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Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationTue, 05 Mar 2013 13:11:18 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2013/Mar/05/t1362507094r898opauop0ghcc.htm/, Retrieved Sat, 04 May 2024 08:02:02 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=207438, Retrieved Sat, 04 May 2024 08:02:02 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact54
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [] [2013-03-05 18:11:18] [01f42343b359ee979b76c94d8b15b060] [Current]
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Dataseries X:
22,38
22,38
22,38
22,38
22,41
22,41
22,41
22,41
22,41
22,41
22,41
22,41
22,41
22,41
22,41
22,41
23,11
23,11
23,11
23,11
23,11
23,11
23,11
23,11
23,11
23,11
23,11
23,11
23,82
23,82
23,82
23,82
23,82
23,82
23,82
23,82
23,82
23,82
23,82
23,82
26,1
26,1
26,1
26,1
26,1
26,1
26,1
26,1
26,1
26,1
26,1
26,1
27,07
27,07
27,07
27,07
27,07
27,07
27,07
27,07
27,07
27,07
27,07
27,07
27,45
27,45
27,45
27,45
27,45
27,45
27,45
27,45




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'George Udny Yule' @ yule.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 3 seconds \tabularnewline
R Server & 'George Udny Yule' @ yule.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=207438&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'George Udny Yule' @ yule.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=207438&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=207438&T=0

As an alternative you can also use a QR Code:  

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

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'George Udny Yule' @ yule.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean24.71166666666670.232148989583483106.447444423531
Geometric Mean24.6347968891103
Harmonic Mean24.5587561481405
Quadratic Mean24.7889669678535
Winsorized Mean ( 1 / 24 )24.71166666666670.232148989583483106.447444423531
Winsorized Mean ( 2 / 24 )24.71166666666670.232148989583483106.447444423531
Winsorized Mean ( 3 / 24 )24.71166666666670.232148989583483106.447444423531
Winsorized Mean ( 4 / 24 )24.71333333333330.231914532851503106.562245278339
Winsorized Mean ( 5 / 24 )24.71333333333330.231914532851503106.562245278339
Winsorized Mean ( 6 / 24 )24.71333333333330.231914532851503106.562245278339
Winsorized Mean ( 7 / 24 )24.71333333333330.231914532851503106.562245278339
Winsorized Mean ( 8 / 24 )24.67111111111110.225233972901785109.53547900995
Winsorized Mean ( 9 / 24 )24.67111111111110.225233972901785109.53547900995
Winsorized Mean ( 10 / 24 )24.67111111111110.225233972901785109.53547900995
Winsorized Mean ( 11 / 24 )24.67111111111110.225233972901785109.53547900995
Winsorized Mean ( 12 / 24 )24.67111111111110.225233972901785109.53547900995
Winsorized Mean ( 13 / 24 )24.67111111111110.225233972901785109.53547900995
Winsorized Mean ( 14 / 24 )24.67111111111110.225233972901785109.53547900995
Winsorized Mean ( 15 / 24 )24.67111111111110.225233972901785109.53547900995
Winsorized Mean ( 16 / 24 )24.82666666666670.204976429043009121.119617424194
Winsorized Mean ( 17 / 24 )24.82666666666670.204976429043009121.119617424194
Winsorized Mean ( 18 / 24 )24.82666666666670.204976429043009121.119617424194
Winsorized Mean ( 19 / 24 )24.82666666666670.204976429043009121.119617424194
Winsorized Mean ( 20 / 24 )24.55722222222220.166274094259568147.691210296935
Winsorized Mean ( 21 / 24 )24.55722222222220.166274094259568147.691210296935
Winsorized Mean ( 22 / 24 )24.55722222222220.166274094259568147.691210296935
Winsorized Mean ( 23 / 24 )24.55722222222220.166274094259568147.691210296935
Winsorized Mean ( 24 / 24 )24.55722222222220.166274094259568147.691210296935
Trimmed Mean ( 1 / 24 )24.70585714285710.233154752086647105.963343752375
Trimmed Mean ( 2 / 24 )24.69970588235290.234071960392851105.521848242304
Trimmed Mean ( 3 / 24 )24.69318181818180.234880236217404105.130947651662
Trimmed Mean ( 4 / 24 )24.686250.235554847773345104.800432822141
Trimmed Mean ( 5 / 24 )24.67838709677420.236142339093285104.506405719244
Trimmed Mean ( 6 / 24 )24.670.236538598276426104.295874668074
Trimmed Mean ( 7 / 24 )24.66103448275860.23669951413393104.187093805376
Trimmed Mean ( 8 / 24 )24.65142857142860.236570111044703104.203478886521
Trimmed Mean ( 9 / 24 )24.64814814814810.237547608097395103.760877011409
Trimmed Mean ( 10 / 24 )24.64461538461540.238319984259231103.409772626573
Trimmed Mean ( 11 / 24 )24.64080.238829943769236103.172992511394
Trimmed Mean ( 12 / 24 )24.63666666666670.239003793356446103.080651234368
