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Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationWed, 12 Oct 2016 10:35:38 +0100
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2016/Oct/12/t1476264989r7wl0lzm4ji5cxs.htm/, Retrieved Fri, 17 May 2024 19:14:22 +0200
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=, Retrieved Fri, 17 May 2024 19:14:22 +0200
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact0
Dataseries X:
102,8
103,66
103,55
103,87
104,03
104,02
104,02
102,97
103,18
103,53
103,78
103,85
103,85
104,78
104,76
104,84
104,85
104,83
104,83
103,71
103,84
104,37
104,44
104,4
99,54
100,42
100,34
100,36
100,37
100,42
100,41
99,13
99,42
99,76
99,92
99,92
100,47
100,44
100,47
100,61
100,73
100,64
99,99
99,74
99,49
99,41
99,49
99,53
99,91
99,84
99,67
99,39
99,38
99,29
97,91
97,62
97,67
97,64
97,63
97,66




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gertrude Mary Cox' @ cox.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 1 seconds \tabularnewline
R Server & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=0

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

As an alternative you can also use a QR Code:  

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

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gertrude Mary Cox' @ cox.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean101.35650.303930357860775333.485936427679
Geometric Mean101.329669990661
Harmonic Mean101.302901706291
Quadratic Mean101.383381963384
Winsorized Mean ( 1 / 20 )101.35650.303863244682417333.559592263068
Winsorized Mean ( 2 / 20 )101.35650.303729345860296333.706641723781
Winsorized Mean ( 3 / 20 )101.35750.303522411890414333.937449194345
Winsorized Mean ( 4 / 20 )101.3548333333330.302742034812123334.789430203284
Winsorized Mean ( 5 / 20 )101.3731666666670.298391118192543339.732520460792
Winsorized Mean ( 6 / 20 )101.4631666666670.271293458771361373.997836609018
Winsorized Mean ( 7 / 20 )101.4771666666670.26777479065857378.964600876326
Winsorized Mean ( 8 / 20 )101.4851666666670.265398910039386382.387277519737
Winsorized Mean ( 9 / 20 )101.4356666666670.256114862855551396.055369593589
Winsorized Mean ( 10 / 20 )101.4373333333330.255379065397527397.203009477047
Winsorized Mean ( 11 / 20 )101.4391666666670.255132766109627397.593645902306
Winsorized Mean ( 12 / 20 )101.4231666666670.248190341989518408.650738999949
Winsorized Mean ( 13 / 20 )101.4188333333330.247467522455843409.826842435173
Winsorized Mean ( 14 / 20 )101.4281666666670.246241291298778411.905599307463
Winsorized Mean ( 15 / 20 )101.4281666666670.245498511814637413.151859524304
Winsorized Mean ( 16 / 20 )101.4468333333330.238388953843296425.551736763857
Winsorized Mean ( 17 / 20 )101.4468333333330.232622301429615436.101064729722
Winsorized Mean ( 18 / 20 )101.4378333333330.229409225510939442.169808591661
Winsorized Mean ( 19 / 20 )101.4283333333330.220593724609518459.797002443637
Winsorized Mean ( 20 / 20 )101.4450.216681898638858468.174778960552
Trimmed Mean ( 1 / 20 )101.3606896551720.301656934871816336.013125964579
Trimmed Mean ( 2 / 20 )101.3651785714290.298704452711327339.349405913911
Trimmed Mean ( 3 / 20 )101.370.294918411297349343.722182532017
Trimmed Mean ( 4 / 20 )101.3748076923080.290102505728425349.444784827913
Trimmed Mean ( 5 / 20 )101.38080.284187469025326356.739163579958
Trimmed Mean ( 6 / 20 )101.3827083333330.278039734452996364.63388419209
Trimmed Mean ( 7 / 20 )101.3652173913040.277990327418431364.635771081091
Trimmed Mean ( 8 / 20 )101.3434090909090.278197714986789364.285555313499
Trimmed Mean ( 9 / 20 )101.3180952380950.278317543160754364.037760923949
Trimmed Mean ( 10 / 20 )101.29850.279995318184301361.786406490277
Trimmed Mean ( 11 / 20 )101.2765789473680.28136612382312359.945886772907
Trimmed Mean ( 12 / 20 )101.2519444444440.282159422302989358.84658260931
Trimmed Mean ( 13 / 20 )101.2267647058820.283744606798765356.753088095428
Trimmed Mean ( 14 / 20 )101.19906250.284709585825782355.44662890952
Trimmed Mean ( 15 / 20 )101.1663333333330.284798167424902355.221152748498
Trimmed Mean ( 16 / 20 )101.1289285714290.283433847383797356.799053835268
Trimmed Mean ( 17 / 20 )101.0830769230770.281539050020402359.037500892867
Trimmed Mean ( 18 / 20 )101.0295833333330.278285693549452363.042677633661
Trimmed Mean ( 19 / 20 )100.9677272727270.271812046579764371.461561557752
Trimmed Mean ( 20 / 20 )100.8950.262014965422327385.073424479297
Median100.43
Midrange101.235
Midmean - Weighted Average at Xnp101.113548387097
Midmean - Weighted Average at X(n+1)p101.166333333333
Midmean - Empirical Distribution Function101.113548387097
Midmean - Empirical Distribution Function - Averaging101.166333333333
Midmean - Empirical Distribution Function - Interpolation101.166333333333
Midmean - Closest Observation101.113548387097
Midmean - True Basic - Statistics Graphics Toolkit101.166333333333
Midmean - MS Excel (old versions)101.279393939394
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 101.3565 & 0.303930357860775 & 333.485936427679 \tabularnewline
Geometric Mean & 101.329669990661 &  &  \tabularnewline
