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Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationFri, 10 Oct 2014 15:27:37 +0100
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2014/Oct/10/t141295129620n09md58922ggm.htm/, Retrieved Mon, 13 May 2024 14:43:00 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=240329, Retrieved Mon, 13 May 2024 14:43:00 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact60
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [] [2014-10-10 14:27:37] [72d1b0bbc256d1ec09d716526c8fc98d] [Current]
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Dataseries X:
37,3
39,5
40,6
41,4
41,3
43,5
44
44,9
46,4
47,4
48,7
49,7
51,1
53,2
56,2
58,1
60,6
64,1
67,4
68
70,9
72,8
74,9
76,1
77
78,1
80
79,7
82,7
84,3
83,5
85,9
87
88,6
90,6
91,3
91,6
93,2
95
95,2
97,4
98,6
99,6
100,6
101,3
102,8
103,2
103
105,4
104,7
105,2
105,2
102,8
100,3
99,8
99,4
100,6
100,2
100,4
98,8
96,9
96,3
96,1
93,5
92,1
91,7
87,9
86,4
84,9
81,7
82,6
83,1




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gertrude Mary Cox' @ cox.wessa.net

\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 & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=240329&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]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=240329&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=240329&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'Gertrude Mary Cox' @ cox.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean80.33752.4868263532126432.3052310814605
Geometric Mean77.0430108273797
Harmonic Mean73.206604085817
Quadratic Mean83.0252948403878
Winsorized Mean ( 1 / 24 )80.36527777777782.479162107718432.4163061090583
Winsorized Mean ( 2 / 24 )80.39583333333332.4721511777434232.5205974687676
Winsorized Mean ( 3 / 24 )80.40416666666672.4626636385815832.6492686240241
Winsorized Mean ( 4 / 24 )80.32638888888892.4501516936331932.7842513170184
Winsorized Mean ( 5 / 24 )80.45833333333332.4162973248605733.2981924473952
Winsorized Mean ( 6 / 24 )80.48333333333332.4051742280534833.4625792986602
Winsorized Mean ( 7 / 24 )80.57083333333332.3866169945751633.7594316626726
Winsorized Mean ( 8 / 24 )80.57083333333332.3304832001970434.5725870611387
Winsorized Mean ( 9 / 24 )80.60833333333332.2939796266284835.1390798757029
Winsorized Mean ( 10 / 24 )80.78888888888892.2574962549214135.7869425974758
Winsorized Mean ( 11 / 24 )80.91111111111112.2233234751732536.3919654582903
Winsorized Mean ( 12 / 24 )81.12777777777782.1755085227683737.2914088493395
Winsorized Mean ( 13 / 24 )81.48888888888892.1004215199910438.7964454340749
Winsorized Mean ( 14 / 24 )81.99444444444441.9817722669448341.3743020891346
Winsorized Mean ( 15 / 24 )82.34861111111111.9046921235482843.2346047390076
Winsorized Mean ( 16 / 24 )82.85972222222221.80077324258646.0134126067041
Winsorized Mean ( 17 / 24 )83.54444444444451.6413212368511850.9007271512075
Winsorized Mean ( 18 / 24 )84.31944444444441.5001990463773556.2055046282406
Winsorized Mean ( 19 / 24 )84.16111111111111.4332085265505858.7221674669131
Winsorized Mean ( 20 / 24 )84.82777777777781.2896470235354665.7759652290204
Winsorized Mean ( 21 / 24 )85.20694444444441.1834462790588371.9989964497652
Winsorized Mean ( 22 / 24 )85.78751.0824028822988179.2565332215345
Winsorized Mean ( 23 / 24 )85.88333333333330.99020634576776486.7327640348972
Winsorized Mean ( 24 / 24 )86.11666666666670.93997885635328991.6155359076502
Trimmed Mean ( 1 / 24 )80.59428571428572.4557870013334632.8181090911078
Trimmed Mean ( 2 / 24 )80.83676470588242.4267593876609133.3105808169135
Trimmed Mean ( 3 / 24 )81.07727272727272.3953449371826333.8478485785996
Trimmed Mean ( 4 / 24 )81.32968752.360718001493834.4512506146591
Trimmed Mean ( 5 / 24 )81.62096774193552.3220565852885135.1502923137398
Trimmed Mean ( 6 / 24 )81.92.2846453816235935.8480141639301
Trimmed Mean ( 7 / 24 )82.19310344827592.2407433599176236.6811768444993
Trimmed Mean ( 8 / 24 )82.49107142857142.190505303719137.6584668790875
Trimmed Mean ( 9 / 24 )82.81111111111112.1408258538691238.6818530621939
Trimmed Mean ( 10 / 24 )83.152.0860603569818739.8598246314896
Trimmed Mean ( 11 / 24 )83.492.0246929724412741.235881754127
Trimmed Mean ( 12 / 24 )83.84166666666671.9535651927117642.9172606982648
Trimmed Mean ( 13 / 24 )84.1956521739131.8729164436890844.9543023970001
Trimmed Mean ( 14 / 24 )84.53636363636361.7866077169724747.3166900787916
Trimmed Mean ( 15 / 24 )84.8476190476191.7038599278800849.7972971012853
Trimmed Mean ( 16 / 24 )85.14751.6137509558280352.7637177796804