Trimmed Mean ( 13 / 24 )24.63217391304350.238745698404424103.17326794855
Trimmed Mean ( 14 / 24 )24.62727272727270.237929396770125103.506641304463
Trimmed Mean ( 15 / 24 )24.62190476190480.236385931734236104.159772035786
Trimmed Mean ( 16 / 24 )24.6160.233884915815779105.248343674241
Trimmed Mean ( 17 / 24 )24.59105263157890.234052610307394105.066346405119
Trimmed Mean ( 18 / 24 )24.56333333333330.23342719200696105.229100012483
Trimmed Mean ( 19 / 24 )24.53235294117650.231685700044062105.886349207184
Trimmed Mean ( 20 / 24 )24.49750.228347411464594107.28170660169
Trimmed Mean ( 21 / 24 )24.49033333333330.232998191169208105.109542741248
Trimmed Mean ( 22 / 24 )24.48214285714290.237748676350839102.974886055791
Trimmed Mean ( 23 / 24 )24.47269230769230.242518552941234100.910598430061
Trimmed Mean ( 24 / 24 )24.46166666666670.24716484162841298.9690382560249
Median23.82
Midrange24.915
Midmean - Weighted Average at Xnp25.025
Midmean - Weighted Average at X(n+1)p25.025
Midmean - Empirical Distribution Function25.025
Midmean - Empirical Distribution Function - Averaging25.025
Midmean - Empirical Distribution Function - Interpolation25.025
Midmean - Closest Observation25.025
Midmean - True Basic - Statistics Graphics Toolkit25.025
Midmean - MS Excel (old versions)25.025
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 24.7116666666667 & 0.232148989583483 & 106.447444423531 \tabularnewline
Geometric Mean & 24.6347968891103 &  &  \tabularnewline
Harmonic Mean & 24.5587561481405 &  &  \tabularnewline
Quadratic Mean & 24.7889669678535 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 24.7116666666667 & 0.232148989583483 & 106.447444423531 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 24.7116666666667 & 0.232148989583483 & 106.447444423531 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 24.7116666666667 & 0.232148989583483 & 106.447444423531 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 24.7133333333333 & 0.231914532851503 & 106.562245278339 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 24.7133333333333 & 0.231914532851503 & 106.562245278339 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 24.7133333333333 & 0.231914532851503 & 106.562245278339 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 24.7133333333333 & 0.231914532851503 & 106.562245278339 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 24.6711111111111 & 0.225233972901785 & 109.53547900995 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 24.6711111111111 & 0.225233972901785 & 109.53547900995 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 24.6711111111111 & 0.225233972901785 & 109.53547900995 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 24.6711111111111 & 0.225233972901785 & 109.53547900995 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 24.6711111111111 & 0.225233972901785 & 109.53547900995 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 24.6711111111111 & 0.225233972901785 & 109.53547900995 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 24.6711111111111 & 0.225233972901785 & 109.53547900995 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 24.6711111111111 & 0.225233972901785 & 109.53547900995 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 24.8266666666667 & 0.204976429043009 & 121.119617424194 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 24.8266666666667 & 0.204976429043009 & 121.119617424194 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 24.8266666666667 & 0.204976429043009 & 121.119617424194 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 24.8266666666667 & 0.204976429043009 & 121.119617424194 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 24.5572222222222 & 0.166274094259568 & 147.691210296935 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 24.5572222222222 & 0.166274094259568 & 147.691210296935 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 24.5572222222222 & 0.166274094259568 & 147.691210296935 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 24.5572222222222 & 0.166274094259568 & 147.691210296935 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 24.5572222222222 & 0.166274094259568 & 147.691210296935 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 24.7058571428571 & 0.233154752086647 & 105.963343752375 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 24.6997058823529 & 0.234071960392851 & 105.521848242304 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 24.6931818181818 & 0.234880236217404 & 105.130947651662 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 