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Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationWed, 03 Jun 2009 04:08:31 -0600
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2009/Jun/03/t124402391794d3fgydjr601ky.htm/, Retrieved Sun, 12 May 2024 05:21:21 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=41436, Retrieved Sun, 12 May 2024 05:21:21 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact171
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [central tendency] [2009-06-03 10:08:31] [d41d8cd98f00b204e9800998ecf8427e] [Current]
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Dataseries X:
62,9
64,92
64
65,01
47
61,35
61
61,71
59,8
57,55
40
45,01
38
40,5
44,5
40,98
36,51
37,49
34,95
38,21
33,63
33,49
28
28
26,75
26,62
29,5
31
34
35
35,9
32,8
33
33,5
34,35
32,6
28,6
27,45
26,51
26,9
24
19,61
20
19,2
20,44
20,3
20,4
23,15
23,78
22
23,4
23,75
24,78
25,28
29,57
22,05
22,75
20,85
20,35
16,8
12,99
9,66
11
12,51
12,7
12,82
12,9
14,5
14,13
14
13,59
13,87




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'George Udny Yule' @ 72.249.76.132

\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 & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=41436&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]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=41436&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=41436&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'George Udny Yule' @ 72.249.76.132







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean30.77944444444441.7516340670602717.5718462110645
Geometric Mean27.5081595543625
Harmonic Mean24.5329605073631
Quadratic Mean34.1352890064747
Winsorized Mean ( 1 / 24 )30.79680555555561.7482257250412417.616034997328
Winsorized Mean ( 2 / 24 )30.81319444444441.7348076501998917.7617353952146
Winsorized Mean ( 3 / 24 )30.77527777777781.7214354767561517.8776830112566
Winsorized Mean ( 4 / 24 )30.71583333333331.7032879548681018.033259288628
Winsorized Mean ( 5 / 24 )30.69638888888891.6960807983561018.0984236827874
Winsorized Mean ( 6 / 24 )30.67472222222221.6875698672399318.1768605956396
Winsorized Mean ( 7 / 24 )30.61638888888891.6497239099590618.5584925477917
Winsorized Mean ( 8 / 24 )30.39751.5838306699764519.1923925809897
Winsorized Mean ( 9 / 24 )29.0951.2901110729680122.5523217416190
Winsorized Mean ( 10 / 24 )28.83666666666671.2345637815963323.3577779427322
Winsorized Mean ( 11 / 24 )28.81527777777781.2108178435435423.7981938665917
Winsorized Mean ( 12 / 24 )28.61194444444451.0455715099547927.3648853015147
Winsorized Mean ( 13 / 24 )28.95861111111110.96559995186439129.9902781221121
Winsorized Mean ( 14 / 24 )28.94111111111110.93808380999135830.8513064641610
Winsorized Mean ( 15 / 24 )28.64944444444440.86667433837541933.0567586645612
Winsorized Mean ( 16 / 24 )28.66944444444440.85013383575112733.723448284015
Winsorized Mean ( 17 / 24 )28.56083333333330.8300614347891734.408095758102
Winsorized Mean ( 18 / 24 )28.32833333333330.79190665994135235.772313539365
Winsorized Mean ( 19 / 24 )28.17791666666670.76728733137265936.7240739088668
Winsorized Mean ( 20 / 24 )28.04180555555560.71630330690288139.1479493188457
Winsorized Mean ( 21 / 24 )28.36263888888890.66803785025129442.4566345727563
Winsorized Mean ( 22 / 24 )28.19458333333330.64084271034428543.9961052505164
Winsorized Mean ( 23 / 24 )28.30638888888890.59596036124354447.4971000249483
Winsorized Mean ( 24 / 24 )28.31638888888890.56206009769907350.3796462421168
Trimmed Mean ( 1 / 24 )30.59214285714291.7064324036886117.9275445022113
Trimmed Mean ( 2 / 24 )30.37544117647061.6563315139226618.3389864415083
Trimmed Mean ( 3 / 24 )30.13666666666671.6045926122967918.7815065554424
Trimmed Mean ( 4 / 24 )29.89718751.5481999671653719.3109340744525
Trimmed Mean ( 5 / 24 )29.65951612903231.4865167393127419.9523593274468
Trimmed Mean ( 6 / 24 )29.41066666666671.4130468316369620.8136531700054
Trimmed Mean ( 7 / 24 )29.14913793103451.3241705112714622.0131302448698
Trimmed Mean ( 8 / 24 )28.87964285714291.2235781826714123.6026134383098
Trimmed Mean ( 9 / 24 )28.62666666666671.115369345588725.6656387230701
Trimmed Mean ( 10 / 24 )28.55461538461541.0651264259624026.8086629799037
Trimmed Mean ( 11 / 24 )28.5141.0161446144870428.0609665135056
Trimmed Mean ( 12 / 24 )28.47291666666670.95967493011094729.6693346604094
Trimmed Mean ( 13 / 24 )28.45478260869570.92861710798871130.6421046563807
Trimmed Mean ( 14 / 24 )28.39136363636360.90631660451661531.3260989535839
Trimmed Mean ( 15 / 24 )28.32404761904760.88280917498271432.0839977898986
