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Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationThu, 15 Oct 2009 16:38:02 -0600
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2009/Oct/16/t1255646340s1to0inpkerrkz5.htm/, Retrieved Tue, 30 Apr 2024 03:29:13 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=46910, Retrieved Tue, 30 Apr 2024 03:29:13 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact124
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [central tendensy] [2009-10-15 22:38:02] [ea241b681aafed79da4b5b99fad98471] [Current]
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Dataseries X:
0.384535633
0.3808246
0.377188781
0.37535941
0.373115667
0.375267632
0.406847169
0.426199688
0.397190396
0.399886149
0.393113384
0.39838006
0.398133245
0.390841886
0.388728808
0.386805095
0.382658744
0.385661163
0.413132818
0.422725018
0.395751888
0.393901819
0.385024286
0.388191399
0.369521476
0.371671593
0.366696045
0.374031922
0.368629916
0.369072262
0.38744478
0.384519877
0.37195362
0.355320145
0.349844982
0.349192677
0.347109045
0.338315836
0.334991621
0.328202632
0.327376829
0.337007833
0.364266911
0.358468343
0.336958629
0.329132753
0.326459362
0.33309545
0.328291309
0.32347245
0.328677972
0.325577316
0.321718862
0.331073328
0.353023114
0.350585656
0.336580139
0.334592452
0.332413433
0.344938689
0.35290465
0.355261923
0.357179083
0.352085139
0.355244587
0.36423704
0.381083247
0.380323972
0.368850158




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'RServer@AstonUniversity' @ vre.aston.ac.uk

\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 & 'RServer@AstonUniversity' @ vre.aston.ac.uk \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=46910&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]'RServer@AstonUniversity' @ vre.aston.ac.uk[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=46910&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=46910&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'RServer@AstonUniversity' @ vre.aston.ac.uk







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean0.3648820840.00319865434564989114.073621145165
Geometric Mean0.363930914060253
Harmonic Mean0.362983041715212
Quadratic Mean0.36583421070007
Winsorized Mean ( 1 / 23 )0.3648571407826090.00317986283360936114.739899132212
Winsorized Mean ( 2 / 23 )0.3646401166086960.00309910752995056117.659717542783
Winsorized Mean ( 3 / 23 )0.3644051773478260.00303242055937286120.169735764880
Winsorized Mean ( 4 / 23 )0.3640548264492750.00294494550689854123.620225092952
Winsorized Mean ( 5 / 23 )0.3640055303623190.00291483152599228124.880469802934
Winsorized Mean ( 6 / 23 )0.3639917792318840.00290972670108673125.094834197294
Winsorized Mean ( 7 / 23 )0.3639353545652170.00288630803378592126.090268365380
Winsorized Mean ( 8 / 23 )0.3638212992608700.00284897458698277127.702542845838
Winsorized Mean ( 9 / 23 )0.3638331043913040.00276506287868588131.582217242097
Winsorized Mean ( 10 / 23 )0.3639130565652170.00271338233862038134.117868825758
Winsorized Mean ( 11 / 23 )0.3636596610434780.00263874057765266137.815617087671
Winsorized Mean ( 12 / 23 )0.3635525173913040.00254009715448946143.125437839552
Winsorized Mean ( 13 / 23 )0.3635264721739130.00251282575148180144.668396509206
Winsorized Mean ( 14 / 23 )0.3636972922608700.00243775740602807149.193390351936
Winsorized Mean ( 15 / 23 )0.3636405107391300.00240450149871012151.233222742512
Winsorized Mean ( 16 / 23 )0.3633866607681160.00236547505100406153.621007591634
Winsorized Mean ( 17 / 23 )0.3635520106521740.00229126921775765158.668395592537
Winsorized Mean ( 18 / 23 )0.3651522367391300.00200463657213715182.153833674619
Winsorized Mean ( 19 / 23 )0.3657455323913040.00191694819476285190.795731147315
Winsorized Mean ( 20 / 23 )0.3658100248550730.00175470028228709208.474363712003
Winsorized Mean ( 21 / 23 )0.3655290533768120.00166017486180427220.175032032201
Winsorized Mean ( 22 / 23 )0.3656827431449280.00161618504586865226.262917157723