24.68625 & 0.235554847773345 & 104.800432822141 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 24.6783870967742 & 0.236142339093285 & 104.506405719244 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 24.67 & 0.236538598276426 & 104.295874668074 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 24.6610344827586 & 0.23669951413393 & 104.187093805376 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 24.6514285714286 & 0.236570111044703 & 104.203478886521 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 24.6481481481481 & 0.237547608097395 & 103.760877011409 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 24.6446153846154 & 0.238319984259231 & 103.409772626573 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 24.6408 & 0.238829943769236 & 103.172992511394 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 24.6366666666667 & 0.239003793356446 & 103.080651234368 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 24.6321739130435 & 0.238745698404424 & 103.17326794855 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 24.6272727272727 & 0.237929396770125 & 103.506641304463 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 24.6219047619048 & 0.236385931734236 & 104.159772035786 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 24.616 & 0.233884915815779 & 105.248343674241 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 24.5910526315789 & 0.234052610307394 & 105.066346405119 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 24.5633333333333 & 0.23342719200696 & 105.229100012483 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 24.5323529411765 & 0.231685700044062 & 105.886349207184 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 24.4975 & 0.228347411464594 & 107.28170660169 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 24.4903333333333 & 0.232998191169208 & 105.109542741248 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 24.4821428571429 & 0.237748676350839 & 102.974886055791 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 24.4726923076923 & 0.242518552941234 & 100.910598430061 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 24.4616666666667 & 0.247164841628412 & 98.9690382560249 \tabularnewline
Median & 23.82 &  &  \tabularnewline
Midrange & 24.915 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 25.025 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 25.025 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 25.025 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 25.025 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 25.025 &  &  \tabularnewline
Midmean - Closest Observation & 25.025 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 25.025 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 25.025 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=207438&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]24.7116666666667[/C][C]0.232148989583483[/C][C]106.447444423531[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]24.6347968891103[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]24.5587561481405[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]24.7889669678535[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]24.7116666666667[/C][C]0.232148989583483[/C][C]106.447444423531[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]24.7116666666667[/C][C]0.232148989583483[/C][C]106.447444423531[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]24.7116666666667[/C][C]0.232148989583483[/C][C]106.447444423531[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]24.7133333333333[/C][C]0.231914532851503[/C][C]106.562245278339[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]24.7133333333333[/C][C]0.231914532851503[/C][C]106.562245278339[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]24.7133333333333[/C][C]0.231914532851503[/C][C]106.562245278339[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]24.7133333333333[/C][C]0.231914532851503[/C][C]106.562245278339[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]24.6711111111111[/C][C]0.225233972901785[/C][C]109.53547900995[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]24.6711111111111[/C][C]0.225233972901785[/C][C]109.53547900995[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]24.6711111111111[/C][C]0.225233972901785[/C][C]109.53547900995[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]24.6711111111111[/C][C]0.225233972901785[/C][C]109.53547900995[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]24.6711111111111[/C][C]0.225233972901785[/C][C]109.53547