Trimmed Mean ( 16 / 24 )28.2850.8678596572115732.5916751227723
Trimmed Mean ( 17 / 24 )28.23947368421050.85037904253581433.2081016484143
Trimmed Mean ( 18 / 24 )28.20166666666670.83041092333091433.9610979026446
Trimmed Mean ( 19 / 24 )28.18676470588240.81155412191453834.7318360473445
Trimmed Mean ( 20 / 24 )28.18781250.79022847022633335.6704593190962
Trimmed Mean ( 21 / 24 )28.20533333333330.77252143270246836.5107453843244
Trimmed Mean ( 22 / 24 )28.18607142857140.7587232277444637.1493456347228
Trimmed Mean ( 23 / 24 )28.1850.74374752746841837.8959243010012
Trimmed Mean ( 24 / 24 )28.16916666666670.73251945531532438.4551788519266
Median27.725
Midrange37.335
Midmean - Weighted Average at Xnp27.9894594594595
Midmean - Weighted Average at X(n+1)p28.2016666666667
Midmean - Empirical Distribution Function27.9894594594595
Midmean - Empirical Distribution Function - Averaging28.2016666666667
Midmean - Empirical Distribution Function - Interpolation28.2016666666667
Midmean - Closest Observation27.9894594594595
Midmean - True Basic - Statistics Graphics Toolkit28.2016666666667
Midmean - MS Excel (old versions)28.2394736842105
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 30.7794444444444 & 1.75163406706027 & 17.5718462110645 \tabularnewline
Geometric Mean & 27.5081595543625 &  &  \tabularnewline
Harmonic Mean & 24.5329605073631 &  &  \tabularnewline
Quadratic Mean & 34.1352890064747 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 30.7968055555556 & 1.74822572504124 & 17.616034997328 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 30.8131944444444 & 1.73480765019989 & 17.7617353952146 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 30.7752777777778 & 1.72143547675615 & 17.8776830112566 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 30.7158333333333 & 1.70328795486810 & 18.033259288628 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 30.6963888888889 & 1.69608079835610 & 18.0984236827874 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 30.6747222222222 & 1.68756986723993 & 18.1768605956396 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 30.6163888888889 & 1.64972390995906 & 18.5584925477917 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 30.3975 & 1.58383066997645 & 19.1923925809897 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 29.095 & 1.29011107296801 & 22.5523217416190 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 28.8366666666667 & 1.23456378159633 & 23.3577779427322 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 28.8152777777778 & 1.21081784354354 & 23.7981938665917 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 28.6119444444445 & 1.04557150995479 & 27.3648853015147 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 28.9586111111111 & 0.965599951864391 & 29.9902781221121 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 28.9411111111111 & 0.938083809991358 & 30.8513064641610 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 28.6494444444444 & 0.866674338375419 & 33.0567586645612 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 28.6694444444444 & 0.850133835751127 & 33.723448284015 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 28.5608333333333 & 0.83006143478917 & 34.408095758102 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 28.3283333333333 & 0.791906659941352 & 35.772313539365 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 28.1779166666667 & 0.767287331372659 & 36.7240739088668 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 28.0418055555556 & 0.716303306902881 & 39.1479493188457 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 28.3626388888889 & 0.668037850251294 & 42.4566345727563 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 28.1945833333333 & 0.640842710344285 & 43.9961052505164 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 28.3063888888889 & 0.595960361243544 & 47.4971000249483 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 28.3163888888889 & 0.562060097699073 & 50.3796462421168 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 30.5921428571429 & 1.70643240368861 & 17.9275445022113 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 30.3754411764706 & 1.65633151392266 & 18.3389864415083 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 30.1366666666667 & 1.60459261229679 & 18.7815065554424 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 29.8971875 & 1.54819996716537 & 19.3109340744525 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 29.6595161290323 & 1.48651673931274 & 19.9523593274468 