Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationThu, 20 Feb 2014 04:43:48 -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/2014/Feb/20/t1392889582d05f75r6dsep36b.htm/, Retrieved Sat, 18 May 2024 04:28:58 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=233907, Retrieved Sat, 18 May 2024 04:28:58 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact110
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [gemiddelde prijze...] [2014-02-20 09:43:48] [dea6f921e04cc33dad49f75b9d343660] [Current]
Feedback Forum

Post a new message
Dataseries X:
 107,00 
 116,14 
 117,18 
 102,28 
 109,43 
 114,28 
 117,39 
 116,66 
 114,29 
 114,18 
 114,12 
 122,62 
 115,70 
 127,91 
 119,55 
 115,08 
 116,63 
 121,38 
 123,41 
 120,70 
 119,40 
 116,83 
 116,40 
 121,67 
 116,54 
 129,61 
 119,93 
 117,64 
 121,01 
 124,20 
 125,23 
 123,24 
 121,58 
 120,89 
 117,77 
 110,91 
 124,23 
 127,70 
 129,45 
 120,13 
 122,02 
 126,59 
 126,34 
 125,15 
 125,02 
 124,40 
 127,55 
 126,63 
 130,18 
 136,95 
 136,81 
 129,59 
 133,37 
 140,02 
 139,67 
 139,99 
 134,57 
 134,41 
 134,99 
 135,70 




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gwilym Jenkins' @ jenkins.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 & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=233907&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]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=233907&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=233907&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 time2 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean123.0041.07592496535467114.323957488479
Geometric Mean122.727159073457
Harmonic Mean122.450887204246
Quadratic Mean123.281317616796
Winsorized Mean ( 1 / 20 )123.0821666666671.05273555657229116.916509467414
Winsorized Mean ( 2 / 20 )123.15251.03018973144191119.543513433811
Winsorized Mean ( 3 / 20 )123.09050.979173536699063125.708564811664
Winsorized Mean ( 4 / 20 )123.2951666666670.936477909635569131.658382326015
Winsorized Mean ( 5 / 20 )123.2076666666670.913605119568044134.858774352009
Winsorized Mean ( 6 / 20 )123.1466666666670.895743313043711137.47986155567
Winsorized Mean ( 7 / 20 )123.0988333333330.884671508242066139.146374882066
Winsorized Mean ( 8 / 20 )123.1828333333330.862695653454706142.788285579094
Winsorized Mean ( 9 / 20 )123.1198333333330.814240955038816151.208106852675
Winsorized Mean ( 10 / 20 )122.66150.696807969275035176.033434473515
Winsorized Mean ( 11 / 20 )122.6046666666670.670473964520482182.862680960852
Winsorized Mean ( 12 / 20 )122.6286666666670.665397866055084184.293748030318
Winsorized Mean ( 13 / 20 )122.6178333333330.657017017367976186.628093477005
Winsorized Mean ( 14 / 20 )122.26550.59523780677152205.406139544713
Winsorized Mean ( 15 / 20 )122.25550.580081594932697210.755695522773
Winsorized Mean ( 16 / 20 )122.3088333333330.559065306094326218.773785459506
Winsorized Mean ( 17 / 20 )122.1076666666670.509399800067541239.708901830108
Winsorized Mean ( 18 / 20 )122.1706666666670.495896316087195246.363327783191
Winsorized Mean ( 19 / 20 )122.1326666666670.477632276272343255.704383338255
Winsorized Mean ( 20 / 20 )122.3060.341281748176515358.372519636597
Trimmed Mean ( 1 / 20 )123.0679310344831.01093386589988121.736876353365
Trimmed Mean ( 2 / 20 )123.0526785714290.959258049699729128.279015860171
Trimmed Mean ( 3 / 20 )122.9972222222220.910430144483964135.097923731356
Trimmed Mean ( 4 / 20 )122.9613461538460.87521068477743140.493424374859
Trimmed Mean ( 5 / 20 )122.86120.84779650234461144.918267131585
Trimmed Mean ( 6 / 20 )122.7745833333330.820936476491212149.554303955512
Trimmed Mean ( 7 / 20 )122.6936956521740.792088254408893154.899021629523
Trimmed Mean ( 8 / 20 )122.6147727272730.757898193099317161.782642898061
Trimmed Mean ( 9 / 20 )122.5133333333330.719098486021042170.370729065543
Trimmed Mean ( 10 / 20 )122.412250.682075122516875179.470333924943
Trimmed Mean ( 11 / 20 )122.3728947368420.667267299025795183.394113446748
Trimmed Mean ( 12 / 20 )122.3377777777780.653391531799395187.235021918432
Trimmed Mean ( 13 / 20 )122.2950.634459536726587192.754609113397
Trimmed Mean ( 14 / 20 )122.24843750.60931365230899200.633018867607
Trimmed Mean ( 15 / 20 )122.2460.592102158007587206.460993844974
Trimmed Mean ( 16 / 20 )122.2446428571430.570354127936955214.331126697229
Trimmed Mean ( 17 / 20 )122.2353846153850.543677005574572224.830889226597
Trimmed Mean ( 18 / 20 )122.2541666666670.520122587510529235.048755047947
Trimmed Mean ( 19 / 20 )122.2668181818180.48625629960136251.445211675518
Trimmed Mean ( 20 / 20 )122.2880.436542998424765280.12818998648
Median121.845
Midrange121.15
Midmean - Weighted Average at Xnp122.065806451613
Midmean - Weighted Average at X(n+1)p122.246
Midmean - Empirical Distribution Function122.065806451613
Midmean - Empirical Distribution Function - Averaging122.246
Midmean - Empirical Distribution Function - Interpolation122.246