900995[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]24.6711111111111[/C][C]0.225233972901785[/C][C]109.53547900995[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]24.6711111111111[/C][C]0.225233972901785[/C][C]109.53547900995[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]24.6711111111111[/C][C]0.225233972901785[/C][C]109.53547900995[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]24.8266666666667[/C][C]0.204976429043009[/C][C]121.119617424194[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]24.8266666666667[/C][C]0.204976429043009[/C][C]121.119617424194[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]24.8266666666667[/C][C]0.204976429043009[/C][C]121.119617424194[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]24.8266666666667[/C][C]0.204976429043009[/C][C]121.119617424194[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]24.5572222222222[/C][C]0.166274094259568[/C][C]147.691210296935[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]24.5572222222222[/C][C]0.166274094259568[/C][C]147.691210296935[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]24.5572222222222[/C][C]0.166274094259568[/C][C]147.691210296935[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]24.5572222222222[/C][C]0.166274094259568[/C][C]147.691210296935[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]24.5572222222222[/C][C]0.166274094259568[/C][C]147.691210296935[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]24.7058571428571[/C][C]0.233154752086647[/C][C]105.963343752375[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]24.6997058823529[/C][C]0.234071960392851[/C][C]105.521848242304[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]24.6931818181818[/C][C]0.234880236217404[/C][C]105.130947651662[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]24.68625[/C][C]0.235554847773345[/C][C]104.800432822141[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]24.6783870967742[/C][C]0.236142339093285[/C][C]104.506405719244[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]24.67[/C][C]0.236538598276426[/C][C]104.295874668074[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]24.6610344827586[/C][C]0.23669951413393[/C][C]104.187093805376[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]24.6514285714286[/C][C]0.236570111044703[/C][C]104.203478886521[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]24.6481481481481[/C][C]0.237547608097395[/C][C]103.760877011409[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]24.6446153846154[/C][C]0.238319984259231[/C][C]103.409772626573[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]24.6408[/C][C]0.238829943769236[/C][C]103.172992511394[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]24.6366666666667[/C][C]0.239003793356446[/C][C]103.080651234368[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]24.6321739130435[/C][C]0.238745698404424[/C][C]103.17326794855[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]24.6272727272727[/C][C]0.237929396770125[/C][C]103.506641304463[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]24.6219047619048[/C][C]0.236385931734236[/C][C]104.159772035786[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]24.616[/C][C]0.233884915815779[/C][C]105.248343674241[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]24.5910526315789[/C][C]0.234052610307394[/C][C]105.066346405119[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]24.5633333333333[/C][C]0.23342719200696[/C][C]105.229100012483[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]24.5323529411765[/C][C]0.231685700044062[/C][C]105.886349207184[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]24.4975[/C][C]0.228347411464594[/C][C]107.28170660169[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]24.4903333333333[/C][C]0.232998191169208[/C][C]105.109542741248[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]24.4821428571429[/C][C]0.237748676350839[/C][C]102.974886055791[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]24.4726923076923[/C][C]0.242518552941234[/C][C]100.910598430061[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]24.4616666666667[/C][C]0.247164841628412[/C][C]98.9690382560249[/C][/ROW]