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 29.4106666666667 & 1.41304683163696 & 20.8136531700054 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 29.1491379310345 & 1.32417051127146 & 22.0131302448698 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 28.8796428571429 & 1.22357818267141 & 23.6026134383098 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 28.6266666666667 & 1.1153693455887 & 25.6656387230701 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 28.5546153846154 & 1.06512642596240 & 26.8086629799037 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 28.514 & 1.01614461448704 & 28.0609665135056 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 28.4729166666667 & 0.959674930110947 & 29.6693346604094 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 28.4547826086957 & 0.928617107988711 & 30.6421046563807 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 28.3913636363636 & 0.906316604516615 & 31.3260989535839 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 28.3240476190476 & 0.882809174982714 & 32.0839977898986 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 28.285 & 0.86785965721157 & 32.5916751227723 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 28.2394736842105 & 0.850379042535814 & 33.2081016484143 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 28.2016666666667 & 0.830410923330914 & 33.9610979026446 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 28.1867647058824 & 0.811554121914538 & 34.7318360473445 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 28.1878125 & 0.790228470226333 & 35.6704593190962 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 28.2053333333333 & 0.772521432702468 & 36.5107453843244 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 28.1860714285714 & 0.75872322774446 & 37.1493456347228 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 28.185 & 0.743747527468418 & 37.8959243010012 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 28.1691666666667 & 0.732519455315324 & 38.4551788519266 \tabularnewline
Median & 27.725 &  &  \tabularnewline
Midrange & 37.335 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 27.9894594594595 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 28.2016666666667 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 27.9894594594595 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 28.2016666666667 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 28.2016666666667 &  &  \tabularnewline
Midmean - Closest Observation & 27.9894594594595 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 28.2016666666667 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 28.2394736842105 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=41436&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]30.7794444444444[/C][C]1.75163406706027[/C][C]17.5718462110645[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]27.5081595543625[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]24.5329605073631[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]34.1352890064747[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]30.7968055555556[/C][C]1.74822572504124[/C][C]17.616034997328[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]30.8131944444444[/C][C]1.73480765019989[/C][C]17.7617353952146[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]30.7752777777778[/C][C]1.72143547675615[/C][C]17.8776830112566[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]30.7158333333333[/C][C]1.70328795486810[/C][C]18.033259288628[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]30.6963888888889[/C][C]1.69608079835610[/C][C]18.0984236827874[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]30.6747222222222[/C][C]1.68756986723993[/C][C]18.1768605956396[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]30.6163888888889[/C][C]1.64972390995906[/C][C]18.5584925477917[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]30.3975[/C][C]1.58383066997645[/C][C]19.1923925809897[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]29.095[/C][C]1.29011107296801[/C][C]22.5523217416190[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]28.8366666666667[/C][C]1.23456378159633[/C][C]23.3577779427322[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]28.8152777777778[/C][C]1.21081784354354[/C][C]23.7981938665917[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]28.6119444444445[/C][C]1.04557150995479[/C][C]27.3648853015147[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]28.9586111111111[/C][C]0.965599951864391[/C][C]29.