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of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationThu, 13 Oct 2016 16:58:44 +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/2016/Oct/13/t14763743697fiuobmdjpkiwji.htm/, Retrieved Tue, 30 Apr 2024 19:00:17 +0200
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=, Retrieved Tue, 30 Apr 2024 19:00:17 +0200
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact0
Dataseries X:
95,31
93,47
98,92
101,21
95,19
90,95
93,09
90,16
91,86
88,82
91,58
94,9
99,85
98,03
93,46
94,15
93,47
88,98
89,26
84,62
82,7
84,37
89,52
89,82
93,08
98,02
97,49
97,35
99,33
96,92
96,42
93,94
89,95
94,38
95,13
96,01
100,37
99,57
100,53
106,51
106,22
106,93
103,24
98,54
95,6
91,97
93,99
96,53
102,37
98,81
96,88
100,4
91,54
90,36
94,28
84,17
86,65
84,09
90,2
92,47
96,92
98,3
94,27
105,58
99,89
97,46
99,21
97,72
99,31
102,57
102,16
99,12




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=&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=&T=0

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

As an alternative you can also use a QR Code:  

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

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Herman Ole Andreas Wold' @ wold.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean95.36722222222220.646221932831065147.576579155126
Geometric Mean95.2101229682513
Harmonic Mean95.0512834772739
Quadratic Mean95.5225464077577
Winsorized Mean ( 1 / 24 )95.38069444444450.639706209660928149.100779395279
Winsorized Mean ( 2 / 24 )95.37486111111110.637202291499088149.677523736977
Winsorized Mean ( 3 / 24 )95.35652777777780.628895097617718151.625490704241
Winsorized Mean ( 4 / 24 )95.24041666666670.598260959093986159.195440081699
Winsorized Mean ( 5 / 24 )95.33486111111110.556418410283703171.336640465405
Winsorized Mean ( 6 / 24 )95.49902777777780.516874377440844184.762549559167
Winsorized Mean ( 7 / 24 )95.49416666666670.510270485438712187.144209574583
Winsorized Mean ( 8 / 24 )95.41972222222220.486111087636932196.29200947889
Winsorized Mean ( 9 / 24 )95.36722222222220.466578010618851204.397164143528
Winsorized Mean ( 10 / 24 )95.39083333333330.456516747863441208.953633748981
Winsorized Mean ( 11 / 24 )95.40611111111110.452414776191684210.881951987104
Winsorized Mean ( 12 / 24 )95.36111111111110.434430065521767219.50854390471
Winsorized Mean ( 13 / 24 )95.36111111111110.432155203979889220.664035126484
Winsorized Mean ( 14 / 24 )95.33777777777780.419079783238442227.493144720689
Winsorized Mean ( 15 / 24 )95.41069444444440.391851086658403243.487124810806
Winsorized Mean ( 16 / 24 )95.53736111111110.370738223972419257.69493117661
Winsorized Mean ( 17 / 24 )95.52319444444440.365937058262611261.037225631007
Winsorized Mean ( 18 / 24 )95.57069444444440.352236723199249271.325186018106
Winsorized Mean ( 19 / 24 )95.54694444444440.34050768956735280.601429488557
Winsorized Mean ( 20 / 24 )95.65527777777780.316082360123356302.627700389375
Winsorized Mean ( 21 / 24 )95.75444444444450.280420534918725341.46730542468
Winsorized Mean ( 22 / 24 )95.68416666666670.269870408098867354.555978703722
Winsorized Mean ( 23 / 24 )95.71611111111110.242419384302463394.836870766438
Winsorized Mean ( 24 / 24 )95.71611111111110.241534653562383396.283140739429
Trimmed Mean ( 1 / 24 )95.3830.6173159812478154.512442407856
Trimmed Mean ( 2 / 24 )95.38544117647060.590618284162143161.50099604821
Trimmed Mean ( 3 / 24 )95.39121212121210.560155927140851170.294033320522
Trimmed Mean ( 4 / 24 )95.404218750.527235405536808180.951843802795
Trimmed Mean ( 5 / 24 )95.45177419354840.499329244650643191.159991560942
Trimmed Mean ( 6 / 24 )95.47983333333330.479753143424027199.018671669117
Trimmed Mean ( 7 / 24 )95.47586206896550.467629917277688204.169704591997
Trimmed Mean ( 8 / 24 )95.47250.45444201907537210.087307054601
Trimmed Mean ( 9 / 24 )95.48129629629630.444138708753581214.980803101474
Trimmed Mean ( 10 / 24 )95.49884615384620.435731268789337219.169137021509
Trimmed Mean ( 11 / 24 )95.51440.427250646695872223.555893334878
Trimmed Mean ( 12 / 24 )95.52916666666670.417205732849464228.973763170065
Trimmed Mean ( 13 / 24 )95.55108695652170.408138134741212234.114577450862
Trimmed Mean ( 14 / 24 )95.5750.396652150023661240.95419625054
Trimmed Mean ( 15 / 24 )95.60404761904760.384425459279953248.693330036253
Trimmed Mean ( 16 / 24 )95.627250.37460902481702255.27214686488
Trimmed Mean ( 17 / 24 )95.63789473684210.36629438018894261.095719479809
