Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationTue, 05 Mar 2013 08:53:49 -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/t13624917058epwwyqrizams7u.htm/, Retrieved Mon, 06 May 2024 19:27:10 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=207389, Retrieved Mon, 06 May 2024 19:27:10 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact114
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [Centrummaten USD ...] [2013-03-05 13:53:49] [e9fe483ee534263de9102ab1dada7978] [Current]
Feedback Forum

Post a new message
Dataseries X:
63,52
61,71
63,01
68,18
72,03
69,75
74,41
74,33
64,24
60,03
59,44
62,5
55,04
58,34
61,92
67,65
67,68
70,3
75,26
71,44
76,36
81,71
92,6
90,6
92,23
94,09
102,79
109,65
124,05
132,69
135,81
116,07
101,42
75,73
55,48
43,8
45,29
44,01
47,48
51,07
57,84
69,04
65,61
72,87
68,41
73,25
77,43
75,28
77,33
74,31
79,7
85,47
77,98
75,69
75,2
77,21
77,85
83,53
85,99
91,77
96,59
103,57
114,46
122,54
115,08
113,93
116,29
110,12
110,86
108,53
110,61
108,1




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'George Udny Yule' @ yule.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 & 3 seconds \tabularnewline
R Server & 'George Udny Yule' @ yule.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=207389&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]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'George Udny Yule' @ yule.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=207389&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=207389&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 time3 seconds
R Server'George Udny Yule' @ yule.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean81.75208333333332.6390728882705930.9775768970543
Geometric Mean78.8150041351438
Harmonic Mean75.9771453491036
Quadratic Mean84.7224718402516
Winsorized Mean ( 1 / 24 )81.71166666666672.6263075288904631.1127565099687
Winsorized Mean ( 2 / 24 )81.50722222222222.5581919890472631.861260832334
Winsorized Mean ( 3 / 24 )81.53555555555552.5258652965737132.2802469578077
Winsorized Mean ( 4 / 24 )81.38777777777782.414114292607333.7133076205258
Winsorized Mean ( 5 / 24 )81.64819444444442.3647380335644234.5273739778163
Winsorized Mean ( 6 / 24 )81.60236111111112.3421906376929234.8401875568464
Winsorized Mean ( 7 / 24 )81.77152777777782.2951968001283335.6272402319512
Winsorized Mean ( 8 / 24 )81.76819444444442.2753203039095435.937003816099
Winsorized Mean ( 9 / 24 )81.52194444444442.1809503054169637.3790930687249
Winsorized Mean ( 10 / 24 )81.56916666666672.1627873518908937.7148343295757
Winsorized Mean ( 11 / 24 )81.75097222222222.1134814964846238.6807134854029
Winsorized Mean ( 12 / 24 )81.70763888888892.0940493367931739.0189655292535
Winsorized Mean ( 13 / 24 )81.61013888888892.0424033210948839.9578957035479
Winsorized Mean ( 14 / 24 )81.62569444444442.0139118734185740.5309167306744
Winsorized Mean ( 15 / 24 )80.78819444444441.8295947190377244.1563334239045
Winsorized Mean ( 16 / 24 )80.77486111111111.7781668942033245.4259166417003
Winsorized Mean ( 17 / 24 )80.77486111111111.6802075170043148.0743362314715
Winsorized Mean ( 18 / 24 )80.07736111111111.4117208473710456.7232263093897
Winsorized Mean ( 19 / 24 )79.42555555555561.3040579930256460.9064596669314
Winsorized Mean ( 20 / 24 )79.15055555555561.2215738695050864.7939167097796
Winsorized Mean ( 21 / 24 )79.10972222222221.1964042530133466.1229028758225
Winsorized Mean ( 22 / 24 )79.16166666666671.150650680041768.7973057677222
Winsorized Mean ( 23 / 24 )79.01472222222221.0652281594931174.1763363257514
Winsorized Mean ( 24 / 24 )77.66138888888890.81288352704607295.5381506759052
Trimmed Mean ( 1 / 24 )81.5222.5430964855839932.0561962403402
Trimmed Mean ( 2 / 24 )81.32117647058822.443801807679133.2765022986131
Trimmed Mean ( 3 / 24 )81.2196969696972.3694105565590934.278439734668
Trimmed Mean ( 4 / 24 )81.101252.2950669525023135.3372043946584
Trimmed Mean ( 5 / 24 )81.0180645161292.2471164181352736.0542354914395
Trimmed Mean ( 6 / 24 )80.86683333333332.2037756826447236.6946754019385
Trimmed Mean ( 7 / 24 )80.71465517241382.1566092537622637.426647887931
Trimmed Mean ( 8 / 24 )80.52053571428572.1099622145266138.1620747328649
Trimmed Mean ( 9 / 24 )80.31259259259262.056289752475239.0570407190516
Trimmed Mean ( 10 / 24 )80.12653846153852.0115488746633939.8332545983736
Trimmed Mean ( 11 / 24 )79.91881.9582993588252840.8103080051768
Trimmed Mean ( 12 / 24 )79.66895833333331.9005557520445841.9187694165915
Trimmed Mean ( 13 / 24 )79.40304347826091.8299420510231843.3910152695076
Trimmed Mean ( 14 / 24 )79.12522727272731.7500068706792445.2142380686858
