[/C][C]56.0347222222222[/C][C]1.64346948785257[/C][C]34.095383356[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 48 )[/C][C]56.0347222222222[/C][C]1.64346948785257[/C][C]34.095383356[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 48 )[/C][C]56.0347222222222[/C][C]1.64346948785257[/C][C]34.095383356[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 48 )[/C][C]56.1666666666667[/C][C]1.62619867928926[/C][C]34.5386251889065[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 48 )[/C][C]56.3055555555556[/C][C]1.60834066382914[/C][C]35.0084760162087[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 48 )[/C][C]56.5972222222222[/C][C]1.57184580883142[/C][C]36.0068537920389[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 48 )[/C][C]56.5972222222222[/C][C]1.57184580883142[/C][C]36.0068537920389[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 48 )[/C][C]56.7569444444444[/C][C]1.55241391999666[/C][C]36.5604454542424[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 48 )[/C][C]56.5902777777778[/C][C]1.53518097086012[/C][C]36.8622845462133[/C][/ROW]
[ROW][C]Winsorized Mean ( 25 / 48 )[/C][C]56.4166666666667[/C][C]1.51768581757564[/C][C]37.1728232637681[/C][/ROW]
[ROW][C]Winsorized Mean ( 26 / 48 )[/C][C]56.2361111111111[/C][C]1.49996717495524[/C][C]37.4915611821901[/C][/ROW]
[ROW][C]Winsorized Mean ( 27 / 48 )[/C][C]56.0486111111111[/C][C]1.48206481277862[/C][C]37.8179217452909[/C][/ROW]
[ROW][C]Winsorized Mean ( 28 / 48 )[/C][C]56.2430555555556[/C][C]1.45834570516823[/C][C]38.5663394874315[/C][/ROW]
[ROW][C]Winsorized Mean ( 29 / 48 )[/C][C]57.0486111111111[/C][C]1.36395239950908[/C][C]41.8259545799725[/C][/ROW]
[ROW][C]Winsorized Mean ( 30 / 48 )[/C][C]56.8402777777778[/C][C]1.34398654906225[/C][C]42.2922966137104[/C][/ROW]
[ROW][C]Winsorized Mean ( 31 / 48 )[/C][C]56.8402777777778[/C][C]1.34398654906225[/C][C]42.2922966137104[/C][/ROW]
[ROW][C]Winsorized Mean ( 32 / 48 )[/C][C]56.6180555555556[/C][C]1.32327927469165[/C][C]42.7861726835771[/C][/ROW]
[ROW][C]Winsorized Mean ( 33 / 48 )[/C][C]57.3055555555556[/C][C]1.24672366965843[/C][C]45.9649214579009[/C][/ROW]
[ROW][C]Winsorized Mean ( 34 / 48 )[/C][C]56.8333333333333[/C][C]1.20378837388739[/C][C]47.2120636535154[/C][/ROW]
[ROW][C]Winsorized Mean ( 35 / 48 )[/C][C]56.8333333333333[/C][C]1.20378837388739[/C][C]47.2120636535154[/C][/ROW]
[ROW][C]Winsorized Mean ( 36 / 48 )[/C][C]56.8333333333333[/C][C]1.15486875172975[/C][C]49.2119413987165[/C][/ROW]
[ROW][C]Winsorized Mean ( 37 / 48 )[/C][C]56.8333333333333[/C][C]1.15486875172975[/C][C]49.2119413987165[/C][/ROW]
[ROW][C]Winsorized Mean ( 38 / 48 )[/C][C]57.0972222222222[/C][C]1.12661519397861[/C][C]50.680323261561[/C][/ROW]
[ROW][C]Winsorized Mean ( 39 / 48 )[/C][C]57.0972222222222[/C][C]1.12661519397861[/C][C]50.680323261561[/C][/ROW]
[ROW][C]Winsorized Mean ( 40 / 48 )[/C][C]57.0972222222222[/C][C]1.12661519397861[/C][C]50.680323261561[/C][/ROW]
[ROW][C]Winsorized Mean ( 41 / 48 )[/C][C]56.8125[/C][C]1.10241702869969[/C][C]51.5344905974564[/C][/ROW]
[ROW][C]Winsorized Mean ( 42 / 48 )[/C][C]56.8125[/C][C]1.10241702869969[/C][C]51.5344905974564[/C][/ROW]
[ROW][C]Winsorized Mean ( 43 / 48 )[/C][C]56.8125[/C][C]1.10241702869969[/C][C]51.5344905974564[/C][/ROW]
[ROW][C]Winsorized Mean ( 44 / 48 )[/C][C]56.8125[/C][C]1.10241702869969[/C][C]51.5344905974564[/C][/ROW]
[ROW][C]Winsorized Mean ( 45 / 48 )[/C][C]56.8125[/C][C]1.10241702869969[/C][C]51.5344905974564[/C][/ROW]
[ROW][C]Winsorized Mean ( 46 / 48 )[/C][C]56.8125[/C][C]1.10241702869969[/C][C]51.5344905974564[/C][/ROW]
