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Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationTue, 05 Mar 2013 11:53:34 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2013/Mar/05/t1362502461a9yv2ia0k4uir4x.htm/, Retrieved Sat, 04 May 2024 17:59:09 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=207420, Retrieved Sat, 04 May 2024 17:59:09 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact67
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [central tendency ...] [2013-03-05 16:53:34] [ee59fc3ebc5330cd5b5b7eda83654419] [Current]
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Dataseries X:
65
65,3
62,9
63,5
62,1
59,3
61,6
61,5
60,1
59,5
62,7
65,5
63,8
63,8
62,7
62,3
62,4
64,8
66,4
65,1
67,4
68,8
68,6
71,5
75
84,3
84
79,1
78,8
82,7
85,3
84,5
80,8
70,1
68,2
68,1
72,3
73,1
71,5
74,1
80,3
80,6
81,4
87,4
89,3
93,2
92,8
96,8
100,3
95,6
89
87,4
86,7
92,8
98,6
100,8
105,5
107,8
113,7
120,3
126,5
134,8
134,5
133,1
128,8
127,1
129,1
128,4
126,5
117,1
114,2
109,1




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=207420&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=207420&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=207420&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 Mean85.80555555555562.6978037558723831.8057069083622
Geometric Mean83.0505773142718
Harmonic Mean80.5853985513846
Quadratic Mean88.7656558961103
Winsorized Mean ( 1 / 24 )85.80416666666672.6963579138550531.8222466779235
Winsorized Mean ( 2 / 24 )85.78194444444442.6843160991478531.9567224112229
Winsorized Mean ( 3 / 24 )85.67361111111112.6365842780284732.4941674821691
Winsorized Mean ( 4 / 24 )85.66252.6320110466796132.5464059537541
Winsorized Mean ( 5 / 24 )85.66944444444442.6211816545955932.6835205390075
Winsorized Mean ( 6 / 24 )85.57777777777782.5944250919982132.985256749836
Winsorized Mean ( 7 / 24 )85.52916666666672.5800990184168733.1495675383602
Winsorized Mean ( 8 / 24 )85.56252.5759112199505833.2164009913515
Winsorized Mean ( 9 / 24 )84.78752.4084910579961835.2035768281164
Winsorized Mean ( 10 / 24 )84.37083333333332.3144350699208436.4541803007759
Winsorized Mean ( 11 / 24 )84.01944444444442.2158128177324237.9181146403995
Winsorized Mean ( 12 / 24 )83.98611111111112.1933677109228838.2909398605914
Winsorized Mean ( 13 / 24 )83.15555555555562.0395520704887940.7714795610132
Winsorized Mean ( 14 / 24 )83.09722222222221.9688417710654842.2061454828096
Winsorized Mean ( 15 / 24 )82.65972222222221.8799937773785643.9680828824243
Winsorized Mean ( 16 / 24 )81.63751.7046383807125947.8913891202386
Winsorized Mean ( 17 / 24 )81.56666666666671.6795721006597348.5639566379004
Winsorized Mean ( 18 / 24 )81.19166666666671.6068962662003550.527011839197
Winsorized Mean ( 19 / 24 )80.95416666666671.5028193867377853.8681942627825
Winsorized Mean ( 20 / 24 )80.89861111111111.4160858973259657.1283219922427
Winsorized Mean ( 21 / 24 )80.40277777777781.2884067939114262.4048073618784
Winsorized Mean ( 22 / 24 )80.31111111111111.2672635046127863.3736478789002
Winsorized Mean ( 23 / 24 )80.43888888888891.2501417064521564.343816763918
Winsorized Mean ( 24 / 24 )79.33888888888891.0839950228339573.1911929645845
Trimmed Mean ( 1 / 24 )85.48428571428572.6569044673667532.1743919528311
Trimmed Mean ( 2 / 24 )85.14558823529412.6089149802390232.6363982269339
Trimmed Mean ( 3 / 24 )84.79848484848482.5581931017876233.1478045145338
Trimmed Mean ( 4 / 24 )84.47031252.5179383018852333.5474115615761
Trimmed Mean ( 5 / 24 )84.12419354838712.4696643745922134.0630064610612
Trimmed Mean ( 6 / 24 )83.75333333333332.413103900196834.7077195169685
Trimmed Mean ( 7 / 24 )83.37586206896552.3505689292716535.4705029198188
Trimmed Mean ( 8 / 24 )82.98035714285712.2762030066650536.4556047504896
Trimmed Mean ( 9 / 24 )82.552.1832965253670837.8097977259965
Trimmed Mean ( 10 / 24 )82.20576923076922.1109218488011738.9430661667818
Trimmed Mean ( 11 / 24 )81.8942.042618187822840.0926617065375
Trimmed Mean ( 12 / 24 )81.60416666666671.979063640468941.2337253830464
Trimmed Mean ( 13 / 24 )81.29347826086961.9014980165633442.7523339770791
Trimmed Mean ( 14 / 24 )81.05909090909091.8396109013339644.0631716469566
Trimmed Mean ( 15 / 24 )80.80952380952381.7742506213632245.5457210139991
Trimmed Mean ( 16 / 24 )80.58751.709562800235447.1392451853206
Trimmed Mean ( 17 / 24 )80.46315789473681.6676719535637648.2487924095563
Trimmed Mean ( 18 / 24 )80.33333333333331.6149696542433849.7429367308885
