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of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationWed, 12 Oct 2016 13:12:52 +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/t1476274865odo8axyfdwdt9r0.htm/, Retrieved Sun, 05 May 2024 12:17:42 +0200
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=, Retrieved Sun, 05 May 2024 12:17:42 +0200
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact0
Dataseries X:
100
100
100
100
100
100
100
100
100
100
100
100
100,4
100,4
100,4
100,4
100,4
100,4
100,4
100,4
100,4
100,4
101,4
101,4
102
102
102,6
102,6
102,6
102,6
102,6
102,6
102,3
102,4
102,4
102,4
102,9
102,9
102,9
104,9
104,9
105,5
105,5
105,5
105,5
105,5
105,5
105,5
105,5
106,8
106,8
106,8
106,9
107,5
107,6
107,6
107,6
107,8
107,8
107,8




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

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

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

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

As an alternative you can also use a QR Code:  

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

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







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean102.990.358068421325146287.626592758034
Geometric Mean102.953562918396
Harmonic Mean102.917423313075
Quadratic Mean103.026718217493
Winsorized Mean ( 1 / 20 )102.990.358068421325146287.626592758034
Winsorized Mean ( 2 / 20 )102.990.358068421325146287.626592758034
Winsorized Mean ( 3 / 20 )102.980.355829578963774289.408205748079
Winsorized Mean ( 4 / 20 )102.980.355829578963774289.408205748079
Winsorized Mean ( 5 / 20 )102.980.355829578963774289.408205748079
Winsorized Mean ( 6 / 20 )102.970.353643665018772291.168795557342
Winsorized Mean ( 7 / 20 )102.90.339033188382581303.510109116169
Winsorized Mean ( 8 / 20 )102.8866666666670.336385461796019305.859433155456
Winsorized Mean ( 9 / 20 )102.8866666666670.336385461796019305.859433155456
Winsorized Mean ( 10 / 20 )102.8866666666670.336385461796019305.859433155456
Winsorized Mean ( 11 / 20 )102.6483333333330.292963541306491350.379207172217
Winsorized Mean ( 12 / 20 )102.7283333333330.281210977623509365.306981261834
Winsorized Mean ( 13 / 20 )102.7283333333330.281210977623509365.306981261834
Winsorized Mean ( 14 / 20 )102.7283333333330.281210977623509365.306981261834
Winsorized Mean ( 15 / 20 )102.7283333333330.281210977623509365.306981261834
Winsorized Mean ( 16 / 20 )102.7283333333330.281210977623509365.306981261834
Winsorized Mean ( 17 / 20 )102.7283333333330.281210977623509365.306981261834
Winsorized Mean ( 18 / 20 )102.7283333333330.281210977623509365.306981261834
Winsorized Mean ( 19 / 20 )102.5383333333330.250097062137167409.994153698197
Winsorized Mean ( 20 / 20 )102.5383333333330.250097062137167409.994153698197
Trimmed Mean ( 1 / 20 )102.9586206896550.357167001112022288.264650343113
Trimmed Mean ( 2 / 20 )102.9250.355606761509351289.434879030818
Trimmed Mean ( 3 / 20 )102.8888888888890.353228759758095291.281176989527
Trimmed Mean ( 4 / 20 )102.8538461538460.350871158221441293.138503247774
Trimmed Mean ( 5 / 20 )102.8160.347437969797693295.926205359385
Trimmed Mean ( 6 / 20 )102.7750.342633987872467299.955648411197
Trimmed Mean ( 7 / 20 )102.7326086956520.336751379037033305.06960057424
Trimmed Mean ( 8 / 20 )102.70.333046035456985308.365778499905
Trimmed Mean ( 9 / 20 )102.6666666666670.328401376655043312.625567262798
Trimmed Mean ( 10 / 20 )102.630.32171814388151319.005943406782
Trimmed Mean ( 11 / 20 )102.5894736842110.312262187718694328.536331707987
Trimmed Mean ( 12 / 20 )102.5805555555560.311061149616446329.776173212381
Trimmed Mean ( 13 / 20 )102.5588235294120.311145249453905329.61719232228
Trimmed Mean ( 14 / 20 )102.5343750.309936562675436330.823747011009
Trimmed Mean ( 15 / 20 )102.5066666666670.306854015735789334.056787299561
Trimmed Mean ( 16 / 20 )102.4750.300995921855338340.453117664666
Trimmed Mean ( 17 / 20 )102.4384615384620.290891305265884352.153741566216
Trimmed Mean ( 18 / 20 )102.3958333333330.273959108253712373.763201326036
Trimmed Mean ( 19 / 20 )102.3454545454550.245101557953305417.563459816737
Trimmed Mean ( 20 / 20 )102.3150.214141492820444477.791569734644
Median102.5
Midrange103.9
Midmean - Weighted Average at Xnp102.659459459459
Midmean - Weighted Average at X(n+1)p102.659459459459
Midmean - Empirical Distribution Function102.659459459459
Midmean - Empirical Distribution Function - Averaging102.659459459459
Midmean - Empirical Distribution Function - Interpolation102.659459459459
Midmean - Closest Observation102.659459459459
Midmean - True Basic - Statistics Graphics Toolkit102.659459459459
Midmean - MS Excel (old versions)102.659459459459
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 102.99 & 0.358068421325146 & 287.626592758034 \tabularnewline
Geometric Mean & 102.953562918396 &  &  \tabularnewline
Harmonic Mean & 102.917423313075 &  &  \tabularnewline
Quadratic Mean & 103.026718217493 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 102.99 & 0.358068421325146 & 287.626592758034 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 102.99 & 0.358068421325146 & 287.626592758034 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 102.98 & 0.355829578963774 & 289.408205748079 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 102.98 & 0.355829578963774 & 289.408205748079 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 102.98 & 0.355829578963774 & 289.408205748079 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 102.97 & 0.353643665018772 & 291.168795557342 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 102.9 & 0.339033188382581 & 303.510109116169 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 102.886666666667 & 0.336385461796019 & 305.859433155456 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 102.886666666667 & 0.336385461796019 & 305.859433155456 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 