Midmean - Closest Observation122.065806451613
Midmean - True Basic - Statistics Graphics Toolkit122.246
Midmean - MS Excel (old versions)122.2484375
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 123.004 & 1.07592496535467 & 114.323957488479 \tabularnewline
Geometric Mean & 122.727159073457 &  &  \tabularnewline
Harmonic Mean & 122.450887204246 &  &  \tabularnewline
Quadratic Mean & 123.281317616796 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 123.082166666667 & 1.05273555657229 & 116.916509467414 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 123.1525 & 1.03018973144191 & 119.543513433811 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 123.0905 & 0.979173536699063 & 125.708564811664 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 123.295166666667 & 0.936477909635569 & 131.658382326015 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 123.207666666667 & 0.913605119568044 & 134.858774352009 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 123.146666666667 & 0.895743313043711 & 137.47986155567 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 123.098833333333 & 0.884671508242066 & 139.146374882066 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 123.182833333333 & 0.862695653454706 & 142.788285579094 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 123.119833333333 & 0.814240955038816 & 151.208106852675 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 122.6615 & 0.696807969275035 & 176.033434473515 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 122.604666666667 & 0.670473964520482 & 182.862680960852 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 122.628666666667 & 0.665397866055084 & 184.293748030318 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 122.617833333333 & 0.657017017367976 & 186.628093477005 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 122.2655 & 0.59523780677152 & 205.406139544713 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 122.2555 & 0.580081594932697 & 210.755695522773 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 122.308833333333 & 0.559065306094326 & 218.773785459506 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 122.107666666667 & 0.509399800067541 & 239.708901830108 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 122.170666666667 & 0.495896316087195 & 246.363327783191 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 122.132666666667 & 0.477632276272343 & 255.704383338255 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 122.306 & 0.341281748176515 & 358.372519636597 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 123.067931034483 & 1.01093386589988 & 121.736876353365 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 123.052678571429 & 0.959258049699729 & 128.279015860171 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 122.997222222222 & 0.910430144483964 & 135.097923731356 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 122.961346153846 & 0.87521068477743 & 140.493424374859 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 122.8612 & 0.84779650234461 & 144.918267131585 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 122.774583333333 & 0.820936476491212 & 149.554303955512 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 122.693695652174 & 0.792088254408893 & 154.899021629523 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 122.614772727273 & 0.757898193099317 & 161.782642898061 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 122.513333333333 & 0.719098486021042 & 170.370729065543 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 122.41225 & 0.682075122516875 & 179.470333924943 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 122.372894736842 & 0.667267299025795 & 183.394113446748 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 122.337777777778 & 0.653391531799395 & 187.235021918432 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 122.295 & 0.634459536726587 & 192.754609113397 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 122.2484375 & 0.60931365230899 & 200.633018867607 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 122.246 & 0.592102158007587 & 206.460993844974 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 122.244642857143 & 0.570354127936955 & 214.331126697229 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 122.235384615385 & 0.543677005574572 & 224.830889226597 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 122.254166666667 & 0.520122587510529 & 235.048755047947 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 122.266818181818 & 0.48625629960136 & 251.445211675518 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 122.288 & 0.436542998424765 & 280.12818998648 \tabularnewline
Median & 121.845 &  &  \tabularnewline