[ROW][C]Winsorized Mean ( 47 / 48 )[/C][C]56.8125[/C][C]1.10241702869969[/C][C]51.5344905974564[/C][/ROW]
[ROW][C]Winsorized Mean ( 48 / 48 )[/C][C]58.4791666666667[/C][C]0.928586871066637[/C][C]62.9765167791933[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 48 )[/C][C]55.7605633802817[/C][C]1.89397652993403[/C][C]29.4410001913931[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 48 )[/C][C]55.8071428571429[/C][C]1.85950231571106[/C][C]30.0118705879657[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 48 )[/C][C]55.8695652173913[/C][C]1.83708710711725[/C][C]30.4120392554829[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 48 )[/C][C]55.9485294117647[/C][C]1.81476994745726[/C][C]30.829543706163[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 48 )[/C][C]56.0298507462687[/C][C]1.79035121049140[/C][C]31.2954522095640[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 48 )[/C][C]56.1212121212121[/C][C]1.76473114122609[/C][C]31.8015650147255[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 48 )[/C][C]56.2153846153846[/C][C]1.73662310906653[/C][C]32.3705151232276[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 48 )[/C][C]56.2890625[/C][C]1.71057791811587[/C][C]32.9064592170113[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 48 )[/C][C]56.3492063492063[/C][C]1.68512888529047[/C][C]33.4391077389272[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 48 )[/C][C]56.4112903225806[/C][C]1.66563089097940[/C][C]33.8678218734348[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 48 )[/C][C]56.516393442623[/C][C]1.64985470272710[/C][C]34.2553761547638[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 48 )[/C][C]56.6083333333333[/C][C]1.63553398167961[/C][C]34.6115299146518[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 48 )[/C][C]56.7203389830508[/C][C]1.62172727719979[/C][C]34.9752635850024[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 48 )[/C][C]56.8362068965517[/C][C]1.60625389308262[/C][C]35.3843232015304[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 48 )[/C][C]56.9561403508772[/C][C]1.58892057202586[/C][C]35.8458071181359[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 48 )[/C][C]57.0446428571429[/C][C]1.57667544808891[/C][C]36.1803330712651[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 48 )[/C][C]57.1272727272727[/C][C]1.56457387958258[/C][C]36.5129914750425[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 48 )[/C][C]57.212962962963[/C][C]1.55085986075664[/C][C]36.8911236989844[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 48 )[/C][C]57.3018867924528[/C][C]1.53533814469848[/C][C]37.3219977568564[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 48 )[/C][C]57.3846153846154[/C][C]1.51974235343337[/C][C]37.7594368249152[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 48 )[/C][C]57.4607843137255[/C][C]1.50406629122258[/C][C]38.203624832931[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 48 )[/C][C]57.52[/C][C]1.49027012669014[/C][C]38.5970294712615[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 48 )[/C][C]57.5816326530612[/C][C]1.47451336489083[/C][C]39.0512788992756[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 48 )[/C][C]57.6354166666667[/C][C]1.45864932353520[/C][C]39.512866963103[/C][/ROW]
[ROW][C]Trimmed Mean ( 25 / 48 )[/C][C]57.7021276595745[/C][C]1.44223239057136[/C][C]40.0088973433157[/C][/ROW]
[ROW][C]Trimmed Mean ( 26 / 48 )[/C][C]57.7826086956522[/C][C]1.42513660898377[/C][C]40.545312169656[/C][/ROW]
[ROW][C]Trimmed Mean ( 27 / 48 )[/C][C]57.8777777777778[/C][C]1.40720704051531[/C][C]41.1295396564982[/C][/ROW]