102.886666666667 & 0.336385461796019 & 305.859433155456 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 102.648333333333 & 0.292963541306491 & 350.379207172217 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 102.728333333333 & 0.281210977623509 & 365.306981261834 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 102.728333333333 & 0.281210977623509 & 365.306981261834 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 102.728333333333 & 0.281210977623509 & 365.306981261834 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 102.728333333333 & 0.281210977623509 & 365.306981261834 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 102.728333333333 & 0.281210977623509 & 365.306981261834 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 102.728333333333 & 0.281210977623509 & 365.306981261834 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 102.728333333333 & 0.281210977623509 & 365.306981261834 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 102.538333333333 & 0.250097062137167 & 409.994153698197 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 102.538333333333 & 0.250097062137167 & 409.994153698197 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 102.958620689655 & 0.357167001112022 & 288.264650343113 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 102.925 & 0.355606761509351 & 289.434879030818 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 102.888888888889 & 0.353228759758095 & 291.281176989527 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 102.853846153846 & 0.350871158221441 & 293.138503247774 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 102.816 & 0.347437969797693 & 295.926205359385 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 102.775 & 0.342633987872467 & 299.955648411197 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 102.732608695652 & 0.336751379037033 & 305.06960057424 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 102.7 & 0.333046035456985 & 308.365778499905 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 102.666666666667 & 0.328401376655043 & 312.625567262798 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 102.63 & 0.32171814388151 & 319.005943406782 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 102.589473684211 & 0.312262187718694 & 328.536331707987 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 102.580555555556 & 0.311061149616446 & 329.776173212381 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 102.558823529412 & 0.311145249453905 & 329.61719232228 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 102.534375 & 0.309936562675436 & 330.823747011009 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 102.506666666667 & 0.306854015735789 & 334.056787299561 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 102.475 & 0.300995921855338 & 340.453117664666 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 102.438461538462 & 0.290891305265884 & 352.153741566216 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 102.395833333333 & 0.273959108253712 & 373.763201326036 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 102.345454545455 & 0.245101557953305 & 417.563459816737 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 102.315 & 0.214141492820444 & 477.791569734644 \tabularnewline
Median & 102.5 &  &  \tabularnewline
Midrange & 103.9 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 102.659459459459 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 102.659459459459 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 102.659459459459 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 102.659459459459 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 102.659459459459 &  &  \tabularnewline
Midmean - Closest Observation & 102.659459459459 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 102.659459459459 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 102.659459459459 &  &  \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]102.99[/C][C]0.358068421325146[/C][C]287.626592758034[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]102.953562918396[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]102.917423313075[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]103.026718217493[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]102.99[/C][C]0.358068421325146[/C][C]287.626592758034[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]102.99[/C][C]0.358068421325146[/C][C]287.626592758034[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]102.98[/C][C]0.355829578963774[/C][C]289.408205748079[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]102.98[/C][C]0.355829578963774[/C][C]289.408205748079[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]102.98[/C][C]0.355829578963774[/C][C]289.408205748079[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]102.97[/C][C]0.353643665018772[/C][C]291.168795557342[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]102.9[/C][C]0.339033188382581[/C][C]303.510109116169[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]102.886666666667[/C][C]0.336385461796019[/C][C]305.859433155456[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]102.886666666667[/C][C]0.336385461796019[/C][C]305.859433155456[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]102.886666666667[/C][C]0.336385461796019[/C][C]305.859433155456[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]102.648333333333[/C][C]0.292963541306491[/C][C]350.379207172217[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]102.728333333333[/C][C]0.281210977623509[/C][C]365.306981261834[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]102.728333333333[/C][C]0.281210977623509[/C][C]365.306981261834[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]102.728333333333[/C][C]0.281210977623509[/C][C]365.306981261834[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]102.728333333333[/C][