Midrange & 121.15 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 122.065806451613 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 122.246 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 122.065806451613 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 122.246 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 122.246 &  &  \tabularnewline
Midmean - Closest Observation & 122.065806451613 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 122.246 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 122.2484375 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=233907&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]123.004[/C][C]1.07592496535467[/C][C]114.323957488479[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]122.727159073457[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]122.450887204246[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]123.281317616796[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]123.082166666667[/C][C]1.05273555657229[/C][C]116.916509467414[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]123.1525[/C][C]1.03018973144191[/C][C]119.543513433811[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]123.0905[/C][C]0.979173536699063[/C][C]125.708564811664[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]123.295166666667[/C][C]0.936477909635569[/C][C]131.658382326015[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]123.207666666667[/C][C]0.913605119568044[/C][C]134.858774352009[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]123.146666666667[/C][C]0.895743313043711[/C][C]137.47986155567[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]123.098833333333[/C][C]0.884671508242066[/C][C]139.146374882066[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]123.182833333333[/C][C]0.862695653454706[/C][C]142.788285579094[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]123.119833333333[/C][C]0.814240955038816[/C][C]151.208106852675[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]122.6615[/C][C]0.696807969275035[/C][C]176.033434473515[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]122.604666666667[/C][C]0.670473964520482[/C][C]182.862680960852[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]122.628666666667[/C][C]0.665397866055084[/C][C]184.293748030318[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]122.617833333333[/C][C]0.657017017367976[/C][C]186.628093477005[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]122.2655[/C][C]0.59523780677152[/C][C]205.406139544713[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]122.2555[/C][C]0.580081594932697[/C][C]210.755695522773[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]122.308833333333[/C][C]0.559065306094326[/C][C]218.773785459506[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]122.107666666667[/C][C]0.509399800067541[/C][C]239.708901830108[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]122.170666666667[/C][C]0.495896316087195[/C][C]246.363327783191[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]122.132666666667[/C][C]0.477632276272343[/C][C]255.704383338255[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]122.306[/C][C]0.341281748176515[/C][C]358.372519636597[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]123.067931034483[/C][C]1.01093386589988[/C][C]121.736876353365[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]123.052678571429[/C][C]0.959258049699729[/C][C]128.279015860171[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]122.997222222222[/C][C]0.910430144483964[/C][C]135.097923731356[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]122.961346153846[/C][C]0.87521068477743[/C][C]140.493424374859[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]122.8612[/C][C]0.84779650234461[/C][C]144.918267131585[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]122.774583333333[/C][C]0.820936476491212[/C][C]149.554303955512[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]122.693695652174[/C][C]0.792088254408893[/C][C]154.899021629523[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]122.614772727273[/C][C]0.757898193099317[/C][C]161.782642898061[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]122.513333333333[/C][C]0.719098486021042[/C][C]170.370729065543[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]122.41225[/C][C]0.682075122516875[/C][C]179.470333924943[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]122.372894736842[/C][C]0.667267299025795[/C][C]183.394113446748[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]122.337777777778[/C][C]0.653391531799395[/C][C]187.235021918432[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]122.295[/C][C]0.634459536726587[/C][C]192.754609113397[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]122.2484375[/C][C]0.60931365230899[/C][C]200.633018867607[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]122.246[/C][C]0.592102158007587[/C][C]206.460993844974[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]122.244642857143[/C][C]0.570354127936955[/C][C]214.331126697229[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]122.235384615385[/C][C]0.543677005574572[/C][C]224.830889226597[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]122.254166666667[/C][C]0.520122587510529[/C][C]235.048755047947[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]122.266818181818[/C][C]0.48625629960136[/C][C]251.445211675518[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]122.288[/C][C]0.436542998424765[/C][C]280.12818998648[/C][/ROW]