Winsorized Mean ( 23 / 23 )0.3660156948115940.00152525956977460239.969446555044
Trimmed Mean ( 1 / 23 )0.3646111230746270.00309570867275406117.77953341787
Trimmed Mean ( 2 / 23 )0.3643499658153850.00299453830880380121.671499324024
Trimmed Mean ( 3 / 23 )0.3641910737142860.00292503734961024124.508178934130
Trimmed Mean ( 4 / 23 )0.3641103461147540.00287135383569861126.807898625341
Trimmed Mean ( 5 / 23 )0.3641265785593220.00283720727125701128.339787596131
Trimmed Mean ( 6 / 23 )0.3641558849649120.00280319075324846129.907636340093
Trimmed Mean ( 7 / 23 )0.3641901979818180.00276105395687553131.902600843753
Trimmed Mean ( 8 / 23 )0.3642375947358490.00271340969070675134.236122168849
Trimmed Mean ( 9 / 23 )0.3643079976470590.00266167797481015136.871552868090
Trimmed Mean ( 10 / 23 )0.3643823006734690.00261511684446387139.336910105893
Trimmed Mean ( 11 / 23 )0.3643823006734690.0025661674661549141.994747217123
Trimmed Mean ( 12 / 23 )0.3645615240.00251832042352713144.763756269506
Trimmed Mean ( 13 / 23 )0.3646964493023260.00247624942517519147.277752230684
Trimmed Mean ( 14 / 23 )0.3648479097560980.00242430792471874150.49569653922
Trimmed Mean ( 15 / 23 )0.3649933174615380.00237056440231574153.968952332612
Trimmed Mean ( 16 / 23 )0.3651615042432430.00230312931943952158.550152247685
Trimmed Mean ( 17 / 23 )0.3653801903142860.00221737371535706164.780608601852
Trimmed Mean ( 18 / 23 )0.3656050466363640.00211660322064956172.731971240299
Trimmed Mean ( 19 / 23 )0.3656610392580650.00205968133042543177.532822119884
Trimmed Mean ( 20 / 23 )0.3656504584482760.00199922755450176182.895867768990
Trimmed Mean ( 21 / 23 )0.3656300694074070.00195582991822708186.943693825302
Trimmed Mean ( 22 / 23 )0.3656300694074070.00191370753640146191.058488537354
Trimmed Mean ( 23 / 23 )0.3656379734347830.00185446835434478197.165927678485
Median0.368629916
Midrange0.373959275
Midmean - Weighted Average at Xnp0.364802422794118
Midmean - Weighted Average at X(n+1)p0.365380190314286
Midmean - Empirical Distribution Function0.365380190314286
Midmean - Empirical Distribution Function - Averaging0.365380190314286
Midmean - Empirical Distribution Function - Interpolation0.365380190314286
Midmean - Closest Observation0.364592069277778
Midmean - True Basic - Statistics Graphics Toolkit0.365380190314286
Midmean - MS Excel (old versions)0.365380190314286
Number of observations69

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 0.364882084 & 0.00319865434564989 & 114.073621145165 \tabularnewline
Geometric Mean & 0.363930914060253 &  &  \tabularnewline
Harmonic Mean & 0.362983041715212 &  &  \tabularnewline
Quadratic Mean & 0.36583421070007 &  &  \tabularnewline
Winsorized Mean ( 1 / 23 ) & 0.364857140782609 & 0.00317986283360936 & 114.739899132212 \tabularnewline
Winsorized Mean ( 2 / 23 ) & 0.364640116608696 & 0.00309910752995056 & 117.659717542783 \tabularnewline
Winsorized Mean ( 3 / 23 ) & 0.364405177347826 & 0.00303242055937286 & 120.169735764880 \tabularnewline
Winsorized Mean ( 4 / 23 ) & 0.364054826449275 & 0.00294494550689854 & 123.620225092952 \tabularnewline
Winsorized Mean ( 5 / 23 ) & 0.364005530362319 & 0.00291483152599228 & 124.880469802934 \tabularnewline
Winsorized Mean ( 6 / 23 ) & 0.363991779231884 & 0.00290972670108673 & 125.094834197294 \tabularnewline
Winsorized Mean ( 7 / 23 ) & 0.363935354565217 & 0.00288630803378592 & 126.090268365380 \tabularnewline
Winsorized Mean ( 8 / 23 ) & 0.363821299260870 & 0.00284897458698277 & 127.702542845838 \tabularnewline
Winsorized Mean ( 9 / 23 ) & 0.363833104391304 & 0.00276506287868588 & 131.582217242097 \tabularnewline
Winsorized Mean ( 10 / 23 ) & 0.363913056565217 & 0.00271338233862038 & 134.117868825758 \tabularnewline
Winsorized Mean ( 11 / 23 ) & 0.363659661043478 & 0.00263874057765266 & 137.815617087671 \tabularnewline
Winsorized Mean ( 12 / 23 ) & 0.363552517391304 & 0.00254009715448946 & 143.125437839552 \tabularnewline