[ROW][C]Trimmed Mean ( 28 / 48 )[/C][C]57.9886363636364[/C][C]1.38825254175608[/C][C]41.7709563782128[/C][/ROW]
[ROW][C]Trimmed Mean ( 29 / 48 )[/C][C]58.093023255814[/C][C]1.36905690196370[/C][C]42.4328770940702[/C][/ROW]
[ROW][C]Trimmed Mean ( 30 / 48 )[/C][C]58.1547619047619[/C][C]1.35744415433342[/C][C]42.8413660474445[/C][/ROW]
[ROW][C]Trimmed Mean ( 31 / 48 )[/C][C]58.2317073170732[/C][C]1.34561851359426[/C][C]43.2750491530706[/C][/ROW]
[ROW][C]Trimmed Mean ( 32 / 48 )[/C][C]58.3125[/C][C]1.33153021208540[/C][C]43.7935988764931[/C][/ROW]
[ROW][C]Trimmed Mean ( 33 / 48 )[/C][C]58.4102564102564[/C][C]1.31684391175418[/C][C]44.3562489744496[/C][/ROW]
[ROW][C]Trimmed Mean ( 34 / 48 )[/C][C]58.4736842105263[/C][C]1.30820268886805[/C][C]44.6977251370138[/C][/ROW]
[ROW][C]Trimmed Mean ( 35 / 48 )[/C][C]58.5675675675676[/C][C]1.30162104966648[/C][C]44.995866948045[/C][/ROW]
[ROW][C]Trimmed Mean ( 36 / 48 )[/C][C]58.6666666666667[/C][C]1.29311406107925[/C][C]45.3685165388292[/C][/ROW]
[ROW][C]Trimmed Mean ( 37 / 48 )[/C][C]58.7714285714286[/C][C]1.28764979688130[/C][C]45.6424011511309[/C][/ROW]
[ROW][C]Trimmed Mean ( 38 / 48 )[/C][C]58.8823529411765[/C][C]1.28021505062256[/C][C]45.9941108429732[/C][/ROW]
[ROW][C]Trimmed Mean ( 39 / 48 )[/C][C]58.9848484848485[/C][C]1.27399897615940[/C][C]46.298976363909[/C][/ROW]
[ROW][C]Trimmed Mean ( 40 / 48 )[/C][C]59.09375[/C][C]1.26552242137701[/C][C]46.6951426555526[/C][/ROW]
[ROW][C]Trimmed Mean ( 41 / 48 )[/C][C]59.2096774193548[/C][C]1.25431820950255[/C][C]47.2046702111076[/C][/ROW]
[ROW][C]Trimmed Mean ( 42 / 48 )[/C][C]59.35[/C][C]1.24233810003648[/C][C]47.7728244817229[/C][/ROW]
[ROW][C]Trimmed Mean ( 43 / 48 )[/C][C]59.5[/C][C]1.22665742783022[/C][C]48.5058001118102[/C][/ROW]
[ROW][C]Trimmed Mean ( 44 / 48 )[/C][C]59.6607142857143[/C][C]1.20638904843260[/C][C]49.4539587898519[/C][/ROW]
[ROW][C]Trimmed Mean ( 45 / 48 )[/C][C]59.8333333333333[/C][C]1.1803628526903[/C][C]50.6906272058295[/C][/ROW]
[ROW][C]Trimmed Mean ( 46 / 48 )[/C][C]60.0192307692308[/C][C]1.14699764965201[/C][C]52.3272482619649[/C][/ROW]
[ROW][C]Trimmed Mean ( 47 / 48 )[/C][C]60.22[/C][C]1.10408887545250[/C][C]54.5427105905035[/C][/ROW]
[ROW][C]Trimmed Mean ( 48 / 48 )[/C][C]60.4375[/C][C]1.04843105087541[/C][C]57.645660102814[/C][/ROW]
[ROW][C]Median[/C][C]60.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]50[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]57.84[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]58.6666666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]57.84[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]58.6666666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]58.6666666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]57.84[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]58.6666666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]58.2077922077922[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]144[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=94947&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=94947&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 Mean55.68055555555561.9323155823739528.8154564727720
Geometric Mean0
Harmonic Mean0
Quadratic Mean60.2848562152129
Winsorized Mean ( 1 / 48 )55.71527777777781.9256191850336528.9336947880503
Winsorized Mean ( 2 / 48 )55.68751.8988727269254729.3266100515149
Winsorized Mean ( 3 / 48 )55.64583333333331.8932892969348629.3910885269467
Winsorized Mean ( 4 / 48 )55.64583333333331.8932892969348629.3910885269467
Winsorized Mean ( 5 / 48 )55.61111111111111.8888117585605329.4423787119435