Trimmed Mean ( 18 / 24 )95.65138888888890.355693187027893268.915437172509
Trimmed Mean ( 19 / 24 )95.66088235294120.344298187629304277.843119104468
Trimmed Mean ( 20 / 24 )95.6743750.331104255064435288.955437861653
Trimmed Mean ( 21 / 24 )95.67666666666670.319217193863735299.722785945886
Trimmed Mean ( 22 / 24 )95.66714285714280.312247297675284306.382612657965
Trimmed Mean ( 23 / 24 )95.6650.304163544065461314.518297365089
Trimmed Mean ( 24 / 24 )95.65833333333330.299996175498971318.865176111758
Median95.455
Midrange94.815
Midmean - Weighted Average at Xnp95.5413513513514
Midmean - Weighted Average at X(n+1)p95.6513888888889
Midmean - Empirical Distribution Function95.5413513513514
Midmean - Empirical Distribution Function - Averaging95.6513888888889
Midmean - Empirical Distribution Function - Interpolation95.6513888888889
Midmean - Closest Observation95.5413513513514
Midmean - True Basic - Statistics Graphics Toolkit95.6513888888889
Midmean - MS Excel (old versions)95.6378947368421
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 95.3672222222222 & 0.646221932831065 & 147.576579155126 \tabularnewline
Geometric Mean & 95.2101229682513 &  &  \tabularnewline
Harmonic Mean & 95.0512834772739 &  &  \tabularnewline
Quadratic Mean & 95.5225464077577 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 95.3806944444445 & 0.639706209660928 & 149.100779395279 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 95.3748611111111 & 0.637202291499088 & 149.677523736977 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 95.3565277777778 & 0.628895097617718 & 151.625490704241 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 95.2404166666667 & 0.598260959093986 & 159.195440081699 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 95.3348611111111 & 0.556418410283703 & 171.336640465405 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 95.4990277777778 & 0.516874377440844 & 184.762549559167 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 95.4941666666667 & 0.510270485438712 & 187.144209574583 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 95.4197222222222 & 0.486111087636932 & 196.29200947889 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 95.3672222222222 & 0.466578010618851 & 204.397164143528 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 95.3908333333333 & 0.456516747863441 & 208.953633748981 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 95.4061111111111 & 0.452414776191684 & 210.881951987104 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 95.3611111111111 & 0.434430065521767 & 219.50854390471 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 95.3611111111111 & 0.432155203979889 & 220.664035126484 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 95.3377777777778 & 0.419079783238442 & 227.493144720689 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 95.4106944444444 & 0.391851086658403 & 243.487124810806 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 95.5373611111111 & 0.370738223972419 & 257.69493117661 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 95.5231944444444 & 0.365937058262611 & 261.037225631007 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 95.5706944444444 & 0.352236723199249 & 271.325186018106 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 95.5469444444444 & 0.34050768956735 & 280.601429488557 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 95.6552777777778 & 0.316082360123356 & 302.627700389375 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 95.7544444444445 & 0.280420534918725 & 341.46730542468 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 95.6841666666667 & 0.269870408098867 & 354.555978703722 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 95.7161111111111 & 0.242419384302463 & 394.836870766438 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 95.7161111111111 & 0.241534653562383 & 396.283140739429 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 95.383 & 0.6173159812478 & 154.512442407856 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 95.3854411764706 & 0.590618284162143 & 161.50099604821 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 95.3912121212121 & 0.560155927140851 & 170.294033320522 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 95.40421875 & 0.527235405536808 & 180.951843802795 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 95.4517741935484 & 0.499329244650643 & 191.159991560942 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 95.4798333333333 & 0.479753143424027 & 199.018671669117 