Harmonic Mean & 101.302901706291 &  &  \tabularnewline
Quadratic Mean & 101.383381963384 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 101.3565 & 0.303863244682417 & 333.559592263068 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 101.3565 & 0.303729345860296 & 333.706641723781 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 101.3575 & 0.303522411890414 & 333.937449194345 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 101.354833333333 & 0.302742034812123 & 334.789430203284 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 101.373166666667 & 0.298391118192543 & 339.732520460792 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 101.463166666667 & 0.271293458771361 & 373.997836609018 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 101.477166666667 & 0.26777479065857 & 378.964600876326 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 101.485166666667 & 0.265398910039386 & 382.387277519737 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 101.435666666667 & 0.256114862855551 & 396.055369593589 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 101.437333333333 & 0.255379065397527 & 397.203009477047 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 101.439166666667 & 0.255132766109627 & 397.593645902306 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 101.423166666667 & 0.248190341989518 & 408.650738999949 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 101.418833333333 & 0.247467522455843 & 409.826842435173 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 101.428166666667 & 0.246241291298778 & 411.905599307463 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 101.428166666667 & 0.245498511814637 & 413.151859524304 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 101.446833333333 & 0.238388953843296 & 425.551736763857 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 101.446833333333 & 0.232622301429615 & 436.101064729722 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 101.437833333333 & 0.229409225510939 & 442.169808591661 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 101.428333333333 & 0.220593724609518 & 459.797002443637 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 101.445 & 0.216681898638858 & 468.174778960552 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 101.360689655172 & 0.301656934871816 & 336.013125964579 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 101.365178571429 & 0.298704452711327 & 339.349405913911 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 101.37 & 0.294918411297349 & 343.722182532017 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 101.374807692308 & 0.290102505728425 & 349.444784827913 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 101.3808 & 0.284187469025326 & 356.739163579958 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 101.382708333333 & 0.278039734452996 & 364.63388419209 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 101.365217391304 & 0.277990327418431 & 364.635771081091 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 101.343409090909 & 0.278197714986789 & 364.285555313499 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 101.318095238095 & 0.278317543160754 & 364.037760923949 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 101.2985 & 0.279995318184301 & 361.786406490277 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 101.276578947368 & 0.28136612382312 & 359.945886772907 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 101.251944444444 & 0.282159422302989 & 358.84658260931 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 101.226764705882 & 0.283744606798765 & 356.753088095428 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 101.1990625 & 0.284709585825782 & 355.44662890952 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 101.166333333333 & 0.284798167424902 & 355.221152748498 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 101.128928571429 & 0.283433847383797 & 356.799053835268 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 101.083076923077 & 0.281539050020402 & 359.037500892867 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 101.029583333333 & 0.278285693549452 & 363.042677633661 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 100.967727272727 & 0.271812046579764 & 371.461561557752 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 100.895 & 0.262014965422327 & 385.073424479297 \tabularnewline
Median & 100.43 &  &  \tabularnewline
Midrange & 101.235 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 101.113548387097 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 101.166333333333 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 101.113548387097 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 101.166333333333 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 101.166333333333 &  &  \tabularnewline
Midmean - Closest Observation & 101.113548387097 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 101.166333333333 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 101.279393939394 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&T=1