[ROW][C]Median[/C][C]23.82[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]24.915[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]25.025[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]25.025[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]25.025[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]25.025[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]25.025[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]25.025[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]25.025[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]25.025[/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=207438&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=207438&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 Mean24.71166666666670.232148989583483106.447444423531
Geometric Mean24.6347968891103
Harmonic Mean24.5587561481405
Quadratic Mean24.7889669678535
Winsorized Mean ( 1 / 24 )24.71166666666670.232148989583483106.447444423531
Winsorized Mean ( 2 / 24 )24.71166666666670.232148989583483106.447444423531
Winsorized Mean ( 3 / 24 )24.71166666666670.232148989583483106.447444423531
Winsorized Mean ( 4 / 24 )24.71333333333330.231914532851503106.562245278339
Winsorized Mean ( 5 / 24 )24.71333333333330.231914532851503106.562245278339
Winsorized Mean ( 6 / 24 )24.71333333333330.231914532851503106.562245278339
Winsorized Mean ( 7 / 24 )24.71333333333330.231914532851503106.562245278339
Winsorized Mean ( 8 / 24 )24.67111111111110.225233972901785109.53547900995
Winsorized Mean ( 9 / 24 )24.67111111111110.225233972901785109.53547900995
Winsorized Mean ( 10 / 24 )24.67111111111110.225233972901785109.53547900995
Winsorized Mean ( 11 / 24 )24.67111111111110.225233972901785109.53547900995
Winsorized Mean ( 12 / 24 )24.67111111111110.225233972901785109.53547900995
Winsorized Mean ( 13 / 24 )24.67111111111110.225233972901785109.53547900995
Winsorized Mean ( 14 / 24 )24.67111111111110.225233972901785109.53547900995
Winsorized Mean ( 15 / 24 )24.67111111111110.225233972901785109.53547900995
Winsorized Mean ( 16 / 24 )24.82666666666670.204976429043009121.119617424194
Winsorized Mean ( 17 / 24 )24.82666666666670.204976429043009121.119617424194
Winsorized Mean ( 18 / 24 )24.82666666666670.204976429043009121.119617424194
Winsorized Mean ( 19 / 24 )24.82666666666670.204976429043009121.119617424194
Winsorized Mean ( 20 / 24 )24.55722222222220.166274094259568147.691210296935
Winsorized Mean ( 21 / 24 )24.55722222222220.166274094259568147.691210296935
Winsorized Mean ( 22 / 24 )24.55722222222220.166274094259568147.691210296935
Winsorized Mean ( 23 / 24 )24.55722222222220.166274094259568147.691210296935
Winsorized Mean ( 24 / 24 )24.55722222222220.166274094259568147.691210296935
Trimmed Mean ( 1 / 24 )24.70585714285710.233154752086647105.963343752375
Trimmed Mean ( 2 / 24 )24.69970588235290.234071960392851105.521848242304
Trimmed Mean ( 3 / 24 )24.69318181818180.234880236217404105.130947651662
Trimmed Mean ( 4 / 24 )24.686250.235554847773345104.800432822141
Trimmed Mean ( 5 / 24 )24.67838709677420.236142339093285104.506405719244
Trimmed Mean ( 6 / 24 )24.670.236538598276426104.295874668074
Trimmed Mean ( 7 / 24 )24.66103448275860.23669951413393104.187093805376
Trimmed Mean ( 8 / 24 )24.65142857142860.236570111044703104.203478886521
Trimmed Mean ( 9 / 24 )24.64814814814810.237547608097395103.760877011409
Trimmed Mean ( 10 / 24 )24.64461538461540.238319984259231103.409772626573
Trimmed Mean ( 11 / 24 )24.64080.238829943769236103.172992511394
Trimmed Mean ( 12 / 24 )24.63666666666670.239003793356446103.080651234368
Trimmed Mean ( 13 / 24 )24.63217391304350.238745698404424103.17326794855
Trimmed Mean ( 14 / 24 )24.62727272727270.237929396770125103.506641304463
Trimmed Mean ( 15 / 24 )24.62190476190480.236385931734236104.159772035786
Trimmed Mean ( 16 / 24 )24.6160.233884915815779105.248343674241
Trimmed Mean ( 17 / 24 )24.59105263157890.234052610307394105.066346405119
Trimmed Mean ( 18 / 24 )24.56333333333330.23342719200696105.229100012483
Trimmed Mean ( 19 / 24 )24.53235294117650.231685700044062105.886349207184
Trimmed Mean ( 20 / 24 )24.49750.228347411464594107.28170660169
Trimmed Mean ( 21 / 24 )24.49033333333330.232998191169208105.109542741248
Trimmed Mean ( 22 / 24 )24.48214285714290.237748676350839102.974886055791
Trimmed Mean ( 23 / 24 )24.47269230769230.242518552941234100.910598430061
Trimmed Mean ( 24 / 24 )24.46166666666670.24716484162841298.9690382560249
Median23.82
Midrange24.915
Midmean - Weighted Average at Xnp25.025
Midmean - Weighted Average at X(n+1)p25.025
Midmean - Empirical Distribution Function25.025
Midmean - Empirical Distribution Function - Averaging25.025
Midmean - Empirical Distribution Function - Interpolation25.025
Midmean - Closest Observation25.025
Midmean - True Basic - Statistics Graphics Toolkit25.025
Midmean - MS Excel (old versions)25.025
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')