Trimmed Mean ( 17 / 24 )85.41842105263161.5213130477433356.1478264972081
Trimmed Mean ( 18 / 24 )85.63888888888891.4416551212187259.4031732197457
Trimmed Mean ( 19 / 24 )85.79411764705881.3737022148128262.4546693758873
Trimmed Mean ( 20 / 24 )85.98751.295446040384766.3767515738943
Trimmed Mean ( 21 / 24 )86.12666666666671.2305772249287869.9888352570896
Trimmed Mean ( 22 / 24 )86.23928571428571.1706320285140573.6689955628108
Trimmed Mean ( 23 / 24 )86.29615384615381.1163881427205877.2994181359314
Trimmed Mean ( 24 / 24 )86.351.0656018235611381.0340204856511
Median86.15
Midrange71.35
Midmean - Weighted Average at Xnp85.0567567567568
Midmean - Weighted Average at X(n+1)p85.6388888888889
Midmean - Empirical Distribution Function85.0567567567568
Midmean - Empirical Distribution Function - Averaging85.6388888888889
Midmean - Empirical Distribution Function - Interpolation85.6388888888889
Midmean - Closest Observation85.0567567567568
Midmean - True Basic - Statistics Graphics Toolkit85.6388888888889
Midmean - MS Excel (old versions)85.4184210526316
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 80.3375 & 2.48682635321264 & 32.3052310814605 \tabularnewline
Geometric Mean & 77.0430108273797 &  &  \tabularnewline
Harmonic Mean & 73.206604085817 &  &  \tabularnewline
Quadratic Mean & 83.0252948403878 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 80.3652777777778 & 2.4791621077184 & 32.4163061090583 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 80.3958333333333 & 2.47215117774342 & 32.5205974687676 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 80.4041666666667 & 2.46266363858158 & 32.6492686240241 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 80.3263888888889 & 2.45015169363319 & 32.7842513170184 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 80.4583333333333 & 2.41629732486057 & 33.2981924473952 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 80.4833333333333 & 2.40517422805348 & 33.4625792986602 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 80.5708333333333 & 2.38661699457516 & 33.7594316626726 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 80.5708333333333 & 2.33048320019704 & 34.5725870611387 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 80.6083333333333 & 2.29397962662848 & 35.1390798757029 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 80.7888888888889 & 2.25749625492141 & 35.7869425974758 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 80.9111111111111 & 2.22332347517325 & 36.3919654582903 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 81.1277777777778 & 2.17550852276837 & 37.2914088493395 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 81.4888888888889 & 2.10042151999104 & 38.7964454340749 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 81.9944444444444 & 1.98177226694483 & 41.3743020891346 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 82.3486111111111 & 1.90469212354828 & 43.2346047390076 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 82.8597222222222 & 1.800773242586 & 46.0134126067041 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 83.5444444444445 & 1.64132123685118 & 50.9007271512075 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 84.3194444444444 & 1.50019904637735 & 56.2055046282406 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 84.1611111111111 & 1.43320852655058 & 58.7221674669131 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 84.8277777777778 & 1.28964702353546 & 65.7759652290204 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 85.2069444444444 & 1.18344627905883 & 71.9989964497652 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 85.7875 & 1.08240288229881 & 79.2565332215345 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 85.8833333333333 & 0.990206345767764 & 86.7327640348972 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 86.1166666666667 & 0.939978856353289 & 91.6155359076502 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 80.5942857142857 & 2.45578700133346 & 32.8181090911078 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 80.8367647058824 & 2.42675938766091 & 33.3105808169135 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 81.0772727272727 & 2.39534493718263 & 33.8478485785996 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 81.3296875 & 2.3607180014938 & 34.4512506146591 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 81.6209677419355 & 2.32205658528851 & 35.1502923137398 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 