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 95.4758620689655 & 0.467629917277688 & 204.169704591997 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 95.4725 & 0.45444201907537 & 210.087307054601 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 95.4812962962963 & 0.444138708753581 & 214.980803101474 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 95.4988461538462 & 0.435731268789337 & 219.169137021509 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 95.5144 & 0.427250646695872 & 223.555893334878 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 95.5291666666667 & 0.417205732849464 & 228.973763170065 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 95.5510869565217 & 0.408138134741212 & 234.114577450862 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 95.575 & 0.396652150023661 & 240.95419625054 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 95.6040476190476 & 0.384425459279953 & 248.693330036253 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 95.62725 & 0.37460902481702 & 255.27214686488 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 95.6378947368421 & 0.36629438018894 & 261.095719479809 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 95.6513888888889 & 0.355693187027893 & 268.915437172509 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 95.6608823529412 & 0.344298187629304 & 277.843119104468 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 95.674375 & 0.331104255064435 & 288.955437861653 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 95.6766666666667 & 0.319217193863735 & 299.722785945886 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 95.6671428571428 & 0.312247297675284 & 306.382612657965 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 95.665 & 0.304163544065461 & 314.518297365089 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 95.6583333333333 & 0.299996175498971 & 318.865176111758 \tabularnewline
Median & 95.455 &  &  \tabularnewline
Midrange & 94.815 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 95.5413513513514 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 95.6513888888889 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 95.5413513513514 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 95.6513888888889 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 95.6513888888889 &  &  \tabularnewline
Midmean - Closest Observation & 95.5413513513514 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 95.6513888888889 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 95.6378947368421 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]95.3672222222222[/C][C]0.646221932831065[/C][C]147.576579155126[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]95.2101229682513[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]95.0512834772739[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]95.5225464077577[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]95.3806944444445[/C][C]0.639706209660928[/C][C]149.100779395279[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]95.3748611111111[/C][C]0.637202291499088[/C][C]149.677523736977[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]95.3565277777778[/C][C]0.628895097617718[/C][C]151.625490704241[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]95.2404166666667[/C][C]0.598260959093986[/C][C]159.195440081699[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]95.3348611111111[/C][C]0.556418410283703[/C][C]171.336640465405[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]95.4990277777778[/C][C]0.516874377440844[/C][C]184.762549559167[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]95.4941666666667[/C][C]0.510270485438712[/C][C]187.144209574583[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]95.4197222222222[/C][C]0.486111087636932[/C][C]196.29200947889[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]95.3672222222222[/C][C]0.466578010618851[/C][C]204.397164143528[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]95.3908333333333[/C][C]0.456516747863441[/C][C]208.953633748981[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]95.4061111111111[/C][C]0.452414776191684[/C][C]210.881951987104[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]95.3611111111111[/C][C]0.434430065521767[/C][C]219.50854390471[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]95.3611111111111[/C][C]0.432155203979889[/C][C]220.664035126484[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]95.3377777777778[/C][C]0.419079