Trimmed Mean ( 15 / 24 )78.81904761904761.6505234734161747.7539695063603
Trimmed Mean ( 16 / 24 )78.582751.5693817575598250.0724247758467
Trimmed Mean ( 17 / 24 )78.32315789473681.4723506768717453.1959940828417
Trimmed Mean ( 18 / 24 )78.03472222222221.3656402932301957.1414907783986
Trimmed Mean ( 19 / 24 )77.79441176470591.2998567856926859.8484483990672
Trimmed Mean ( 20 / 24 )77.601251.2405776937027862.5525111356645
Trimmed Mean ( 21 / 24 )77.41533333333331.1802792123718465.590694576212
Trimmed Mean ( 22 / 24 )77.20785714285711.0972462352778670.3651146484046
Trimmed Mean ( 23 / 24 )76.96192307692310.98437266539593578.1837263288567
Trimmed Mean ( 24 / 24 )76.69416666666670.84067086665272791.2297186793655
Median75.71
Midrange89.805
Midmean - Weighted Average at Xnp77.6989189189189
Midmean - Weighted Average at X(n+1)p78.0347222222222
Midmean - Empirical Distribution Function77.6989189189189
Midmean - Empirical Distribution Function - Averaging78.0347222222222
Midmean - Empirical Distribution Function - Interpolation78.0347222222222
Midmean - Closest Observation77.6989189189189
Midmean - True Basic - Statistics Graphics Toolkit78.0347222222222
Midmean - MS Excel (old versions)78.3231578947368
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 81.7520833333333 & 2.63907288827059 & 30.9775768970543 \tabularnewline
Geometric Mean & 78.8150041351438 &  &  \tabularnewline
Harmonic Mean & 75.9771453491036 &  &  \tabularnewline
Quadratic Mean & 84.7224718402516 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 81.7116666666667 & 2.62630752889046 & 31.1127565099687 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 81.5072222222222 & 2.55819198904726 & 31.861260832334 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 81.5355555555555 & 2.52586529657371 & 32.2802469578077 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 81.3877777777778 & 2.4141142926073 & 33.7133076205258 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 81.6481944444444 & 2.36473803356442 & 34.5273739778163 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 81.6023611111111 & 2.34219063769292 & 34.8401875568464 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 81.7715277777778 & 2.29519680012833 & 35.6272402319512 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 81.7681944444444 & 2.27532030390954 & 35.937003816099 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 81.5219444444444 & 2.18095030541696 & 37.3790930687249 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 81.5691666666667 & 2.16278735189089 & 37.7148343295757 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 81.7509722222222 & 2.11348149648462 & 38.6807134854029 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 81.7076388888889 & 2.09404933679317 & 39.0189655292535 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 81.6101388888889 & 2.04240332109488 & 39.9578957035479 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 81.6256944444444 & 2.01391187341857 & 40.5309167306744 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 80.7881944444444 & 1.82959471903772 & 44.1563334239045 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 80.7748611111111 & 1.77816689420332 & 45.4259166417003 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 80.7748611111111 & 1.68020751700431 & 48.0743362314715 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 80.0773611111111 & 1.41172084737104 & 56.7232263093897 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 79.4255555555556 & 1.30405799302564 & 60.9064596669314 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 79.1505555555556 & 1.22157386950508 & 64.7939167097796 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 79.1097222222222 & 1.19640425301334 & 66.1229028758225 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 79.1616666666667 & 1.1506506800417 & 68.7973057677222 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 79.0147222222222 & 1.06522815949311 & 74.1763363257514 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 77.6613888888889 & 0.812883527046072 & 95.5381506759052 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 81.522 & 2.54309648558399 & 32.0561962403402 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 81.3211764705882 & 2.4438018076791 & 33.2765022986131 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 81.219696969697 & 2.36941055655909 & 34.278439734668 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 81.10125 & 2.29506695250231 & 35.3372043946584 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 