81.9 & 2.28464538162359 & 35.8480141639301 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 82.1931034482759 & 2.24074335991762 & 36.6811768444993 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 82.4910714285714 & 2.1905053037191 & 37.6584668790875 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 82.8111111111111 & 2.14082585386912 & 38.6818530621939 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 83.15 & 2.08606035698187 & 39.8598246314896 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 83.49 & 2.02469297244127 & 41.235881754127 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 83.8416666666667 & 1.95356519271176 & 42.9172606982648 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 84.195652173913 & 1.87291644368908 & 44.9543023970001 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 84.5363636363636 & 1.78660771697247 & 47.3166900787916 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 84.847619047619 & 1.70385992788008 & 49.7972971012853 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 85.1475 & 1.61375095582803 & 52.7637177796804 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 85.4184210526316 & 1.52131304774333 & 56.1478264972081 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 85.6388888888889 & 1.44165512121872 & 59.4031732197457 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 85.7941176470588 & 1.37370221481282 & 62.4546693758873 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 85.9875 & 1.2954460403847 & 66.3767515738943 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 86.1266666666667 & 1.23057722492878 & 69.9888352570896 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 86.2392857142857 & 1.17063202851405 & 73.6689955628108 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 86.2961538461538 & 1.11638814272058 & 77.2994181359314 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 86.35 & 1.06560182356113 & 81.0340204856511 \tabularnewline
Median & 86.15 &  &  \tabularnewline
Midrange & 71.35 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 85.0567567567568 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 85.6388888888889 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 85.0567567567568 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 85.6388888888889 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 85.6388888888889 &  &  \tabularnewline
Midmean - Closest Observation & 85.0567567567568 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 85.6388888888889 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 85.4184210526316 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=240329&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]80.3375[/C][C]2.48682635321264[/C][C]32.3052310814605[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]77.0430108273797[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]73.206604085817[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]83.0252948403878[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]80.3652777777778[/C][C]2.4791621077184[/C][C]32.4163061090583[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]80.3958333333333[/C][C]2.47215117774342[/C][C]32.5205974687676[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]80.4041666666667[/C][C]2.46266363858158[/C][C]32.6492686240241[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]80.3263888888889[/C][C]2.45015169363319[/C][C]32.7842513170184[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]80.4583333333333[/C][C]2.41629732486057[/C][C]33.2981924473952[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]80.4833333333333[/C][C]2.40517422805348[/C][C]33.4625792986602[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]80.5708333333333[/C][C]2.38661699457516[/C][C]33.7594316626726[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]80.5708333333333[/C][C]2.33048320019704[/C][C]34.5725870611387[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]80.6083333333333[/C][C]2.29397962662848[/C][C]35.1390798757029[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]80.7888888888889[/C][C]2.25749625492141[/C][C]35.7869425974758[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]80.9111111111111[/C][C]2.22332347517325[/C][C]36.3919654582903[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]81.1277777777778[/C][C]2.17550852276837[/C][C]37.2914088493395[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]81.4888888888889[/C][C]2.10042151999104[/C][C]38.7964454340749[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