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Description of Statistical Computation

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationSat, 10 Oct 2015 12:37:00 +0100
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2015/Oct/10/t1444477040y8qs8n6kvmgbx60.htm/, Retrieved Tue, 14 May 2024 11:33:49 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=282159, Retrieved Tue, 14 May 2024 11:33:49 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact97

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Central Tendency] [] [2015-10-10 11:24:03] [0018d7578cf543a80e31e68d42751f97]
-    D    [Central Tendency] [] [2015-10-10 11:37:00] [cb8108074d5ede30ed5e3c15decd01d7] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
143,7
149,3
121,7
81
68,1
92,3
107,7
114,4
98,6
106,7
73,9
85,9
118,4
144,2
118,4
82,6
68
99,8
93,4
107,9
101,1
100,4
76,7
89,1
105,3
124,8
111,9
89
88,6
84,5
91,1
118,1
103,6
92,6
70,2
70,2
114,3
125,3
98,9
65,4
66
71,2
84,6
102,6
91,8
97,4
64,1
62,3
96,2
104,9
90,3
65,2
57,8
70,5
93,2
74,2
91,1
85
58,9
68,3
98,1
110,5
77,6
55,1
49,8
58,5
86,5
88,8
94
65
52,2
70,9

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Herman Ole Andreas Wold' @ wold.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 & 1 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=282159&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]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=282159&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=282159&T=0

As an alternative you can also use a QR Code:  
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'Herman Ole Andreas Wold' @ wold.wessa.net






Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean90.27361111111112.6248108904647834.3924247796482
Geometric Mean87.5793294227073
Harmonic Mean84.9010643912723
Quadratic Mean92.9434707228001
Winsorized Mean ( 1 / 24 )90.23611111111112.5961602692825234.7575271753346
Winsorized Mean ( 2 / 24 )90.30277777777782.5760338886646335.0549649890628
Winsorized Mean ( 3 / 24 )89.64861111111112.3596926547963837.9916473142758
Winsorized Mean ( 4 / 24 )89.65972222222222.3464742803212238.2104005887284
Winsorized Mean ( 5 / 24 )89.47222222222222.2972862998747938.9469184694562
Winsorized Mean ( 6 / 24 )89.48055555555562.1932208460467440.7986982783076
Winsorized Mean ( 7 / 24 )89.65555555555562.1633849188429341.4422578130512
Winsorized Mean ( 8 / 24 )89.72222222222222.1407014249665441.9125344505363
Winsorized Mean ( 9 / 24 )89.28472222222222.053523499404543.4787925475963
Winsorized Mean ( 10 / 24 )89.29861111111112.0465537399986643.6336507396917
Winsorized Mean ( 11 / 24 )89.02361111111111.9699100861406645.191712930168
Winsorized Mean ( 12 / 24 )89.12361111111111.8782572053170347.4501632996893
Winsorized Mean ( 13 / 24 )88.67222222222221.8024362124008649.1957616098437
Winsorized Mean ( 14 / 24 )88.67222222222221.7903619796241849.5275386940666
Winsorized Mean ( 15 / 24 )88.85972222222221.696940609568652.3646624526313
Winsorized Mean ( 16 / 24 )88.54861111111111.6516755293361853.6113840390305
Winsorized Mean ( 17 / 24 )88.5251.6271690110773254.4043055130391
Winsorized Mean ( 18 / 24 )88.31.5661396576391456.3806679495664
Winsorized Mean ( 19 / 24 )88.11527777777781.5178369056498458.0531923092572
Winsorized Mean ( 20 / 24 )88.44861111111111.3461851174065565.7031562505376
Winsorized Mean ( 21 / 24 )88.33194444444441.3060573133468667.6325177630127
Winsorized Mean ( 22 / 24 )88.91251.1675062999766476.1559059696546
Winsorized Mean ( 23 / 24 )88.91251.08778776794581.7369919207397
Winsorized Mean ( 24 / 24 )89.94583333333330.91304649530139498.5117776544801
Trimmed Mean ( 1 / 24 )90.00857142857142.4960695752442936.0601212086655
Trimmed Mean ( 2 / 24 )89.76764705882352.3761004947003337.7793983289183
Trimmed Mean ( 3 / 24 )89.47575757575762.244202123915939.8697410639786
Trimmed Mean ( 4 / 24 )89.41093752.18895033234640.8464898352326
Trimmed Mean ( 5 / 24 )89.33870967741942.1270553936090342.0011203966982
Trimmed Mean ( 6 / 24 )89.30666666666672.0678680670559143.1877971759657
Trimmed Mean ( 7 / 24 )89.27068965517242.0253580096555344.076498687931
Trimmed Mean ( 8 / 24 )89.21.980349896933845.0425453290398
Trimmed Mean ( 9 / 24 )89.1129629629631.9297444573916146.1786339748915
Trimmed Mean ( 10 / 24 )89.08653846153851.8873377965048547.2022224248978
Trimmed Mean ( 11 / 24 )89.0561.8350024411928448.5318155446755
Trimmed Mean ( 12 / 24 )89.06041666666671.7860142726534349.8654563013947
Trimmed Mean ( 13 / 24 )89.05217391304351.7436004149624851.0737283318206
Trimmed Mean ( 14 / 24 )89.11.704793639437252.2643902105444
Trimmed Mean ( 15 / 24 )89.1523809523811.655604068821253.8488534978403
Trimmed Mean ( 16 / 24 )89.18751.6118320023644455.3329998840875
Trimmed Mean ( 17 / 24 )89.26315789473681.5624797969795257.1291597288454
Trimmed Mean ( 18 / 24 )89.351.5001825285769859.5594191359863
Trimmed Mean ( 19 / 24 )89.47352941176471.4291671959080662.605361827463
Trimmed Mean ( 20 / 24 )89.6343751.3412846617518666.8272571483282
Trimmed Mean ( 21 / 24 )89.77666666666671.2708100713906470.6452275503485
Trimmed Mean ( 22 / 24 )89.95357142857141.1777532433374976.3772648790698
Trimmed Mean ( 23 / 24 )90.08461538461541.0923466948616482.4688863053921
Trimmed Mean ( 24 / 24 )90.23750.9904034549733791.1118590579092
Median90.7
Midrange99.55
Midmean - Weighted Average at Xnp88.8405405405405
Midmean - Weighted Average at X(n+1)p89.35
Midmean - Empirical Distribution Function88.8405405405405
Midmean - Empirical Distribution Function - Averaging89.35
Midmean - Empirical Distribution Function - Interpolation89.35
Midmean - Closest Observation88.8405405405405
Midmean - True Basic - Statistics Graphics Toolkit89.35
Midmean - MS Excel (old versions)89.2631578947368
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 90.2736111111111 & 2.62481089046478 & 34.3924247796482 \tabularnewline
Geometric Mean & 87.5793294227073 &  &  \tabularnewline
Harmonic Mean & 84.9010643912723 &  &  \tabularnewline
Quadratic Mean & 92.9434707228001 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 90.2361111111111 & 2.59616026928252 & 34.7575271753346 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 90.3027777777778 & 2.57603388866463 & 35.0549649890628 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 89.6486111111111 & 2.35969265479638 & 37.9916473142758 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 89.6597222222222 & 2.34647428032122 & 38.2104005887284 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 89.4722222222222 & 2.29728629987479 & 38.9469184694562 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 89.4805555555556 & 2.19322084604674 & 40.7986982783076 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 89.6555555555556 & 2.16338491884293 & 41.4422578130512 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 89.7222222222222 & 2.14070142496654 & 41.9125344505363 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 89.2847222222222 & 2.0535234994045 & 43.4787925475963 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 89.2986111111111 & 2.04655373999866 & 43.6336507396917 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 89.0236111111111 & 1.96991008614066 & 45.191712930168 