81.018064516129 & 2.24711641813527 & 36.0542354914395 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 80.8668333333333 & 2.20377568264472 & 36.6946754019385 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 80.7146551724138 & 2.15660925376226 & 37.426647887931 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 80.5205357142857 & 2.10996221452661 & 38.1620747328649 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 80.3125925925926 & 2.0562897524752 & 39.0570407190516 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 80.1265384615385 & 2.01154887466339 & 39.8332545983736 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 79.9188 & 1.95829935882528 & 40.8103080051768 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 79.6689583333333 & 1.90055575204458 & 41.9187694165915 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 79.4030434782609 & 1.82994205102318 & 43.3910152695076 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 79.1252272727273 & 1.75000687067924 & 45.2142380686858 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 78.8190476190476 & 1.65052347341617 & 47.7539695063603 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 78.58275 & 1.56938175755982 & 50.0724247758467 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 78.3231578947368 & 1.47235067687174 & 53.1959940828417 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 78.0347222222222 & 1.36564029323019 & 57.1414907783986 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 77.7944117647059 & 1.29985678569268 & 59.8484483990672 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 77.60125 & 1.24057769370278 & 62.5525111356645 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 77.4153333333333 & 1.18027921237184 & 65.590694576212 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 77.2078571428571 & 1.09724623527786 & 70.3651146484046 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 76.9619230769231 & 0.984372665395935 & 78.1837263288567 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 76.6941666666667 & 0.840670866652727 & 91.2297186793655 \tabularnewline
Median & 75.71 &  &  \tabularnewline
Midrange & 89.805 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 77.6989189189189 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 78.0347222222222 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 77.6989189189189 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 78.0347222222222 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 78.0347222222222 &  &  \tabularnewline
Midmean - Closest Observation & 77.6989189189189 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 78.0347222222222 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 78.3231578947368 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=207389&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]81.7520833333333[/C][C]2.63907288827059[/C][C]30.9775768970543[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]78.8150041351438[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]75.9771453491036[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]84.7224718402516[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]81.7116666666667[/C][C]2.62630752889046[/C][C]31.1127565099687[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]81.5072222222222[/C][C]2.55819198904726[/C][C]31.861260832334[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]81.5355555555555[/C][C]2.52586529657371[/C][C]32.2802469578077[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]81.3877777777778[/C][C]2.4141142926073[/C][C]33.7133076205258[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]81.6481944444444[/C][C]2.36473803356442[/C][C]34.5273739778163[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]81.6023611111111[/C][C]2.34219063769292[/C][C]34.8401875568464[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]81.7715277777778[/C][C]2.29519680012833[/C][C]35.6272402319512[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]81.7681944444444[/C][C]2.27532030390954[/C][C]35.937003816099[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]81.5219444444444[/C][C]2.18095030541696[/C][C]37.3790930687249[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]81.5691666666667[/C][C]2.16278735189089[/C][C]37.7148343295757[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]81.7509722222222[/C][C]2.11348149648462[/C][C]38.6807134854029[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]81.7076388888889[/C][C]2.09404933679317[/C][C]39.0189655292535[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