Winsorized Mean ( 13 / 23 ) & 0.363526472173913 & 0.00251282575148180 & 144.668396509206 \tabularnewline
Winsorized Mean ( 14 / 23 ) & 0.363697292260870 & 0.00243775740602807 & 149.193390351936 \tabularnewline
Winsorized Mean ( 15 / 23 ) & 0.363640510739130 & 0.00240450149871012 & 151.233222742512 \tabularnewline
Winsorized Mean ( 16 / 23 ) & 0.363386660768116 & 0.00236547505100406 & 153.621007591634 \tabularnewline
Winsorized Mean ( 17 / 23 ) & 0.363552010652174 & 0.00229126921775765 & 158.668395592537 \tabularnewline
Winsorized Mean ( 18 / 23 ) & 0.365152236739130 & 0.00200463657213715 & 182.153833674619 \tabularnewline
Winsorized Mean ( 19 / 23 ) & 0.365745532391304 & 0.00191694819476285 & 190.795731147315 \tabularnewline
Winsorized Mean ( 20 / 23 ) & 0.365810024855073 & 0.00175470028228709 & 208.474363712003 \tabularnewline
Winsorized Mean ( 21 / 23 ) & 0.365529053376812 & 0.00166017486180427 & 220.175032032201 \tabularnewline
Winsorized Mean ( 22 / 23 ) & 0.365682743144928 & 0.00161618504586865 & 226.262917157723 \tabularnewline
Winsorized Mean ( 23 / 23 ) & 0.366015694811594 & 0.00152525956977460 & 239.969446555044 \tabularnewline
Trimmed Mean ( 1 / 23 ) & 0.364611123074627 & 0.00309570867275406 & 117.77953341787 \tabularnewline
Trimmed Mean ( 2 / 23 ) & 0.364349965815385 & 0.00299453830880380 & 121.671499324024 \tabularnewline
Trimmed Mean ( 3 / 23 ) & 0.364191073714286 & 0.00292503734961024 & 124.508178934130 \tabularnewline
Trimmed Mean ( 4 / 23 ) & 0.364110346114754 & 0.00287135383569861 & 126.807898625341 \tabularnewline
Trimmed Mean ( 5 / 23 ) & 0.364126578559322 & 0.00283720727125701 & 128.339787596131 \tabularnewline
Trimmed Mean ( 6 / 23 ) & 0.364155884964912 & 0.00280319075324846 & 129.907636340093 \tabularnewline
Trimmed Mean ( 7 / 23 ) & 0.364190197981818 & 0.00276105395687553 & 131.902600843753 \tabularnewline
Trimmed Mean ( 8 / 23 ) & 0.364237594735849 & 0.00271340969070675 & 134.236122168849 \tabularnewline
Trimmed Mean ( 9 / 23 ) & 0.364307997647059 & 0.00266167797481015 & 136.871552868090 \tabularnewline
Trimmed Mean ( 10 / 23 ) & 0.364382300673469 & 0.00261511684446387 & 139.336910105893 \tabularnewline
Trimmed Mean ( 11 / 23 ) & 0.364382300673469 & 0.0025661674661549 & 141.994747217123 \tabularnewline
Trimmed Mean ( 12 / 23 ) & 0.364561524 & 0.00251832042352713 & 144.763756269506 \tabularnewline
Trimmed Mean ( 13 / 23 ) & 0.364696449302326 & 0.00247624942517519 & 147.277752230684 \tabularnewline
Trimmed Mean ( 14 / 23 ) & 0.364847909756098 & 0.00242430792471874 & 150.49569653922 \tabularnewline
Trimmed Mean ( 15 / 23 ) & 0.364993317461538 & 0.00237056440231574 & 153.968952332612 \tabularnewline
Trimmed Mean ( 16 / 23 ) & 0.365161504243243 & 0.00230312931943952 & 158.550152247685 \tabularnewline
Trimmed Mean ( 17 / 23 ) & 0.365380190314286 & 0.00221737371535706 & 164.780608601852 \tabularnewline
Trimmed Mean ( 18 / 23 ) & 0.365605046636364 & 0.00211660322064956 & 172.731971240299 \tabularnewline
Trimmed Mean ( 19 / 23 ) & 0.365661039258065 & 0.00205968133042543 & 177.532822119884 \tabularnewline
Trimmed Mean ( 20 / 23 ) & 0.365650458448276 & 0.00199922755450176 & 182.895867768990 \tabularnewline
Trimmed Mean ( 21 / 23 ) & 0.365630069407407 & 0.00195582991822708 & 186.943693825302 \tabularnewline
Trimmed Mean ( 22 / 23 ) & 0.365630069407407 & 0.00191370753640146 & 191.058488537354 \tabularnewline
Trimmed Mean ( 23 / 23 ) & 0.365637973434783 & 0.00185446835434478 & 197.165927678485 \tabularnewline
Median & 0.368629916 &  &  \tabularnewline
Midrange & 0.373959275 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 0.364802422794118 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 0.365380190314286 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 0.365380190314286 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 0.365380190314286 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 0.365380190314286 &  &  \tabularnewline