Trimmed Mean ( 19 / 24 )80.23235294117651.5604841825298251.4150376142267
Trimmed Mean ( 20 / 24 )80.1468751.5114281350962453.0272482951344
Trimmed Mean ( 21 / 24 )80.05666666666671.4639788590061254.6843051552099
Trimmed Mean ( 22 / 24 )80.01428571428571.43134519078355.9014598501671
Trimmed Mean ( 23 / 24 )79.97692307692311.3843999832452657.7700982698976
Trimmed Mean ( 24 / 24 )79.91666666666671.3131258572232260.8598682502995
Median80.7
Midrange97.05
Midmean - Weighted Average at Xnp79.927027027027
Midmean - Weighted Average at X(n+1)p80.3333333333333
Midmean - Empirical Distribution Function79.927027027027
Midmean - Empirical Distribution Function - Averaging80.3333333333333
Midmean - Empirical Distribution Function - Interpolation80.3333333333333
Midmean - Closest Observation79.927027027027
Midmean - True Basic - Statistics Graphics Toolkit80.3333333333333
Midmean - MS Excel (old versions)80.4631578947369
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 85.8055555555556 & 2.69780375587238 & 31.8057069083622 \tabularnewline
Geometric Mean & 83.0505773142718 &  &  \tabularnewline
Harmonic Mean & 80.5853985513846 &  &  \tabularnewline
Quadratic Mean & 88.7656558961103 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 85.8041666666667 & 2.69635791385505 & 31.8222466779235 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 85.7819444444444 & 2.68431609914785 & 31.9567224112229 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 85.6736111111111 & 2.63658427802847 & 32.4941674821691 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 85.6625 & 2.63201104667961 & 32.5464059537541 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 85.6694444444444 & 2.62118165459559 & 32.6835205390075 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 85.5777777777778 & 2.59442509199821 & 32.985256749836 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 85.5291666666667 & 2.58009901841687 & 33.1495675383602 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 85.5625 & 2.57591121995058 & 33.2164009913515 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 84.7875 & 2.40849105799618 & 35.2035768281164 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 84.3708333333333 & 2.31443506992084 & 36.4541803007759 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 84.0194444444444 & 2.21581281773242 & 37.9181146403995 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 83.9861111111111 & 2.19336771092288 & 38.2909398605914 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 83.1555555555556 & 2.03955207048879 & 40.7714795610132 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 83.0972222222222 & 1.96884177106548 & 42.2061454828096 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 82.6597222222222 & 1.87999377737856 & 43.9680828824243 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 81.6375 & 1.70463838071259 & 47.8913891202386 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 81.5666666666667 & 1.67957210065973 & 48.5639566379004 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 81.1916666666667 & 1.60689626620035 & 50.527011839197 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 80.9541666666667 & 1.50281938673778 & 53.8681942627825 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 80.8986111111111 & 1.41608589732596 & 57.1283219922427 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 80.4027777777778 & 1.28840679391142 & 62.4048073618784 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 80.3111111111111 & 1.26726350461278 & 63.3736478789002 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 80.4388888888889 & 1.25014170645215 & 64.343816763918 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 79.3388888888889 & 1.08399502283395 & 73.1911929645845 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 85.4842857142857 & 2.65690446736675 & 32.1743919528311 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 85.1455882352941 & 2.60891498023902 & 32.6363982269339 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 84.7984848484848 & 2.55819310178762 & 33.1478045145338 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 84.4703125 & 2.51793830188523 & 33.5474115615761 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 84.1241935483871 & 2.46966437459221 & 34.0630064610612 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 83.7533333333333 & 2.4131039001968 & 34.7077195169685 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 83.3758620689655 & 2.35056892927165 & 35.4705029198188 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 82.9803571428571 & 2.27620300666505 & 36.4556047504896 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 82.55 & 2.18329652536708 & 37.8097977259965 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 82.2057692307692 & 2.11092184880117 & 38.9430661667818 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 81.894 & 2.0426181878228 & 40.0926617065375 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 81.6041666666667 & 1.9790636404689 & 41.2337253830464 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 81.2934782608696 & 1.90149801656334 & 42.7523339770791 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 81.0590909090909 & 1.83961090133396 & 44.0631716469566 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 80.8095238095238 & 1.77425062136322 & 45.5457210139991 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 80.5875 & 1.7095628002354 & 47.1392451853206 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 80.4631578947368 & 1.66767195356376 & 48.2487924095563 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 80.3333333333333 & 1.61496965424338 & 49.7429367308885 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 80.2323529411765 & 1.56048418252982 & 51.4150376142267 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 80.146875 & 1.51142813509624 & 53.0272482951344 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 80.0566666666667 & 1.46397885900612 & 54.6843051552099 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 80.0142857142857 & 1.431345190783 & 55.9014598501671 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 79.9769230769231 & 1.38439998324526 & 57.7700982698976 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 79.9166666666667 & 1.31312585722322 & 60.8598682502995 \tabularnewline
Median & 80.7 &  &  \tabularnewline
Midrange & 97.05 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 79.927027027027 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 80.3333333333333 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 79.927027027027 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 80.3333333333333 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 80.3333333333333 &  &  \tabularnewline
Midmean - Closest Observation & 79.927027027027 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 80.3333333333333 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 80.4631578947369 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=207420&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]85.8055555555556[/C][C]2.69780375587238[/C][C]31.8057069083622[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]83.0505773142718[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]80.5853985513846[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]88.7656558961103[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]85.8041666666667[/C][C]2.69635791385505[/C][C]31.8222466779235[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]85.7819444444444[/C][C]2.68431609914785[/C][C]31.9567224112229[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]85.6736111111111[/C][C]2.63658427802847[/C][C]32.4941674821691[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]85.6625[/C][C]2.63201104667961[/C][C]32.5464059537541[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]85.6694444444444[/C][C]2.62118165459559[/C][C]32.6835205390075[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]85.5777777777778[/C][C]2.59442509199821[/C][C]32.985256749836[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]85.5291666666667[/C][C]2.58009901841687[/C][C]33.1495675383602[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]85.5625[/C][C]2.57591121995058[/C][C]33.2164009913515[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]84.7875[/C][C]2.40849105799618[/C][C]35.2035768281164[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]84.3708333333333[/C][C]2.31443506992084[/C][C]36.4541803007759[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]84.0194444444444[/C][C]2.21581281773242[/C][C]37.9181146403995[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]83.9861111111111[/C][C]2.19336771092288[/C][C]38.2909398605914[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]83.1555555555556[/C][C]2.03955207048879[/C][C]40.7714795610132[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]83.0972222222222[/C][C]1.96884177106