]81.6101388888889[/C][C]2.04240332109488[/C][C]39.9578957035479[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]81.6256944444444[/C][C]2.01391187341857[/C][C]40.5309167306744[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]80.7881944444444[/C][C]1.82959471903772[/C][C]44.1563334239045[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]80.7748611111111[/C][C]1.77816689420332[/C][C]45.4259166417003[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]80.7748611111111[/C][C]1.68020751700431[/C][C]48.0743362314715[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]80.0773611111111[/C][C]1.41172084737104[/C][C]56.7232263093897[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]79.4255555555556[/C][C]1.30405799302564[/C][C]60.9064596669314[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]79.1505555555556[/C][C]1.22157386950508[/C][C]64.7939167097796[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]79.1097222222222[/C][C]1.19640425301334[/C][C]66.1229028758225[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]79.1616666666667[/C][C]1.1506506800417[/C][C]68.7973057677222[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]79.0147222222222[/C][C]1.06522815949311[/C][C]74.1763363257514[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]77.6613888888889[/C][C]0.812883527046072[/C][C]95.5381506759052[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]81.522[/C][C]2.54309648558399[/C][C]32.0561962403402[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]81.3211764705882[/C][C]2.4438018076791[/C][C]33.2765022986131[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]81.219696969697[/C][C]2.36941055655909[/C][C]34.278439734668[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]81.10125[/C][C]2.29506695250231[/C][C]35.3372043946584[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]81.018064516129[/C][C]2.24711641813527[/C][C]36.0542354914395[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]80.8668333333333[/C][C]2.20377568264472[/C][C]36.6946754019385[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]80.7146551724138[/C][C]2.15660925376226[/C][C]37.426647887931[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]80.5205357142857[/C][C]2.10996221452661[/C][C]38.1620747328649[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]80.3125925925926[/C][C]2.0562897524752[/C][C]39.0570407190516[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]80.1265384615385[/C][C]2.01154887466339[/C][C]39.8332545983736[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]79.9188[/C][C]1.95829935882528[/C][C]40.8103080051768[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]79.6689583333333[/C][C]1.90055575204458[/C][C]41.9187694165915[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]79.4030434782609[/C][C]1.82994205102318[/C][C]43.3910152695076[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]79.1252272727273[/C][C]1.75000687067924[/C][C]45.2142380686858[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]78.8190476190476[/C][C]1.65052347341617[/C][C]47.7539695063603[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]78.58275[/C][C]1.56938175755982[/C][C]50.0724247758467[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]78.3231578947368[/C][C]1.47235067687174[/C][C]53.1959940828417[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]78.0347222222222[/C][C]1.36564029323019[/C][C]57.1414907783986[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]77.7944117647059[/C][C]1.29985678569268[/C][C]59.8484483990672[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]77.60125[/C][C]1.24057769370278[/C][C]62.5525111356645[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]77.4153333333333[/C][C]1.18027921237184[/C][C]65.590694576212[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]77.2078571428571[/C][C]1.09724623527786[/C][C]70.3651146484046[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]76.9619230769231[/C][C]0.984372665395935[/C][C]78.1837263288567[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]76.6941666666667[/C][C]0.840670866652727[/C][C]91.2297186793655[/C][/ROW]
[ROW][C]Median[/C][C]75.71[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]89.805[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]77.6989189189189[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]78.0347222222222[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]77.6989189189189[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]78.0347222222222[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]78.0347222222222[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]77.6989189189189[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]78.0347222222222[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]78.3231578947368[/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=207389&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=207389&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 Mean81.75208333333332.6390728882705930.9775768970543