]81.9944444444444[/C][C]1.98177226694483[/C][C]41.3743020891346[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]82.3486111111111[/C][C]1.90469212354828[/C][C]43.2346047390076[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]82.8597222222222[/C][C]1.800773242586[/C][C]46.0134126067041[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]83.5444444444445[/C][C]1.64132123685118[/C][C]50.9007271512075[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]84.3194444444444[/C][C]1.50019904637735[/C][C]56.2055046282406[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]84.1611111111111[/C][C]1.43320852655058[/C][C]58.7221674669131[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]84.8277777777778[/C][C]1.28964702353546[/C][C]65.7759652290204[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]85.2069444444444[/C][C]1.18344627905883[/C][C]71.9989964497652[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]85.7875[/C][C]1.08240288229881[/C][C]79.2565332215345[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]85.8833333333333[/C][C]0.990206345767764[/C][C]86.7327640348972[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]86.1166666666667[/C][C]0.939978856353289[/C][C]91.6155359076502[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]80.5942857142857[/C][C]2.45578700133346[/C][C]32.8181090911078[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]80.8367647058824[/C][C]2.42675938766091[/C][C]33.3105808169135[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]81.0772727272727[/C][C]2.39534493718263[/C][C]33.8478485785996[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]81.3296875[/C][C]2.3607180014938[/C][C]34.4512506146591[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]81.6209677419355[/C][C]2.32205658528851[/C][C]35.1502923137398[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]81.9[/C][C]2.28464538162359[/C][C]35.8480141639301[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]82.1931034482759[/C][C]2.24074335991762[/C][C]36.6811768444993[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]82.4910714285714[/C][C]2.1905053037191[/C][C]37.6584668790875[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]82.8111111111111[/C][C]2.14082585386912[/C][C]38.6818530621939[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]83.15[/C][C]2.08606035698187[/C][C]39.8598246314896[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]83.49[/C][C]2.02469297244127[/C][C]41.235881754127[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]83.8416666666667[/C][C]1.95356519271176[/C][C]42.9172606982648[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]84.195652173913[/C][C]1.87291644368908[/C][C]44.9543023970001[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]84.5363636363636[/C][C]1.78660771697247[/C][C]47.3166900787916[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]84.847619047619[/C][C]1.70385992788008[/C][C]49.7972971012853[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]85.1475[/C][C]1.61375095582803[/C][C]52.7637177796804[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]85.4184210526316[/C][C]1.52131304774333[/C][C]56.1478264972081[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]85.6388888888889[/C][C]1.44165512121872[/C][C]59.4031732197457[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]85.7941176470588[/C][C]1.37370221481282[/C][C]62.4546693758873[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]85.9875[/C][C]1.2954460403847[/C][C]66.3767515738943[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]86.1266666666667[/C][C]1.23057722492878[/C][C]69.9888352570896[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]86.2392857142857[/C][C]1.17063202851405[/C][C]73.6689955628108[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]86.2961538461538[/C][C]1.11638814272058[/C][C]77.2994181359314[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]86.35[/C][C]1.06560182356113[/C][C]81.0340204856511[/C][/ROW]
[ROW][C]Median[/C][C]86.15[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]71.35[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]85.0567567567568[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]85.6388888888889[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]85.0567567567568[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]85.6388888888889[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]85.6388888888889[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]85.0567567567568[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]85.6388888888889[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]85.4184210526316[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]72[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=240329&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=240329&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 Mean80.33752.4868263532126432.3052310814605