548[/C][C]42.2061454828096[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]82.6597222222222[/C][C]1.87999377737856[/C][C]43.9680828824243[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]81.6375[/C][C]1.70463838071259[/C][C]47.8913891202386[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]81.5666666666667[/C][C]1.67957210065973[/C][C]48.5639566379004[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]81.1916666666667[/C][C]1.60689626620035[/C][C]50.527011839197[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]80.9541666666667[/C][C]1.50281938673778[/C][C]53.8681942627825[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]80.8986111111111[/C][C]1.41608589732596[/C][C]57.1283219922427[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]80.4027777777778[/C][C]1.28840679391142[/C][C]62.4048073618784[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]80.3111111111111[/C][C]1.26726350461278[/C][C]63.3736478789002[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]80.4388888888889[/C][C]1.25014170645215[/C][C]64.343816763918[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]79.3388888888889[/C][C]1.08399502283395[/C][C]73.1911929645845[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]85.4842857142857[/C][C]2.65690446736675[/C][C]32.1743919528311[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]85.1455882352941[/C][C]2.60891498023902[/C][C]32.6363982269339[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]84.7984848484848[/C][C]2.55819310178762[/C][C]33.1478045145338[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]84.4703125[/C][C]2.51793830188523[/C][C]33.5474115615761[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]84.1241935483871[/C][C]2.46966437459221[/C][C]34.0630064610612[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]83.7533333333333[/C][C]2.4131039001968[/C][C]34.7077195169685[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]83.3758620689655[/C][C]2.35056892927165[/C][C]35.4705029198188[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]82.9803571428571[/C][C]2.27620300666505[/C][C]36.4556047504896[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]82.55[/C][C]2.18329652536708[/C][C]37.8097977259965[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]82.2057692307692[/C][C]2.11092184880117[/C][C]38.9430661667818[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]81.894[/C][C]2.0426181878228[/C][C]40.0926617065375[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]81.6041666666667[/C][C]1.9790636404689[/C][C]41.2337253830464[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]81.2934782608696[/C][C]1.90149801656334[/C][C]42.7523339770791[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]81.0590909090909[/C][C]1.83961090133396[/C][C]44.0631716469566[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]80.8095238095238[/C][C]1.77425062136322[/C][C]45.5457210139991[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]80.5875[/C][C]1.7095628002354[/C][C]47.1392451853206[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]80.4631578947368[/C][C]1.66767195356376[/C][C]48.2487924095563[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]80.3333333333333[/C][C]1.61496965424338[/C][C]49.7429367308885[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]80.2323529411765[/C][C]1.56048418252982[/C][C]51.4150376142267[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]80.146875[/C][C]1.51142813509624[/C][C]53.0272482951344[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]80.0566666666667[/C][C]1.46397885900612[/C][C]54.6843051552099[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]80.0142857142857[/C][C]1.431345190783[/C][C]55.9014598501671[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]79.9769230769231[/C][C]1.38439998324526[/C][C]57.7700982698976[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]79.9166666666667[/C][C]1.31312585722322[/C][C]60.8598682502995[/C][/ROW]
[ROW][C]Median[/C][C]80.7[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]97.05[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]79.927027027027[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]80.3333333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]79.927027027027[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]80.3333333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]80.3333333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]79.927027027027[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]80.3333333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]80.4631578947369[/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=207420&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=207420&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 Mean85.80555555555562.6978037558723831.8057069083622