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 89.1236111111111 & 1.87825720531703 & 47.4501632996893 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 88.6722222222222 & 1.80243621240086 & 49.1957616098437 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 88.6722222222222 & 1.79036197962418 & 49.5275386940666 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 88.8597222222222 & 1.6969406095686 & 52.3646624526313 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 88.5486111111111 & 1.65167552933618 & 53.6113840390305 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 88.525 & 1.62716901107732 & 54.4043055130391 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 88.3 & 1.56613965763914 & 56.3806679495664 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 88.1152777777778 & 1.51783690564984 & 58.0531923092572 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 88.4486111111111 & 1.34618511740655 & 65.7031562505376 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 88.3319444444444 & 1.30605731334686 & 67.6325177630127 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 88.9125 & 1.16750629997664 & 76.1559059696546 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 88.9125 & 1.087787767945 & 81.7369919207397 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 89.9458333333333 & 0.913046495301394 & 98.5117776544801 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 90.0085714285714 & 2.49606957524429 & 36.0601212086655 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 89.7676470588235 & 2.37610049470033 & 37.7793983289183 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 89.4757575757576 & 2.2442021239159 & 39.8697410639786 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 89.4109375 & 2.188950332346 & 40.8464898352326 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 89.3387096774194 & 2.12705539360903 & 42.0011203966982 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 89.3066666666667 & 2.06786806705591 & 43.1877971759657 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 89.2706896551724 & 2.02535800965553 & 44.076498687931 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 89.2 & 1.9803498969338 & 45.0425453290398 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 89.112962962963 & 1.92974445739161 & 46.1786339748915 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 89.0865384615385 & 1.88733779650485 & 47.2022224248978 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 89.056 & 1.83500244119284 & 48.5318155446755 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 89.0604166666667 & 1.78601427265343 & 49.8654563013947 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 89.0521739130435 & 1.74360041496248 & 51.0737283318206 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 89.1 & 1.7047936394372 & 52.2643902105444 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 89.152380952381 & 1.6556040688212 & 53.8488534978403 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 89.1875 & 1.61183200236444 & 55.3329998840875 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 89.2631578947368 & 1.56247979697952 & 57.1291597288454 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 89.35 & 1.50018252857698 & 59.5594191359863 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 89.4735294117647 & 1.42916719590806 & 62.605361827463 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 89.634375 & 1.34128466175186 & 66.8272571483282 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 89.7766666666667 & 1.27081007139064 & 70.6452275503485 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 89.9535714285714 & 1.17775324333749 & 76.3772648790698 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 90.0846153846154 & 1.09234669486164 & 82.4688863053921 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 90.2375 & 0.99040345497337 & 91.1118590579092 \tabularnewline
Median & 90.7 &  &  \tabularnewline
Midrange & 99.55 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 88.8405405405405 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 89.35 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 88.8405405405405 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 89.35 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 89.35 &  &  \tabularnewline
Midmean - Closest Observation & 88.8405405405405 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 89.35 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 89.2631578947368 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=282159&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]90.2736111111111[/C][C]2.62481089046478[/C][C]34.3924247796482[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]87.5793294227073[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]84.9010643912723[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]92.9434707228001[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]90.2361111111111[/C][C]2.59616026928252[/C][C]34.7575271753346[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]90.3027777777778[/C][C]2.57603388866463[/C][C]35.0549649890628[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]89.6486111111111[/C][C]2.35969265479638[/C][C]37.9916473142758[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]89.6597222222222[/C][C]2.34647428032122[/C][C]38.2104005887284[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]89.4722222222222[/C][C]2.29728629987479[/C][C]38.9469184694562[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]89.4805555555556[/C][C]2.19322084604674[