783238442[/C][C]227.493144720689[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]95.4106944444444[/C][C]0.391851086658403[/C][C]243.487124810806[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]95.5373611111111[/C][C]0.370738223972419[/C][C]257.69493117661[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]95.5231944444444[/C][C]0.365937058262611[/C][C]261.037225631007[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]95.5706944444444[/C][C]0.352236723199249[/C][C]271.325186018106[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]95.5469444444444[/C][C]0.34050768956735[/C][C]280.601429488557[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]95.6552777777778[/C][C]0.316082360123356[/C][C]302.627700389375[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]95.7544444444445[/C][C]0.280420534918725[/C][C]341.46730542468[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]95.6841666666667[/C][C]0.269870408098867[/C][C]354.555978703722[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]95.7161111111111[/C][C]0.242419384302463[/C][C]394.836870766438[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]95.7161111111111[/C][C]0.241534653562383[/C][C]396.283140739429[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]95.383[/C][C]0.6173159812478[/C][C]154.512442407856[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]95.3854411764706[/C][C]0.590618284162143[/C][C]161.50099604821[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]95.3912121212121[/C][C]0.560155927140851[/C][C]170.294033320522[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]95.40421875[/C][C]0.527235405536808[/C][C]180.951843802795[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]95.4517741935484[/C][C]0.499329244650643[/C][C]191.159991560942[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]95.4798333333333[/C][C]0.479753143424027[/C][C]199.018671669117[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]95.4758620689655[/C][C]0.467629917277688[/C][C]204.169704591997[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]95.4725[/C][C]0.45444201907537[/C][C]210.087307054601[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]95.4812962962963[/C][C]0.444138708753581[/C][C]214.980803101474[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]95.4988461538462[/C][C]0.435731268789337[/C][C]219.169137021509[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]95.5144[/C][C]0.427250646695872[/C][C]223.555893334878[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]95.5291666666667[/C][C]0.417205732849464[/C][C]228.973763170065[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]95.5510869565217[/C][C]0.408138134741212[/C][C]234.114577450862[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]95.575[/C][C]0.396652150023661[/C][C]240.95419625054[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]95.6040476190476[/C][C]0.384425459279953[/C][C]248.693330036253[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]95.62725[/C][C]0.37460902481702[/C][C]255.27214686488[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]95.6378947368421[/C][C]0.36629438018894[/C][C]261.095719479809[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]95.6513888888889[/C][C]0.355693187027893[/C][C]268.915437172509[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]95.6608823529412[/C][C]0.344298187629304[/C][C]277.843119104468[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]95.674375[/C][C]0.331104255064435[/C][C]288.955437861653[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]95.6766666666667[/C][C]0.319217193863735[/C][C]299.722785945886[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]95.6671428571428[/C][C]0.312247297675284[/C][C]306.382612657965[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]95.665[/C][C]0.304163544065461[/C][C]314.518297365089[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]95.6583333333333[/C][C]0.299996175498971[/C][C]318.865176111758[/C][/ROW]
[ROW][C]Median[/C][C]95.455[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]94.815[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]95.5413513513514[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]95.6513888888889[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]95.5413513513514[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]95.6513888888889[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]95.6513888888889[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]95.5413513513514[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]95.6513888888889[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]95.6378947368421[/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=&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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 Mean95.36722222222220.646221932831065147.576579155126