Geometric Mean83.0505773142718
Harmonic Mean80.5853985513846
Quadratic Mean88.7656558961103
Winsorized Mean ( 1 / 24 )85.80416666666672.6963579138550531.8222466779235
Winsorized Mean ( 2 / 24 )85.78194444444442.6843160991478531.9567224112229
Winsorized Mean ( 3 / 24 )85.67361111111112.6365842780284732.4941674821691
Winsorized Mean ( 4 / 24 )85.66252.6320110466796132.5464059537541
Winsorized Mean ( 5 / 24 )85.66944444444442.6211816545955932.6835205390075
Winsorized Mean ( 6 / 24 )85.57777777777782.5944250919982132.985256749836
Winsorized Mean ( 7 / 24 )85.52916666666672.5800990184168733.1495675383602
Winsorized Mean ( 8 / 24 )85.56252.5759112199505833.2164009913515
Winsorized Mean ( 9 / 24 )84.78752.4084910579961835.2035768281164
Winsorized Mean ( 10 / 24 )84.37083333333332.3144350699208436.4541803007759
Winsorized Mean ( 11 / 24 )84.01944444444442.2158128177324237.9181146403995
Winsorized Mean ( 12 / 24 )83.98611111111112.1933677109228838.2909398605914
Winsorized Mean ( 13 / 24 )83.15555555555562.0395520704887940.7714795610132
Winsorized Mean ( 14 / 24 )83.09722222222221.9688417710654842.2061454828096
Winsorized Mean ( 15 / 24 )82.65972222222221.8799937773785643.9680828824243
Winsorized Mean ( 16 / 24 )81.63751.7046383807125947.8913891202386
Winsorized Mean ( 17 / 24 )81.56666666666671.6795721006597348.5639566379004
Winsorized Mean ( 18 / 24 )81.19166666666671.6068962662003550.527011839197
Winsorized Mean ( 19 / 24 )80.95416666666671.5028193867377853.8681942627825
Winsorized Mean ( 20 / 24 )80.89861111111111.4160858973259657.1283219922427
Winsorized Mean ( 21 / 24 )80.40277777777781.2884067939114262.4048073618784
Winsorized Mean ( 22 / 24 )80.31111111111111.2672635046127863.3736478789002
Winsorized Mean ( 23 / 24 )80.43888888888891.2501417064521564.343816763918
Winsorized Mean ( 24 / 24 )79.33888888888891.0839950228339573.1911929645845
Trimmed Mean ( 1 / 24 )85.48428571428572.6569044673667532.1743919528311
Trimmed Mean ( 2 / 24 )85.14558823529412.6089149802390232.6363982269339
Trimmed Mean ( 3 / 24 )84.79848484848482.5581931017876233.1478045145338
Trimmed Mean ( 4 / 24 )84.47031252.5179383018852333.5474115615761
Trimmed Mean ( 5 / 24 )84.12419354838712.4696643745922134.0630064610612
Trimmed Mean ( 6 / 24 )83.75333333333332.413103900196834.7077195169685
Trimmed Mean ( 7 / 24 )83.37586206896552.3505689292716535.4705029198188
Trimmed Mean ( 8 / 24 )82.98035714285712.2762030066650536.4556047504896
Trimmed Mean ( 9 / 24 )82.552.1832965253670837.8097977259965
Trimmed Mean ( 10 / 24 )82.20576923076922.1109218488011738.9430661667818
Trimmed Mean ( 11 / 24 )81.8942.042618187822840.0926617065375
Trimmed Mean ( 12 / 24 )81.60416666666671.979063640468941.2337253830464
Trimmed Mean ( 13 / 24 )81.29347826086961.9014980165633442.7523339770791
Trimmed Mean ( 14 / 24 )81.05909090909091.8396109013339644.0631716469566
Trimmed Mean ( 15 / 24 )80.80952380952381.7742506213632245.5457210139991
Trimmed Mean ( 16 / 24 )80.58751.709562800235447.1392451853206
Trimmed Mean ( 17 / 24 )80.46315789473681.6676719535637648.2487924095563
Trimmed Mean ( 18 / 24 )80.33333333333331.6149696542433849.7429367308885
Trimmed Mean ( 19 / 24 )80.23235294117651.5604841825298251.4150376142267
Trimmed Mean ( 20 / 24 )80.1468751.5114281350962453.0272482951344
Trimmed Mean ( 21 / 24 )80.05666666666671.4639788590061254.6843051552099
Trimmed Mean ( 22 / 24 )80.01428571428571.43134519078355.9014598501671
Trimmed Mean ( 23 / 24 )79.97692307692311.3843999832452657.7700982698976
Trimmed Mean ( 24 / 24 )79.91666666666671.3131258572232260.8598682502995
Median80.7
Midrange97.05
Midmean - Weighted Average at Xnp79.927027027027
Midmean - Weighted Average at X(n+1)p80.3333333333333
Midmean - Empirical Distribution Function79.927027027027
Midmean - Empirical Distribution Function - Averaging80.3333333333333
Midmean - Empirical Distribution Function - Interpolation80.3333333333333
Midmean - Closest Observation79.927027027027
Midmean - True Basic - Statistics Graphics Toolkit80.3333333333333
Midmean - MS Excel (old versions)80.4631578947369
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')