Geometric Mean78.8150041351438
Harmonic Mean75.9771453491036
Quadratic Mean84.7224718402516
Winsorized Mean ( 1 / 24 )81.71166666666672.6263075288904631.1127565099687
Winsorized Mean ( 2 / 24 )81.50722222222222.5581919890472631.861260832334
Winsorized Mean ( 3 / 24 )81.53555555555552.5258652965737132.2802469578077
Winsorized Mean ( 4 / 24 )81.38777777777782.414114292607333.7133076205258
Winsorized Mean ( 5 / 24 )81.64819444444442.3647380335644234.5273739778163
Winsorized Mean ( 6 / 24 )81.60236111111112.3421906376929234.8401875568464
Winsorized Mean ( 7 / 24 )81.77152777777782.2951968001283335.6272402319512
Winsorized Mean ( 8 / 24 )81.76819444444442.2753203039095435.937003816099
Winsorized Mean ( 9 / 24 )81.52194444444442.1809503054169637.3790930687249
Winsorized Mean ( 10 / 24 )81.56916666666672.1627873518908937.7148343295757
Winsorized Mean ( 11 / 24 )81.75097222222222.1134814964846238.6807134854029
Winsorized Mean ( 12 / 24 )81.70763888888892.0940493367931739.0189655292535
Winsorized Mean ( 13 / 24 )81.61013888888892.0424033210948839.9578957035479
Winsorized Mean ( 14 / 24 )81.62569444444442.0139118734185740.5309167306744
Winsorized Mean ( 15 / 24 )80.78819444444441.8295947190377244.1563334239045
Winsorized Mean ( 16 / 24 )80.77486111111111.7781668942033245.4259166417003
Winsorized Mean ( 17 / 24 )80.77486111111111.6802075170043148.0743362314715
Winsorized Mean ( 18 / 24 )80.07736111111111.4117208473710456.7232263093897
Winsorized Mean ( 19 / 24 )79.42555555555561.3040579930256460.9064596669314
Winsorized Mean ( 20 / 24 )79.15055555555561.2215738695050864.7939167097796
Winsorized Mean ( 21 / 24 )79.10972222222221.1964042530133466.1229028758225
Winsorized Mean ( 22 / 24 )79.16166666666671.150650680041768.7973057677222
Winsorized Mean ( 23 / 24 )79.01472222222221.0652281594931174.1763363257514
Winsorized Mean ( 24 / 24 )77.66138888888890.81288352704607295.5381506759052
Trimmed Mean ( 1 / 24 )81.5222.5430964855839932.0561962403402
Trimmed Mean ( 2 / 24 )81.32117647058822.443801807679133.2765022986131
Trimmed Mean ( 3 / 24 )81.2196969696972.3694105565590934.278439734668
Trimmed Mean ( 4 / 24 )81.101252.2950669525023135.3372043946584
Trimmed Mean ( 5 / 24 )81.0180645161292.2471164181352736.0542354914395
Trimmed Mean ( 6 / 24 )80.86683333333332.2037756826447236.6946754019385
Trimmed Mean ( 7 / 24 )80.71465517241382.1566092537622637.426647887931
Trimmed Mean ( 8 / 24 )80.52053571428572.1099622145266138.1620747328649
Trimmed Mean ( 9 / 24 )80.31259259259262.056289752475239.0570407190516
Trimmed Mean ( 10 / 24 )80.12653846153852.0115488746633939.8332545983736
Trimmed Mean ( 11 / 24 )79.91881.9582993588252840.8103080051768
Trimmed Mean ( 12 / 24 )79.66895833333331.9005557520445841.9187694165915
Trimmed Mean ( 13 / 24 )79.40304347826091.8299420510231843.3910152695076
Trimmed Mean ( 14 / 24 )79.12522727272731.7500068706792445.2142380686858
Trimmed Mean ( 15 / 24 )78.81904761904761.6505234734161747.7539695063603
Trimmed Mean ( 16 / 24 )78.582751.5693817575598250.0724247758467
Trimmed Mean ( 17 / 24 )78.32315789473681.4723506768717453.1959940828417
Trimmed Mean ( 18 / 24 )78.03472222222221.3656402932301957.1414907783986
Trimmed Mean ( 19 / 24 )77.79441176470591.2998567856926859.8484483990672
Trimmed Mean ( 20 / 24 )77.601251.2405776937027862.5525111356645
Trimmed Mean ( 21 / 24 )77.41533333333331.1802792123718465.590694576212
Trimmed Mean ( 22 / 24 )77.20785714285711.0972462352778670.3651146484046
Trimmed Mean ( 23 / 24 )76.96192307692310.98437266539593578.1837263288567
Trimmed Mean ( 24 / 24 )76.69416666666670.84067086665272791.2297186793655
Median75.71
Midrange89.805
Midmean - Weighted Average at Xnp77.6989189189189
Midmean - Weighted Average at X(n+1)p78.0347222222222
Midmean - Empirical Distribution Function77.6989189189189
Midmean - Empirical Distribution Function - Averaging78.0347222222222
Midmean - Empirical Distribution Function - Interpolation78.0347222222222
Midmean - Closest Observation77.6989189189189
Midmean - True Basic - Statistics Graphics Toolkit78.0347222222222
Midmean - MS Excel (old versions)78.3231578947368
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')