Midmean - Closest Observation & 0.364592069277778 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 0.365380190314286 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 0.365380190314286 &  &  \tabularnewline
Number of observations & 69 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=46910&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]0.364882084[/C][C]0.00319865434564989[/C][C]114.073621145165[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]0.363930914060253[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]0.362983041715212[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]0.36583421070007[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 23 )[/C][C]0.364857140782609[/C][C]0.00317986283360936[/C][C]114.739899132212[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 23 )[/C][C]0.364640116608696[/C][C]0.00309910752995056[/C][C]117.659717542783[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 23 )[/C][C]0.364405177347826[/C][C]0.00303242055937286[/C][C]120.169735764880[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 23 )[/C][C]0.364054826449275[/C][C]0.00294494550689854[/C][C]123.620225092952[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 23 )[/C][C]0.364005530362319[/C][C]0.00291483152599228[/C][C]124.880469802934[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 23 )[/C][C]0.363991779231884[/C][C]0.00290972670108673[/C][C]125.094834197294[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 23 )[/C][C]0.363935354565217[/C][C]0.00288630803378592[/C][C]126.090268365380[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 23 )[/C][C]0.363821299260870[/C][C]0.00284897458698277[/C][C]127.702542845838[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 23 )[/C][C]0.363833104391304[/C][C]0.00276506287868588[/C][C]131.582217242097[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 23 )[/C][C]0.363913056565217[/C][C]0.00271338233862038[/C][C]134.117868825758[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 23 )[/C][C]0.363659661043478[/C][C]0.00263874057765266[/C][C]137.815617087671[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 23 )[/C][C]0.363552517391304[/C][C]0.00254009715448946[/C][C]143.125437839552[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 23 )[/C][C]0.363526472173913[/C][C]0.00251282575148180[/C][C]144.668396509206[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 23 )[/C][C]0.363697292260870[/C][C]0.00243775740602807[/C][C]149.193390351936[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 23 )[/C][C]0.363640510739130[/C][C]0.00240450149871012[/C][C]151.233222742512[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 23 )[/C][C]0.363386660768116[/C][C]0.00236547505100406[/C][C]153.621007591634[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 23 )[/C][C]0.363552010652174[/C][C]0.00229126921775765[/C][C]158.668395592537[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 23 )[/C][C]0.365152236739130[/C][C]0.00200463657213715[/C][C]182.153833674619[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 23 )[/C][C]0.365745532391304[/C][C]0.00191694819476285[/C][C]190.795731147315[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 23 )[/C][C]0.365810024855073[/C][C]0.00175470028228709[/C][C]208.474363712003[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 23 )[/C][C]0.365529053376812[/C][C]0.00166017486180427[/C][C]220.175032032201[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 23 )[/C][C]0.365682743144928[/C][C]0.00161618504586865[/C][C]226.262917157723[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 23 )[/C][C]0.366015694811594[/C][C]0.00152525956977460[/C][C]239.969446555044[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 23 )[/C][C]0.364611123074627[/C][C]0.00309570867275406[/C][C]117.77953341787[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 23 )[/C][C]0.364349965815385[/C][C]0.00299453830880380[/C][C]121.671499324024[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 23 )[/C][C]0.364191073714286[/C][C]0.00292503734961024[/C][C]124.508178934130[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 23 )[/C][C]0.364110346114754[/C][C]0.00287135383569861[/C][C]126.807898625341[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 23 )[/C][C]0.364126578559322[/C][C]0.00283720727125701[/C][C]128.339787596131[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 23 )[/C][C]0.364155884964912[/C][C]0.00280319075324846[/C][C]129.907636340093[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 23 )[/C][C]0.364190197981818[/C][C]0.00276105395687553[/C][C]131.902600843753[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 23 )[/C][C]0.364237594735849[/C][C]0.00271340969070675[/C][C]134.236122168849[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 23 )[/C][C]0.364307997647059[/C][C]0.00266167797481015[/C][C]136.871552868090[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 23 )[/C][C]0.364382300673469[/C][C]0.00261511684446387[/C][C]139.336910105893[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 23 )[/C][C]0.364382300673469[/C][C]0.0025661674661549[/C][C]141.994747217123[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 23 )[/C][C]0.364561524[/C][C]0.00251832042352713[/C][C]144.763756269506[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 23 )[/C][C]0.364696449302326[/C][C]0.00247624942517519[/C][C]147.277752230684[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 23 )[/C][C]0.364847909756098[/C][C]0.00242430792471874[/C][C]150.49569653922[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 23 )[/C][C]0.364993317461538[/C][C]0.00237056440231574[/C][C]153.968952332612[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 23 )[/C][C]0.365161504243243[/C][C]0.00230312931943952[/C][C]158.550152247685[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 23 )[/C][C]0.365380190314286[/C][C]0.00221737371535706[/C][C]164.780608601852[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 23 )[/C][C]0.365605046636364[/C][C]0.00211660322064956[/C][C]172.731971240299[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 23 )[/C][C]0.365661039258065[/C][C]0.00205968133042543[/C][C]177.532822119884[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 23 )[/C][C]0.365650458448276[/C][C]0.00199922755450176[/C][C]182.895867768990[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 23 )[/C][C]0.365630069407407[/C][C]0.00195582991822708[/C][C]186.943693825302[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 23 )[/C][C]0.365630069407407[/C][C]0.00191370753640146[/C][C]191.058488537354[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 23 )[/C][C]0.365637973434783[/C][C]0.00185446835434478[/C][C]197.165927678485[/C][/ROW]
[ROW][C]Median[/C][C]0.368629916[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]0.373959275[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]0.364802422794118[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]0.365380190314286[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]0.365380190314286[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]0.365380190314286[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]0.365380190314286[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]0.364592069277778[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]0.365380190314286[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]0.365380190314286[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]69[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=46910&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=46910&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 Mean0.3648820840.00319865434564989114.073621145165
Geometric Mean0.363930914060253
Harmonic Mean0.362983041715212
Quadratic Mean0.36583421070007
Winsorized Mean ( 1 / 23 )0.3648571407826090.00317986283360936114.739899132212
Winsorized Mean ( 2 / 23 )0.3646401166086960.00309910752995056117.659717542783
Winsorized Mean ( 3 / 23 )0.3644051773478260.00303242055937286120.169735764880