[TABLE]
[ROW][C]Central Tendency - Ungrouped Data[/C][/ROW]
[ROW][C]Measure[/C][C]Value[/C][C]S.E.[/C][C]Value/S.E.[/C][/ROW]
[ROW][C]Arithmetic Mean[/C][C]101.3565[/C][C]0.303930357860775[/C][C]333.485936427679[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]101.329669990661[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]101.302901706291[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]101.383381963384[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]101.3565[/C][C]0.303863244682417[/C][C]333.559592263068[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]101.3565[/C][C]0.303729345860296[/C][C]333.706641723781[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]101.3575[/C][C]0.303522411890414[/C][C]333.937449194345[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]101.354833333333[/C][C]0.302742034812123[/C][C]334.789430203284[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]101.373166666667[/C][C]0.298391118192543[/C][C]339.732520460792[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]101.463166666667[/C][C]0.271293458771361[/C][C]373.997836609018[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]101.477166666667[/C][C]0.26777479065857[/C][C]378.964600876326[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]101.485166666667[/C][C]0.265398910039386[/C][C]382.387277519737[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]101.435666666667[/C][C]0.256114862855551[/C][C]396.055369593589[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]101.437333333333[/C][C]0.255379065397527[/C][C]397.203009477047[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]101.439166666667[/C][C]0.255132766109627[/C][C]397.593645902306[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]101.423166666667[/C][C]0.248190341989518[/C][C]408.650738999949[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]101.418833333333[/C][C]0.247467522455843[/C][C]409.826842435173[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]101.428166666667[/C][C]0.246241291298778[/C][C]411.905599307463[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]101.428166666667[/C][C]0.245498511814637[/C][C]413.151859524304[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]101.446833333333[/C][C]0.238388953843296[/C][C]425.551736763857[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]101.446833333333[/C][C]0.232622301429615[/C][C]436.101064729722[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]101.437833333333[/C][C]0.229409225510939[/C][C]442.169808591661[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]101.428333333333[/C][C]0.220593724609518[/C][C]459.797002443637[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]101.445[/C][C]0.216681898638858[/C][C]468.174778960552[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]101.360689655172[/C][C]0.301656934871816[/C][C]336.013125964579[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]101.365178571429[/C][C]0.298704452711327[/C][C]339.349405913911[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]101.37[/C][C]0.294918411297349[/C][C]343.722182532017[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]101.374807692308[/C][C]0.290102505728425[/C][C]349.444784827913[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]101.3808[/C][C]0.284187469025326[/C][C]356.739163579958[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]101.382708333333[/C][C]0.278039734452996[/C][C]364.63388419209[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]101.365217391304[/C][C]0.277990327418431[/C][C]364.635771081091[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]101.343409090909[/C][C]0.278197714986789[/C][C]364.285555313499[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]101.318095238095[/C][C]0.278317543160754[/C][C]364.037760923949[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]101.2985[/C][C]0.279995318184301[/C][C]361.786406490277[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]101.276578947368[/C][C]0.28136612382312[/C][C]359.945886772907[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]101.251944444444[/C][C]0.282159422302989[/C][C]358.84658260931[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]101.226764705882[/C][C]0.283744606798765[/C][C]356.753088095428[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]101.1990625[/C][C]0.284709585825782[/C][C]355.44662890952[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]101.166333333333[/C][C]0.284798167424902[/C][C]355.221152748498[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]101.128928571429[/C][C]0.283433847383797[/C][C]356.799053835268[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]101.083076923077[/C][C]0.281539050020402[/C][C]359.037500892867[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]101.029583333333[/C][C]0.278285693549452[/C][C]363.042677633661[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]100.967727272727[/C][C]0.271812046579764[/C][C]371.461561557752[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]100.895[/C][C]0.262014965422327[/C][C]385.073424479297[/C][/ROW]
[ROW][C]Median[/C][C]100.43[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]101.235[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]101.113548387097[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]101.166333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]101.113548387097[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]101.166333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]101.166333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]101.113548387097[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]101.166333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]101.279393939394[/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=&T=1

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

As an alternative you can also use a QR Code:  