Winsorized Mean ( 6 / 48 )55.61111111111111.8888117585605329.4423787119435
Winsorized Mean ( 7 / 48 )55.75694444444441.8648031857280129.8996402790234
Winsorized Mean ( 8 / 48 )55.86805555555561.8472991721766830.2431010618199
Winsorized Mean ( 9 / 48 )55.86805555555561.7954673605257931.116163280849
Winsorized Mean ( 10 / 48 )55.52083333333331.7560797031056631.6163516013217
Winsorized Mean ( 11 / 48 )55.67361111111111.7336714599015432.1131266210455
Winsorized Mean ( 12 / 48 )55.50694444444441.7165041826768232.3372031391636
Winsorized Mean ( 13 / 48 )55.50694444444441.7165041826768232.3372031391636
Winsorized Mean ( 14 / 48 )55.50694444444441.7165041826768232.3372031391636
Winsorized Mean ( 15 / 48 )55.92361111111111.6582854493183833.7237543355989
Winsorized Mean ( 16 / 48 )56.03472222222221.6434694878525734.095383356
Winsorized Mean ( 17 / 48 )56.03472222222221.6434694878525734.095383356
Winsorized Mean ( 18 / 48 )56.03472222222221.6434694878525734.095383356
Winsorized Mean ( 19 / 48 )56.16666666666671.6261986792892634.5386251889065
Winsorized Mean ( 20 / 48 )56.30555555555561.6083406638291435.0084760162087
Winsorized Mean ( 21 / 48 )56.59722222222221.5718458088314236.0068537920389
Winsorized Mean ( 22 / 48 )56.59722222222221.5718458088314236.0068537920389
Winsorized Mean ( 23 / 48 )56.75694444444441.5524139199966636.5604454542424
Winsorized Mean ( 24 / 48 )56.59027777777781.5351809708601236.8622845462133
Winsorized Mean ( 25 / 48 )56.41666666666671.5176858175756437.1728232637681
Winsorized Mean ( 26 / 48 )56.23611111111111.4999671749552437.4915611821901
Winsorized Mean ( 27 / 48 )56.04861111111111.4820648127786237.8179217452909
Winsorized Mean ( 28 / 48 )56.24305555555561.4583457051682338.5663394874315
Winsorized Mean ( 29 / 48 )57.04861111111111.3639523995090841.8259545799725
Winsorized Mean ( 30 / 48 )56.84027777777781.3439865490622542.2922966137104
Winsorized Mean ( 31 / 48 )56.84027777777781.3439865490622542.2922966137104
Winsorized Mean ( 32 / 48 )56.61805555555561.3232792746916542.7861726835771
Winsorized Mean ( 33 / 48 )57.30555555555561.2467236696584345.9649214579009
Winsorized Mean ( 34 / 48 )56.83333333333331.2037883738873947.2120636535154
Winsorized Mean ( 35 / 48 )56.83333333333331.2037883738873947.2120636535154
Winsorized Mean ( 36 / 48 )56.83333333333331.1548687517297549.2119413987165
Winsorized Mean ( 37 / 48 )56.83333333333331.1548687517297549.2119413987165
Winsorized Mean ( 38 / 48 )57.09722222222221.1266151939786150.680323261561
Winsorized Mean ( 39 / 48 )57.09722222222221.1266151939786150.680323261561
Winsorized Mean ( 40 / 48 )57.09722222222221.1266151939786150.680323261561
Winsorized Mean ( 41 / 48 )56.81251.1024170286996951.5344905974564
Winsorized Mean ( 42 / 48 )56.81251.1024170286996951.5344905974564
Winsorized Mean ( 43 / 48 )56.81251.1024170286996951.5344905974564
Winsorized Mean ( 44 / 48 )56.81251.1024170286996951.5344905974564
Winsorized Mean ( 45 / 48 )56.81251.1024170286996951.5344905974564
Winsorized Mean ( 46 / 48 )56.81251.1024170286996951.5344905974564
Winsorized Mean ( 47 / 48 )56.81251.1024170286996951.5344905974564
Winsorized Mean ( 48 / 48 )58.47916666666670.92858687106663762.9765167791933
Trimmed Mean ( 1 / 48 )55.76056338028171.8939765299340329.4410001913931
Trimmed Mean ( 2 / 48 )55.80714285714291.8595023157110630.0118705879657
Trimmed Mean ( 3 / 48 )55.86956521739131.8370871071172530.4120392554829
Trimmed Mean ( 4 / 48 )55.94852941176471.8147699474572630.829543706163
Trimmed Mean ( 5 / 48 )56.02985074626871.7903512104914031.2954522095640