9902781221121[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]28.9411111111111[/C][C]0.938083809991358[/C][C]30.8513064641610[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]28.6494444444444[/C][C]0.866674338375419[/C][C]33.0567586645612[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]28.6694444444444[/C][C]0.850133835751127[/C][C]33.723448284015[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]28.5608333333333[/C][C]0.83006143478917[/C][C]34.408095758102[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]28.3283333333333[/C][C]0.791906659941352[/C][C]35.772313539365[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]28.1779166666667[/C][C]0.767287331372659[/C][C]36.7240739088668[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]28.0418055555556[/C][C]0.716303306902881[/C][C]39.1479493188457[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]28.3626388888889[/C][C]0.668037850251294[/C][C]42.4566345727563[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]28.1945833333333[/C][C]0.640842710344285[/C][C]43.9961052505164[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]28.3063888888889[/C][C]0.595960361243544[/C][C]47.4971000249483[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]28.3163888888889[/C][C]0.562060097699073[/C][C]50.3796462421168[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]30.5921428571429[/C][C]1.70643240368861[/C][C]17.9275445022113[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]30.3754411764706[/C][C]1.65633151392266[/C][C]18.3389864415083[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]30.1366666666667[/C][C]1.60459261229679[/C][C]18.7815065554424[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]29.8971875[/C][C]1.54819996716537[/C][C]19.3109340744525[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]29.6595161290323[/C][C]1.48651673931274[/C][C]19.9523593274468[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]29.4106666666667[/C][C]1.41304683163696[/C][C]20.8136531700054[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]29.1491379310345[/C][C]1.32417051127146[/C][C]22.0131302448698[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]28.8796428571429[/C][C]1.22357818267141[/C][C]23.6026134383098[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]28.6266666666667[/C][C]1.1153693455887[/C][C]25.6656387230701[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]28.5546153846154[/C][C]1.06512642596240[/C][C]26.8086629799037[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]28.514[/C][C]1.01614461448704[/C][C]28.0609665135056[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]28.4729166666667[/C][C]0.959674930110947[/C][C]29.6693346604094[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]28.4547826086957[/C][C]0.928617107988711[/C][C]30.6421046563807[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]28.3913636363636[/C][C]0.906316604516615[/C][C]31.3260989535839[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]28.3240476190476[/C][C]0.882809174982714[/C][C]32.0839977898986[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]28.285[/C][C]0.86785965721157[/C][C]32.5916751227723[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]28.2394736842105[/C][C]0.850379042535814[/C][C]33.2081016484143[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]28.2016666666667[/C][C]0.830410923330914[/C][C]33.9610979026446[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]28.1867647058824[/C][C]0.811554121914538[/C][C]34.7318360473445[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]28.1878125[/C][C]0.790228470226333[/C][C]35.6704593190962[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]28.2053333333333[/C][C]0.772521432702468[/C][C]36.5107453843244[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]28.1860714285714[/C][C]0.75872322774446[/C][C]37.1493456347228[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]28.185[/C][C]0.743747527468418[/C][C]37.8959243010012[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]28.1691666666667[/C][C]0.732519455315324[/C][C]38.4551788519266[/C][/ROW]
[ROW][C]Median[/C][C]27.725[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]37.335[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]27.9894594594595[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]28.2016666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]27.9894594594595[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]28.2016666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]28.2016666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]27.9894594594595[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]28.2016666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]28.2394736842105[/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=41436&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=41436&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 Mean30.77944444444441.7516340670602717.5718462110645