/C][C]40.7986982783076[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]89.6555555555556[/C][C]2.16338491884293[/C][C]41.4422578130512[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]89.7222222222222[/C][C]2.14070142496654[/C][C]41.9125344505363[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]89.2847222222222[/C][C]2.0535234994045[/C][C]43.4787925475963[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]89.2986111111111[/C][C]2.04655373999866[/C][C]43.6336507396917[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]89.0236111111111[/C][C]1.96991008614066[/C][C]45.191712930168[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]89.1236111111111[/C][C]1.87825720531703[/C][C]47.4501632996893[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]88.6722222222222[/C][C]1.80243621240086[/C][C]49.1957616098437[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]88.6722222222222[/C][C]1.79036197962418[/C][C]49.5275386940666[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]88.8597222222222[/C][C]1.6969406095686[/C][C]52.3646624526313[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]88.5486111111111[/C][C]1.65167552933618[/C][C]53.6113840390305[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]88.525[/C][C]1.62716901107732[/C][C]54.4043055130391[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]88.3[/C][C]1.56613965763914[/C][C]56.3806679495664[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]88.1152777777778[/C][C]1.51783690564984[/C][C]58.0531923092572[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]88.4486111111111[/C][C]1.34618511740655[/C][C]65.7031562505376[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]88.3319444444444[/C][C]1.30605731334686[/C][C]67.6325177630127[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]88.9125[/C][C]1.16750629997664[/C][C]76.1559059696546[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]88.9125[/C][C]1.087787767945[/C][C]81.7369919207397[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]89.9458333333333[/C][C]0.913046495301394[/C][C]98.5117776544801[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]90.0085714285714[/C][C]2.49606957524429[/C][C]36.0601212086655[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]89.7676470588235[/C][C]2.37610049470033[/C][C]37.7793983289183[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]89.4757575757576[/C][C]2.2442021239159[/C][C]39.8697410639786[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]89.4109375[/C][C]2.188950332346[/C][C]40.8464898352326[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]89.3387096774194[/C][C]2.12705539360903[/C][C]42.0011203966982[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]89.3066666666667[/C][C]2.06786806705591[/C][C]43.1877971759657[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]89.2706896551724[/C][C]2.02535800965553[/C][C]44.076498687931[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]89.2[/C][C]1.9803498969338[/C][C]45.0425453290398[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]89.112962962963[/C][C]1.92974445739161[/C][C]46.1786339748915[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]89.0865384615385[/C][C]1.88733779650485[/C][C]47.2022224248978[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]89.056[/C][C]1.83500244119284[/C][C]48.5318155446755[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]89.0604166666667[/C][C]1.78601427265343[/C][C]49.8654563013947[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]89.0521739130435[/C][C]1.74360041496248[/C][C]51.0737283318206[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]89.1[/C][C]1.7047936394372[/C][C]52.2643902105444[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]89.152380952381[/C][C]1.6556040688212[/C][C]53.8488534978403[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]89.1875[/C][C]1.61183200236444[/C][C]55.3329998840875[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]89.2631578947368[/C][C]1.56247979697952[/C][C]57.1291597288454[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]89.35[/C][C]1.50018252857698[/C][C]59.5594191359863[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]89.4735294117647[/C][C]1.42916719590806[/C][C]62.605361827463[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]89.634375[/C][C]1.34128466175186[/C][C]66.8272571483282[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]89.7766666666667[/C][C]1.27081007139064[/C][C]70.6452275503485[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]89.9535714285714[/C][C]1.17775324333749[/C][C]76.3772648790698[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]90.0846153846154[/C][C]1.09234669486164[/C][C]82.4688863053921[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]90.2375[/C][C]0.99040345497337[/C][C]91.1118590579092[/C][/ROW]
[ROW][C]Median[/C][C]90.7[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]99.55[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]88.8405405405405[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]89.35[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]88.8405405405405[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]89.35[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]89.35[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]88.8405405405405[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]89.35[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]89.2631578947368[/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=282159&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=282159&T=1