[ROW][C]Median[/C][C]121.845[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]121.15[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]122.065806451613[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]122.246[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]122.065806451613[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]122.246[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]122.246[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]122.065806451613[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]122.246[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]122.2484375[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]60[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=233907&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=233907&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 Mean123.0041.07592496535467114.323957488479
Geometric Mean122.727159073457
Harmonic Mean122.450887204246
Quadratic Mean123.281317616796
Winsorized Mean ( 1 / 20 )123.0821666666671.05273555657229116.916509467414
Winsorized Mean ( 2 / 20 )123.15251.03018973144191119.543513433811
Winsorized Mean ( 3 / 20 )123.09050.979173536699063125.708564811664
Winsorized Mean ( 4 / 20 )123.2951666666670.936477909635569131.658382326015
Winsorized Mean ( 5 / 20 )123.2076666666670.913605119568044134.858774352009
Winsorized Mean ( 6 / 20 )123.1466666666670.895743313043711137.47986155567
Winsorized Mean ( 7 / 20 )123.0988333333330.884671508242066139.146374882066
Winsorized Mean ( 8 / 20 )123.1828333333330.862695653454706142.788285579094
Winsorized Mean ( 9 / 20 )123.1198333333330.814240955038816151.208106852675
Winsorized Mean ( 10 / 20 )122.66150.696807969275035176.033434473515
Winsorized Mean ( 11 / 20 )122.6046666666670.670473964520482182.862680960852
Winsorized Mean ( 12 / 20 )122.6286666666670.665397866055084184.293748030318
Winsorized Mean ( 13 / 20 )122.6178333333330.657017017367976186.628093477005
Winsorized Mean ( 14 / 20 )122.26550.59523780677152205.406139544713
Winsorized Mean ( 15 / 20 )122.25550.580081594932697210.755695522773
Winsorized Mean ( 16 / 20 )122.3088333333330.559065306094326218.773785459506
Winsorized Mean ( 17 / 20 )122.1076666666670.509399800067541239.708901830108
Winsorized Mean ( 18 / 20 )122.1706666666670.495896316087195246.363327783191
Winsorized Mean ( 19 / 20 )122.1326666666670.477632276272343255.704383338255
Winsorized Mean ( 20 / 20 )122.3060.341281748176515358.372519636597
Trimmed Mean ( 1 / 20 )123.0679310344831.01093386589988121.736876353365
Trimmed Mean ( 2 / 20 )123.0526785714290.959258049699729128.279015860171
Trimmed Mean ( 3 / 20 )122.9972222222220.910430144483964135.097923731356
Trimmed Mean ( 4 / 20 )122.9613461538460.87521068477743140.493424374859
Trimmed Mean ( 5 / 20 )122.86120.84779650234461144.918267131585
Trimmed Mean ( 6 / 20 )122.7745833333330.820936476491212149.554303955512
Trimmed Mean ( 7 / 20 )122.6936956521740.792088254408893154.899021629523
Trimmed Mean ( 8 / 20 )122.6147727272730.757898193099317161.782642898061
Trimmed Mean ( 9 / 20 )122.5133333333330.719098486021042170.370729065543
Trimmed Mean ( 10 / 20 )122.412250.682075122516875179.470333924943
Trimmed Mean ( 11 / 20 )122.3728947368420.667267299025795183.394113446748
Trimmed Mean ( 12 / 20 )122.3377777777780.653391531799395187.235021918432
Trimmed Mean ( 13 / 20 )122.2950.634459536726587192.754609113397
Trimmed Mean ( 14 / 20 )122.24843750.60931365230899200.633018867607
Trimmed Mean ( 15 / 20 )122.2460.592102158007587206.460993844974
Trimmed Mean ( 16 / 20 )122.2446428571430.570354127936955214.331126697229
Trimmed Mean ( 17 / 20 )122.2353846153850.543677005574572224.830889226597
Trimmed Mean ( 18 / 20 )122.2541666666670.520122587510529235.048755047947
Trimmed Mean ( 19 / 20 )122.2668181818180.48625629960136251.445211675518
Trimmed Mean ( 20 / 20 )122.2880.436542998424765280.12818998648
Median121.845
Midrange121.15
Midmean - Weighted Average at Xnp122.065806451613
Midmean - Weighted Average at X(n+1)p122.246
Midmean - Empirical Distribution Function122.065806451613
Midmean - Empirical Distribution Function - Averaging122.246
Midmean - Empirical Distribution Function - Interpolation122.246
Midmean - Closest Observation122.065806451613
Midmean - True Basic - Statistics Graphics Toolkit122.246
Midmean - MS Excel (old versions)122.2484375
Number of observations60



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')