Geometric Mean27.5081595543625
Harmonic Mean24.5329605073631
Quadratic Mean34.1352890064747
Winsorized Mean ( 1 / 24 )30.79680555555561.7482257250412417.616034997328
Winsorized Mean ( 2 / 24 )30.81319444444441.7348076501998917.7617353952146
Winsorized Mean ( 3 / 24 )30.77527777777781.7214354767561517.8776830112566
Winsorized Mean ( 4 / 24 )30.71583333333331.7032879548681018.033259288628
Winsorized Mean ( 5 / 24 )30.69638888888891.6960807983561018.0984236827874
Winsorized Mean ( 6 / 24 )30.67472222222221.6875698672399318.1768605956396
Winsorized Mean ( 7 / 24 )30.61638888888891.6497239099590618.5584925477917
Winsorized Mean ( 8 / 24 )30.39751.5838306699764519.1923925809897
Winsorized Mean ( 9 / 24 )29.0951.2901110729680122.5523217416190
Winsorized Mean ( 10 / 24 )28.83666666666671.2345637815963323.3577779427322
Winsorized Mean ( 11 / 24 )28.81527777777781.2108178435435423.7981938665917
Winsorized Mean ( 12 / 24 )28.61194444444451.0455715099547927.3648853015147
Winsorized Mean ( 13 / 24 )28.95861111111110.96559995186439129.9902781221121
Winsorized Mean ( 14 / 24 )28.94111111111110.93808380999135830.8513064641610
Winsorized Mean ( 15 / 24 )28.64944444444440.86667433837541933.0567586645612
Winsorized Mean ( 16 / 24 )28.66944444444440.85013383575112733.723448284015
Winsorized Mean ( 17 / 24 )28.56083333333330.8300614347891734.408095758102
Winsorized Mean ( 18 / 24 )28.32833333333330.79190665994135235.772313539365
Winsorized Mean ( 19 / 24 )28.17791666666670.76728733137265936.7240739088668
Winsorized Mean ( 20 / 24 )28.04180555555560.71630330690288139.1479493188457
Winsorized Mean ( 21 / 24 )28.36263888888890.66803785025129442.4566345727563
Winsorized Mean ( 22 / 24 )28.19458333333330.64084271034428543.9961052505164
Winsorized Mean ( 23 / 24 )28.30638888888890.59596036124354447.4971000249483
Winsorized Mean ( 24 / 24 )28.31638888888890.56206009769907350.3796462421168
Trimmed Mean ( 1 / 24 )30.59214285714291.7064324036886117.9275445022113
Trimmed Mean ( 2 / 24 )30.37544117647061.6563315139226618.3389864415083
Trimmed Mean ( 3 / 24 )30.13666666666671.6045926122967918.7815065554424
Trimmed Mean ( 4 / 24 )29.89718751.5481999671653719.3109340744525
Trimmed Mean ( 5 / 24 )29.65951612903231.4865167393127419.9523593274468
Trimmed Mean ( 6 / 24 )29.41066666666671.4130468316369620.8136531700054
Trimmed Mean ( 7 / 24 )29.14913793103451.3241705112714622.0131302448698
Trimmed Mean ( 8 / 24 )28.87964285714291.2235781826714123.6026134383098
Trimmed Mean ( 9 / 24 )28.62666666666671.115369345588725.6656387230701
Trimmed Mean ( 10 / 24 )28.55461538461541.0651264259624026.8086629799037
Trimmed Mean ( 11 / 24 )28.5141.0161446144870428.0609665135056
Trimmed Mean ( 12 / 24 )28.47291666666670.95967493011094729.6693346604094
Trimmed Mean ( 13 / 24 )28.45478260869570.92861710798871130.6421046563807
Trimmed Mean ( 14 / 24 )28.39136363636360.90631660451661531.3260989535839
Trimmed Mean ( 15 / 24 )28.32404761904760.88280917498271432.0839977898986
Trimmed Mean ( 16 / 24 )28.2850.8678596572115732.5916751227723
Trimmed Mean ( 17 / 24 )28.23947368421050.85037904253581433.2081016484143
Trimmed Mean ( 18 / 24 )28.20166666666670.83041092333091433.9610979026446
Trimmed Mean ( 19 / 24 )28.18676470588240.81155412191453834.7318360473445
Trimmed Mean ( 20 / 24 )28.18781250.79022847022633335.6704593190962
Trimmed Mean ( 21 / 24 )28.20533333333330.77252143270246836.5107453843244
Trimmed Mean ( 22 / 24 )28.18607142857140.7587232277444637.1493456347228
Trimmed Mean ( 23 / 24 )28.1850.74374752746841837.8959243010012
Trimmed Mean ( 24 / 24 )28.16916666666670.73251945531532438.4551788519266
Median27.725
Midrange37.335
Midmean - Weighted Average at Xnp27.9894594594595
Midmean - Weighted Average at X(n+1)p28.2016666666667
Midmean - Empirical Distribution Function27.9894594594595
Midmean - Empirical Distribution Function - Averaging28.2016666666667
Midmean - Empirical Distribution Function - Interpolation28.2016666666667
Midmean - Closest Observation27.9894594594595
Midmean - True Basic - Statistics Graphics Toolkit28.2016666666667
Midmean - MS Excel (old versions)28.2394736842105
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')