As an alternative you can also use a QR Code:  
QR Code


The GUIDs for individual cells are displayed in the table below:

Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean90.27361111111112.6248108904647834.3924247796482
Geometric Mean87.5793294227073
Harmonic Mean84.9010643912723
Quadratic Mean92.9434707228001
Winsorized Mean ( 1 / 24 )90.23611111111112.5961602692825234.7575271753346
Winsorized Mean ( 2 / 24 )90.30277777777782.5760338886646335.0549649890628
Winsorized Mean ( 3 / 24 )89.64861111111112.3596926547963837.9916473142758
Winsorized Mean ( 4 / 24 )89.65972222222222.3464742803212238.2104005887284
Winsorized Mean ( 5 / 24 )89.47222222222222.2972862998747938.9469184694562
Winsorized Mean ( 6 / 24 )89.48055555555562.1932208460467440.7986982783076
Winsorized Mean ( 7 / 24 )89.65555555555562.1633849188429341.4422578130512
Winsorized Mean ( 8 / 24 )89.72222222222222.1407014249665441.9125344505363
Winsorized Mean ( 9 / 24 )89.28472222222222.053523499404543.4787925475963
Winsorized Mean ( 10 / 24 )89.29861111111112.0465537399986643.6336507396917
Winsorized Mean ( 11 / 24 )89.02361111111111.9699100861406645.191712930168
Winsorized Mean ( 12 / 24 )89.12361111111111.8782572053170347.4501632996893
Winsorized Mean ( 13 / 24 )88.67222222222221.8024362124008649.1957616098437
Winsorized Mean ( 14 / 24 )88.67222222222221.7903619796241849.5275386940666
Winsorized Mean ( 15 / 24 )88.85972222222221.696940609568652.3646624526313
Winsorized Mean ( 16 / 24 )88.54861111111111.6516755293361853.6113840390305
Winsorized Mean ( 17 / 24 )88.5251.6271690110773254.4043055130391
Winsorized Mean ( 18 / 24 )88.31.5661396576391456.3806679495664
Winsorized Mean ( 19 / 24 )88.11527777777781.5178369056498458.0531923092572
Winsorized Mean ( 20 / 24 )88.44861111111111.3461851174065565.7031562505376
Winsorized Mean ( 21 / 24 )88.33194444444441.3060573133468667.6325177630127
Winsorized Mean ( 22 / 24 )88.91251.1675062999766476.1559059696546
Winsorized Mean ( 23 / 24 )88.91251.08778776794581.7369919207397
Winsorized Mean ( 24 / 24 )89.94583333333330.91304649530139498.5117776544801
Trimmed Mean ( 1 / 24 )90.00857142857142.4960695752442936.0601212086655
Trimmed Mean ( 2 / 24 )89.76764705882352.3761004947003337.7793983289183
Trimmed Mean ( 3 / 24 )89.47575757575762.244202123915939.8697410639786
Trimmed Mean ( 4 / 24 )89.41093752.18895033234640.8464898352326
Trimmed Mean ( 5 / 24 )89.33870967741942.1270553936090342.0011203966982
Trimmed Mean ( 6 / 24 )89.30666666666672.0678680670559143.1877971759657
Trimmed Mean ( 7 / 24 )89.27068965517242.0253580096555344.076498687931
Trimmed Mean ( 8 / 24 )89.21.980349896933845.0425453290398
Trimmed Mean ( 9 / 24 )89.1129629629631.9297444573916146.1786339748915
Trimmed Mean ( 10 / 24 )89.08653846153851.8873377965048547.2022224248978
Trimmed Mean ( 11 / 24 )89.0561.8350024411928448.5318155446755
Trimmed Mean ( 12 / 24 )89.06041666666671.7860142726534349.8654563013947
Trimmed Mean ( 13 / 24 )89.05217391304351.7436004149624851.0737283318206
Trimmed Mean ( 14 / 24 )89.11.704793639437252.2643902105444
Trimmed Mean ( 15 / 24 )89.1523809523811.655604068821253.8488534978403
Trimmed Mean ( 16 / 24 )89.18751.6118320023644455.3329998840875
Trimmed Mean ( 17 / 24 )89.26315789473681.5624797969795257.1291597288454
Trimmed Mean ( 18 / 24 )89.351.5001825285769859.5594191359863
Trimmed Mean ( 19 / 24 )89.47352941176471.4291671959080662.605361827463
Trimmed Mean ( 20 / 24 )89.6343751.3412846617518666.8272571483282
Trimmed Mean ( 21 / 24 )89.77666666666671.2708100713906470.6452275503485
Trimmed Mean ( 22 / 24 )89.95357142857141.1777532433374976.3772648790698
Trimmed Mean ( 23 / 24 )90.08461538461541.0923466948616482.4688863053921
Trimmed Mean ( 24 / 24 )90.23750.9904034549733791.1118590579092
Median90.7
Midrange99.55
Midmean - Weighted Average at Xnp88.8405405405405
Midmean - Weighted Average at X(n+1)p89.35
Midmean - Empirical Distribution Function88.8405405405405
Midmean - Empirical Distribution Function - Averaging89.35
Midmean - Empirical Distribution Function - Interpolation89.35
Midmean - Closest Observation88.8405405405405
Midmean - True Basic - Statistics Graphics Toolkit89.35
Midmean - MS Excel (old versions)89.2631578947368
Number of observations72


Figures (Output of Computation)

Input Parameters & R Code

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')