Geometric Mean95.2101229682513
Harmonic Mean95.0512834772739
Quadratic Mean95.5225464077577
Winsorized Mean ( 1 / 24 )95.38069444444450.639706209660928149.100779395279
Winsorized Mean ( 2 / 24 )95.37486111111110.637202291499088149.677523736977
Winsorized Mean ( 3 / 24 )95.35652777777780.628895097617718151.625490704241
Winsorized Mean ( 4 / 24 )95.24041666666670.598260959093986159.195440081699
Winsorized Mean ( 5 / 24 )95.33486111111110.556418410283703171.336640465405
Winsorized Mean ( 6 / 24 )95.49902777777780.516874377440844184.762549559167
Winsorized Mean ( 7 / 24 )95.49416666666670.510270485438712187.144209574583
Winsorized Mean ( 8 / 24 )95.41972222222220.486111087636932196.29200947889
Winsorized Mean ( 9 / 24 )95.36722222222220.466578010618851204.397164143528
Winsorized Mean ( 10 / 24 )95.39083333333330.456516747863441208.953633748981
Winsorized Mean ( 11 / 24 )95.40611111111110.452414776191684210.881951987104
Winsorized Mean ( 12 / 24 )95.36111111111110.434430065521767219.50854390471
Winsorized Mean ( 13 / 24 )95.36111111111110.432155203979889220.664035126484
Winsorized Mean ( 14 / 24 )95.33777777777780.419079783238442227.493144720689
Winsorized Mean ( 15 / 24 )95.41069444444440.391851086658403243.487124810806
Winsorized Mean ( 16 / 24 )95.53736111111110.370738223972419257.69493117661
Winsorized Mean ( 17 / 24 )95.52319444444440.365937058262611261.037225631007
Winsorized Mean ( 18 / 24 )95.57069444444440.352236723199249271.325186018106
Winsorized Mean ( 19 / 24 )95.54694444444440.34050768956735280.601429488557
Winsorized Mean ( 20 / 24 )95.65527777777780.316082360123356302.627700389375
Winsorized Mean ( 21 / 24 )95.75444444444450.280420534918725341.46730542468
Winsorized Mean ( 22 / 24 )95.68416666666670.269870408098867354.555978703722
Winsorized Mean ( 23 / 24 )95.71611111111110.242419384302463394.836870766438
Winsorized Mean ( 24 / 24 )95.71611111111110.241534653562383396.283140739429
Trimmed Mean ( 1 / 24 )95.3830.6173159812478154.512442407856
Trimmed Mean ( 2 / 24 )95.38544117647060.590618284162143161.50099604821
Trimmed Mean ( 3 / 24 )95.39121212121210.560155927140851170.294033320522
Trimmed Mean ( 4 / 24 )95.404218750.527235405536808180.951843802795
Trimmed Mean ( 5 / 24 )95.45177419354840.499329244650643191.159991560942
Trimmed Mean ( 6 / 24 )95.47983333333330.479753143424027199.018671669117
Trimmed Mean ( 7 / 24 )95.47586206896550.467629917277688204.169704591997
Trimmed Mean ( 8 / 24 )95.47250.45444201907537210.087307054601
Trimmed Mean ( 9 / 24 )95.48129629629630.444138708753581214.980803101474
Trimmed Mean ( 10 / 24 )95.49884615384620.435731268789337219.169137021509
Trimmed Mean ( 11 / 24 )95.51440.427250646695872223.555893334878
Trimmed Mean ( 12 / 24 )95.52916666666670.417205732849464228.973763170065
Trimmed Mean ( 13 / 24 )95.55108695652170.408138134741212234.114577450862
Trimmed Mean ( 14 / 24 )95.5750.396652150023661240.95419625054
Trimmed Mean ( 15 / 24 )95.60404761904760.384425459279953248.693330036253
Trimmed Mean ( 16 / 24 )95.627250.37460902481702255.27214686488
Trimmed Mean ( 17 / 24 )95.63789473684210.36629438018894261.095719479809
Trimmed Mean ( 18 / 24 )95.65138888888890.355693187027893268.915437172509
Trimmed Mean ( 19 / 24 )95.66088235294120.344298187629304277.843119104468
Trimmed Mean ( 20 / 24 )95.6743750.331104255064435288.955437861653
Trimmed Mean ( 21 / 24 )95.67666666666670.319217193863735299.722785945886
Trimmed Mean ( 22 / 24 )95.66714285714280.312247297675284306.382612657965
Trimmed Mean ( 23 / 24 )95.6650.304163544065461314.518297365089
Trimmed Mean ( 24 / 24 )95.65833333333330.299996175498971318.865176111758
Median95.455
Midrange94.815
Midmean - Weighted Average at Xnp95.5413513513514
Midmean - Weighted Average at X(n+1)p95.6513888888889
Midmean - Empirical Distribution Function95.5413513513514
Midmean - Empirical Distribution Function - Averaging95.6513888888889
Midmean - Empirical Distribution Function - Interpolation95.6513888888889
Midmean - Closest Observation95.5413513513514
Midmean - True Basic - Statistics Graphics Toolkit95.6513888888889
Midmean - MS Excel (old versions)95.6378947368421
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')