Geometric Mean77.0430108273797
Harmonic Mean73.206604085817
Quadratic Mean83.0252948403878
Winsorized Mean ( 1 / 24 )80.36527777777782.479162107718432.4163061090583
Winsorized Mean ( 2 / 24 )80.39583333333332.4721511777434232.5205974687676
Winsorized Mean ( 3 / 24 )80.40416666666672.4626636385815832.6492686240241
Winsorized Mean ( 4 / 24 )80.32638888888892.4501516936331932.7842513170184
Winsorized Mean ( 5 / 24 )80.45833333333332.4162973248605733.2981924473952
Winsorized Mean ( 6 / 24 )80.48333333333332.4051742280534833.4625792986602
Winsorized Mean ( 7 / 24 )80.57083333333332.3866169945751633.7594316626726
Winsorized Mean ( 8 / 24 )80.57083333333332.3304832001970434.5725870611387
Winsorized Mean ( 9 / 24 )80.60833333333332.2939796266284835.1390798757029
Winsorized Mean ( 10 / 24 )80.78888888888892.2574962549214135.7869425974758
Winsorized Mean ( 11 / 24 )80.91111111111112.2233234751732536.3919654582903
Winsorized Mean ( 12 / 24 )81.12777777777782.1755085227683737.2914088493395
Winsorized Mean ( 13 / 24 )81.48888888888892.1004215199910438.7964454340749
Winsorized Mean ( 14 / 24 )81.99444444444441.9817722669448341.3743020891346
Winsorized Mean ( 15 / 24 )82.34861111111111.9046921235482843.2346047390076
Winsorized Mean ( 16 / 24 )82.85972222222221.80077324258646.0134126067041
Winsorized Mean ( 17 / 24 )83.54444444444451.6413212368511850.9007271512075
Winsorized Mean ( 18 / 24 )84.31944444444441.5001990463773556.2055046282406
Winsorized Mean ( 19 / 24 )84.16111111111111.4332085265505858.7221674669131
Winsorized Mean ( 20 / 24 )84.82777777777781.2896470235354665.7759652290204
Winsorized Mean ( 21 / 24 )85.20694444444441.1834462790588371.9989964497652
Winsorized Mean ( 22 / 24 )85.78751.0824028822988179.2565332215345
Winsorized Mean ( 23 / 24 )85.88333333333330.99020634576776486.7327640348972
Winsorized Mean ( 24 / 24 )86.11666666666670.93997885635328991.6155359076502
Trimmed Mean ( 1 / 24 )80.59428571428572.4557870013334632.8181090911078
Trimmed Mean ( 2 / 24 )80.83676470588242.4267593876609133.3105808169135
Trimmed Mean ( 3 / 24 )81.07727272727272.3953449371826333.8478485785996
Trimmed Mean ( 4 / 24 )81.32968752.360718001493834.4512506146591
Trimmed Mean ( 5 / 24 )81.62096774193552.3220565852885135.1502923137398
Trimmed Mean ( 6 / 24 )81.92.2846453816235935.8480141639301
Trimmed Mean ( 7 / 24 )82.19310344827592.2407433599176236.6811768444993
Trimmed Mean ( 8 / 24 )82.49107142857142.190505303719137.6584668790875
Trimmed Mean ( 9 / 24 )82.81111111111112.1408258538691238.6818530621939
Trimmed Mean ( 10 / 24 )83.152.0860603569818739.8598246314896
Trimmed Mean ( 11 / 24 )83.492.0246929724412741.235881754127
Trimmed Mean ( 12 / 24 )83.84166666666671.9535651927117642.9172606982648
Trimmed Mean ( 13 / 24 )84.1956521739131.8729164436890844.9543023970001
Trimmed Mean ( 14 / 24 )84.53636363636361.7866077169724747.3166900787916
Trimmed Mean ( 15 / 24 )84.8476190476191.7038599278800849.7972971012853
Trimmed Mean ( 16 / 24 )85.14751.6137509558280352.7637177796804
Trimmed Mean ( 17 / 24 )85.41842105263161.5213130477433356.1478264972081
Trimmed Mean ( 18 / 24 )85.63888888888891.4416551212187259.4031732197457
Trimmed Mean ( 19 / 24 )85.79411764705881.3737022148128262.4546693758873
Trimmed Mean ( 20 / 24 )85.98751.295446040384766.3767515738943
Trimmed Mean ( 21 / 24 )86.12666666666671.2305772249287869.9888352570896
Trimmed Mean ( 22 / 24 )86.23928571428571.1706320285140573.6689955628108
Trimmed Mean ( 23 / 24 )86.29615384615381.1163881427205877.2994181359314
Trimmed Mean ( 24 / 24 )86.351.0656018235611381.0340204856511
Median86.15
Midrange71.35
Midmean - Weighted Average at Xnp85.0567567567568
Midmean - Weighted Average at X(n+1)p85.6388888888889
Midmean - Empirical Distribution Function85.0567567567568
Midmean - Empirical Distribution Function - Averaging85.6388888888889
Midmean - Empirical Distribution Function - Interpolation85.6388888888889
Midmean - Closest Observation85.0567567567568
Midmean - True Basic - Statistics Graphics Toolkit85.6388888888889
Midmean - MS Excel (old versions)85.4184210526316
Number of observations72



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')