Trimmed Mean ( 6 / 48 )56.12121212121211.7647311412260931.8015650147255
Trimmed Mean ( 7 / 48 )56.21538461538461.7366231090665332.3705151232276
Trimmed Mean ( 8 / 48 )56.28906251.7105779181158732.9064592170113
Trimmed Mean ( 9 / 48 )56.34920634920631.6851288852904733.4391077389272
Trimmed Mean ( 10 / 48 )56.41129032258061.6656308909794033.8678218734348
Trimmed Mean ( 11 / 48 )56.5163934426231.6498547027271034.2553761547638
Trimmed Mean ( 12 / 48 )56.60833333333331.6355339816796134.6115299146518
Trimmed Mean ( 13 / 48 )56.72033898305081.6217272771997934.9752635850024
Trimmed Mean ( 14 / 48 )56.83620689655171.6062538930826235.3843232015304
Trimmed Mean ( 15 / 48 )56.95614035087721.5889205720258635.8458071181359
Trimmed Mean ( 16 / 48 )57.04464285714291.5766754480889136.1803330712651
Trimmed Mean ( 17 / 48 )57.12727272727271.5645738795825836.5129914750425
Trimmed Mean ( 18 / 48 )57.2129629629631.5508598607566436.8911236989844
Trimmed Mean ( 19 / 48 )57.30188679245281.5353381446984837.3219977568564
Trimmed Mean ( 20 / 48 )57.38461538461541.5197423534333737.7594368249152
Trimmed Mean ( 21 / 48 )57.46078431372551.5040662912225838.203624832931
Trimmed Mean ( 22 / 48 )57.521.4902701266901438.5970294712615
Trimmed Mean ( 23 / 48 )57.58163265306121.4745133648908339.0512788992756
Trimmed Mean ( 24 / 48 )57.63541666666671.4586493235352039.512866963103
Trimmed Mean ( 25 / 48 )57.70212765957451.4422323905713640.0088973433157
Trimmed Mean ( 26 / 48 )57.78260869565221.4251366089837740.545312169656
Trimmed Mean ( 27 / 48 )57.87777777777781.4072070405153141.1295396564982
Trimmed Mean ( 28 / 48 )57.98863636363641.3882525417560841.7709563782128
Trimmed Mean ( 29 / 48 )58.0930232558141.3690569019637042.4328770940702
Trimmed Mean ( 30 / 48 )58.15476190476191.3574441543334242.8413660474445
Trimmed Mean ( 31 / 48 )58.23170731707321.3456185135942643.2750491530706
Trimmed Mean ( 32 / 48 )58.31251.3315302120854043.7935988764931
Trimmed Mean ( 33 / 48 )58.41025641025641.3168439117541844.3562489744496
Trimmed Mean ( 34 / 48 )58.47368421052631.3082026888680544.6977251370138
Trimmed Mean ( 35 / 48 )58.56756756756761.3016210496664844.995866948045
Trimmed Mean ( 36 / 48 )58.66666666666671.2931140610792545.3685165388292
Trimmed Mean ( 37 / 48 )58.77142857142861.2876497968813045.6424011511309
Trimmed Mean ( 38 / 48 )58.88235294117651.2802150506225645.9941108429732
Trimmed Mean ( 39 / 48 )58.98484848484851.2739989761594046.298976363909
Trimmed Mean ( 40 / 48 )59.093751.2655224213770146.6951426555526
Trimmed Mean ( 41 / 48 )59.20967741935481.2543182095025547.2046702111076
Trimmed Mean ( 42 / 48 )59.351.2423381000364847.7728244817229
Trimmed Mean ( 43 / 48 )59.51.2266574278302248.5058001118102
Trimmed Mean ( 44 / 48 )59.66071428571431.2063890484326049.4539587898519
Trimmed Mean ( 45 / 48 )59.83333333333331.180362852690350.6906272058295
Trimmed Mean ( 46 / 48 )60.01923076923081.1469976496520152.3272482619649
Trimmed Mean ( 47 / 48 )60.221.1040888754525054.5427105905035
Trimmed Mean ( 48 / 48 )60.43751.0484310508754157.645660102814
Median60.5
Midrange50
Midmean - Weighted Average at Xnp57.84
Midmean - Weighted Average at X(n+1)p58.6666666666667
Midmean - Empirical Distribution Function57.84
Midmean - Empirical Distribution Function - Averaging58.6666666666667
Midmean - Empirical Distribution Function - Interpolation58.6666666666667
Midmean - Closest Observation57.84
Midmean - True Basic - Statistics Graphics Toolkit58.6666666666667
Midmean - MS Excel (old versions)58.2077922077922
Number of observations144



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')