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

Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean101.35650.303930357860775333.485936427679
Geometric Mean101.329669990661
Harmonic Mean101.302901706291
Quadratic Mean101.383381963384
Winsorized Mean ( 1 / 20 )101.35650.303863244682417333.559592263068
Winsorized Mean ( 2 / 20 )101.35650.303729345860296333.706641723781
Winsorized Mean ( 3 / 20 )101.35750.303522411890414333.937449194345
Winsorized Mean ( 4 / 20 )101.3548333333330.302742034812123334.789430203284
Winsorized Mean ( 5 / 20 )101.3731666666670.298391118192543339.732520460792
Winsorized Mean ( 6 / 20 )101.4631666666670.271293458771361373.997836609018
Winsorized Mean ( 7 / 20 )101.4771666666670.26777479065857378.964600876326
Winsorized Mean ( 8 / 20 )101.4851666666670.265398910039386382.387277519737
Winsorized Mean ( 9 / 20 )101.4356666666670.256114862855551396.055369593589
Winsorized Mean ( 10 / 20 )101.4373333333330.255379065397527397.203009477047
Winsorized Mean ( 11 / 20 )101.4391666666670.255132766109627397.593645902306
Winsorized Mean ( 12 / 20 )101.4231666666670.248190341989518408.650738999949
Winsorized Mean ( 13 / 20 )101.4188333333330.247467522455843409.826842435173
Winsorized Mean ( 14 / 20 )101.4281666666670.246241291298778411.905599307463
Winsorized Mean ( 15 / 20 )101.4281666666670.245498511814637413.151859524304
Winsorized Mean ( 16 / 20 )101.4468333333330.238388953843296425.551736763857
Winsorized Mean ( 17 / 20 )101.4468333333330.232622301429615436.101064729722
Winsorized Mean ( 18 / 20 )101.4378333333330.229409225510939442.169808591661
Winsorized Mean ( 19 / 20 )101.4283333333330.220593724609518459.797002443637
Winsorized Mean ( 20 / 20 )101.4450.216681898638858468.174778960552
Trimmed Mean ( 1 / 20 )101.3606896551720.301656934871816336.013125964579
Trimmed Mean ( 2 / 20 )101.3651785714290.298704452711327339.349405913911
Trimmed Mean ( 3 / 20 )101.370.294918411297349343.722182532017
Trimmed Mean ( 4 / 20 )101.3748076923080.290102505728425349.444784827913
Trimmed Mean ( 5 / 20 )101.38080.284187469025326356.739163579958
Trimmed Mean ( 6 / 20 )101.3827083333330.278039734452996364.63388419209
Trimmed Mean ( 7 / 20 )101.3652173913040.277990327418431364.635771081091
Trimmed Mean ( 8 / 20 )101.3434090909090.278197714986789364.285555313499
Trimmed Mean ( 9 / 20 )101.3180952380950.278317543160754364.037760923949
Trimmed Mean ( 10 / 20 )101.29850.279995318184301361.786406490277
Trimmed Mean ( 11 / 20 )101.2765789473680.28136612382312359.945886772907
Trimmed Mean ( 12 / 20 )101.2519444444440.282159422302989358.84658260931
Trimmed Mean ( 13 / 20 )101.2267647058820.283744606798765356.753088095428
Trimmed Mean ( 14 / 20 )101.19906250.284709585825782355.44662890952
Trimmed Mean ( 15 / 20 )101.1663333333330.284798167424902355.221152748498
Trimmed Mean ( 16 / 20 )101.1289285714290.283433847383797356.799053835268
Trimmed Mean ( 17 / 20 )101.0830769230770.281539050020402359.037500892867
Trimmed Mean ( 18 / 20 )101.0295833333330.278285693549452363.042677633661
Trimmed Mean ( 19 / 20 )100.9677272727270.271812046579764371.461561557752
Trimmed Mean ( 20 / 20 )100.8950.262014965422327385.073424479297
Median100.43
Midrange101.235
Midmean - Weighted Average at Xnp101.113548387097
Midmean - Weighted Average at X(n+1)p101.166333333333
Midmean - Empirical Distribution Function101.113548387097
Midmean - Empirical Distribution Function - Averaging101.166333333333
Midmean - Empirical Distribution Function - Interpolation101.166333333333
Midmean - Closest Observation101.113548387097
Midmean - True Basic - Statistics Graphics Toolkit101.166333333333
Midmean - MS Excel (old versions)101.279393939394
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')