Winsorized Mean ( 4 / 23 )0.3640548264492750.00294494550689854123.620225092952
Winsorized Mean ( 5 / 23 )0.3640055303623190.00291483152599228124.880469802934
Winsorized Mean ( 6 / 23 )0.3639917792318840.00290972670108673125.094834197294
Winsorized Mean ( 7 / 23 )0.3639353545652170.00288630803378592126.090268365380
Winsorized Mean ( 8 / 23 )0.3638212992608700.00284897458698277127.702542845838
Winsorized Mean ( 9 / 23 )0.3638331043913040.00276506287868588131.582217242097
Winsorized Mean ( 10 / 23 )0.3639130565652170.00271338233862038134.117868825758
Winsorized Mean ( 11 / 23 )0.3636596610434780.00263874057765266137.815617087671
Winsorized Mean ( 12 / 23 )0.3635525173913040.00254009715448946143.125437839552
Winsorized Mean ( 13 / 23 )0.3635264721739130.00251282575148180144.668396509206
Winsorized Mean ( 14 / 23 )0.3636972922608700.00243775740602807149.193390351936
Winsorized Mean ( 15 / 23 )0.3636405107391300.00240450149871012151.233222742512
Winsorized Mean ( 16 / 23 )0.3633866607681160.00236547505100406153.621007591634
Winsorized Mean ( 17 / 23 )0.3635520106521740.00229126921775765158.668395592537
Winsorized Mean ( 18 / 23 )0.3651522367391300.00200463657213715182.153833674619
Winsorized Mean ( 19 / 23 )0.3657455323913040.00191694819476285190.795731147315
Winsorized Mean ( 20 / 23 )0.3658100248550730.00175470028228709208.474363712003
Winsorized Mean ( 21 / 23 )0.3655290533768120.00166017486180427220.175032032201
Winsorized Mean ( 22 / 23 )0.3656827431449280.00161618504586865226.262917157723
Winsorized Mean ( 23 / 23 )0.3660156948115940.00152525956977460239.969446555044
Trimmed Mean ( 1 / 23 )0.3646111230746270.00309570867275406117.77953341787
Trimmed Mean ( 2 / 23 )0.3643499658153850.00299453830880380121.671499324024
Trimmed Mean ( 3 / 23 )0.3641910737142860.00292503734961024124.508178934130
Trimmed Mean ( 4 / 23 )0.3641103461147540.00287135383569861126.807898625341
Trimmed Mean ( 5 / 23 )0.3641265785593220.00283720727125701128.339787596131
Trimmed Mean ( 6 / 23 )0.3641558849649120.00280319075324846129.907636340093
Trimmed Mean ( 7 / 23 )0.3641901979818180.00276105395687553131.902600843753
Trimmed Mean ( 8 / 23 )0.3642375947358490.00271340969070675134.236122168849
Trimmed Mean ( 9 / 23 )0.3643079976470590.00266167797481015136.871552868090
Trimmed Mean ( 10 / 23 )0.3643823006734690.00261511684446387139.336910105893
Trimmed Mean ( 11 / 23 )0.3643823006734690.0025661674661549141.994747217123
Trimmed Mean ( 12 / 23 )0.3645615240.00251832042352713144.763756269506
Trimmed Mean ( 13 / 23 )0.3646964493023260.00247624942517519147.277752230684
Trimmed Mean ( 14 / 23 )0.3648479097560980.00242430792471874150.49569653922
Trimmed Mean ( 15 / 23 )0.3649933174615380.00237056440231574153.968952332612
Trimmed Mean ( 16 / 23 )0.3651615042432430.00230312931943952158.550152247685
Trimmed Mean ( 17 / 23 )0.3653801903142860.00221737371535706164.780608601852
Trimmed Mean ( 18 / 23 )0.3656050466363640.00211660322064956172.731971240299
Trimmed Mean ( 19 / 23 )0.3656610392580650.00205968133042543177.532822119884
Trimmed Mean ( 20 / 23 )0.3656504584482760.00199922755450176182.895867768990
Trimmed Mean ( 21 / 23 )0.3656300694074070.00195582991822708186.943693825302
Trimmed Mean ( 22 / 23 )0.3656300694074070.00191370753640146191.058488537354
Trimmed Mean ( 23 / 23 )0.3656379734347830.00185446835434478197.165927678485
Median0.368629916
Midrange0.373959275
Midmean - Weighted Average at Xnp0.364802422794118
Midmean - Weighted Average at X(n+1)p0.365380190314286
Midmean - Empirical Distribution Function0.365380190314286
Midmean - Empirical Distribution Function - Averaging0.365380190314286
Midmean - Empirical Distribution Function - Interpolation0.365380190314286
Midmean - Closest Observation0.364592069277778
Midmean - True Basic - Statistics Graphics Toolkit0.365380190314286
Midmean - MS Excel (old versions)0.365380190314286
Number of observations69



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')