C]0.281210977623509[/C][C]365.306981261834[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]102.728333333333[/C][C]0.281210977623509[/C][C]365.306981261834[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]102.728333333333[/C][C]0.281210977623509[/C][C]365.306981261834[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]102.728333333333[/C][C]0.281210977623509[/C][C]365.306981261834[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]102.538333333333[/C][C]0.250097062137167[/C][C]409.994153698197[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]102.538333333333[/C][C]0.250097062137167[/C][C]409.994153698197[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]102.958620689655[/C][C]0.357167001112022[/C][C]288.264650343113[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]102.925[/C][C]0.355606761509351[/C][C]289.434879030818[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]102.888888888889[/C][C]0.353228759758095[/C][C]291.281176989527[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]102.853846153846[/C][C]0.350871158221441[/C][C]293.138503247774[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]102.816[/C][C]0.347437969797693[/C][C]295.926205359385[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]102.775[/C][C]0.342633987872467[/C][C]299.955648411197[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]102.732608695652[/C][C]0.336751379037033[/C][C]305.06960057424[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]102.7[/C][C]0.333046035456985[/C][C]308.365778499905[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]102.666666666667[/C][C]0.328401376655043[/C][C]312.625567262798[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]102.63[/C][C]0.32171814388151[/C][C]319.005943406782[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]102.589473684211[/C][C]0.312262187718694[/C][C]328.536331707987[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]102.580555555556[/C][C]0.311061149616446[/C][C]329.776173212381[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]102.558823529412[/C][C]0.311145249453905[/C][C]329.61719232228[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]102.534375[/C][C]0.309936562675436[/C][C]330.823747011009[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]102.506666666667[/C][C]0.306854015735789[/C][C]334.056787299561[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]102.475[/C][C]0.300995921855338[/C][C]340.453117664666[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]102.438461538462[/C][C]0.290891305265884[/C][C]352.153741566216[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]102.395833333333[/C][C]0.273959108253712[/C][C]373.763201326036[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]102.345454545455[/C][C]0.245101557953305[/C][C]417.563459816737[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]102.315[/C][C]0.214141492820444[/C][C]477.791569734644[/C][/ROW]
[ROW][C]Median[/C][C]102.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]103.9[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]102.659459459459[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]102.659459459459[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]102.659459459459[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]102.659459459459[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]102.659459459459[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]102.659459459459[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]102.659459459459[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]102.659459459459[/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 Mean102.990.358068421325146287.626592758034
Geometric Mean102.953562918396
Harmonic Mean102.917423313075
Quadratic Mean103.026718217493
Winsorized Mean ( 1 / 20 )102.990.358068421325146287.626592758034
Winsorized Mean ( 2 / 20 )102.990.358068421325146287.626592758034
Winsorized Mean ( 3 / 20 )102.980.355829578963774289.408205748079
Winsorized Mean ( 4 / 20 )102.980.355829578963774289.408205748079
Winsorized Mean ( 5 / 20 )102.980.355829578963774289.408205748079
Winsorized Mean ( 6 / 20 )102.970.353643665018772291.168795557342
Winsorized Mean ( 7 / 20 )102.90.339033188382581303.510109116169
Winsorized Mean ( 8 / 20 )102.8866666666670.336385461796019305.859433155456
Winsorized Mean ( 9 / 20 )102.8866666666670.336385461796019305.859433155456
Winsorized Mean ( 10 / 20 )102.8866666666670.336385461796019305.859433155456
Winsorized Mean ( 11 / 20 )102.6483333333330.292963541306491350.379207172217
Winsorized Mean ( 12 / 20 )102.7283333333330.281210977623509365.306981261834
Winsorized Mean ( 13 / 20 )102.7283333333330.281210977623509365.306981261834
Winsorized Mean ( 14 / 20 )102.7283333333330.281210977623509365.306981261834
Winsorized Mean ( 15 / 20 )102.7283333333330.281210977623509365.306981261834
Winsorized Mean ( 16 / 20 )102.7283333333330.281210977623509365.306981261834
Winsorized Mean ( 17 / 20 )102.7283333333330.281210977623509365.306981261834
Winsorized Mean ( 18 / 20 )102.7283333333330.281210977623509365.306981261834
Winsorized Mean ( 19 / 20 )102.5383333333330.250097062137167409.994153698197
Winsorized Mean ( 20 / 20 )102.5383333333330.250097062137167409.994153698197
Trimmed Mean ( 1 / 20 )102.9586206896550.357167001112022288.264650343113
Trimmed Mean ( 2 / 20 )102.9250.355606761509351289.434879030818
Trimmed Mean ( 3 / 20 )102.8888888888890.353228759758095291.281176989527
Trimmed Mean ( 4 / 20 )102.8538461538460.350871158221441293.138503247774
Trimmed Mean ( 5 / 20 )102.8160.347437969797693295.926205359385
Trimmed Mean ( 6 / 20 )102.7750.342633987872467299.955648411197
Trimmed Mean ( 7 / 20 )102.7326086956520.336751379037033305.06960057424
Trimmed Mean ( 8 / 20 )102.70.333046035456985308.365778499905
Trimmed Mean ( 9 / 20 )102.6666666666670.328401376655043312.625567262798
Trimmed Mean ( 10 / 20 )102.630.32171814388151319.005943406782
Trimmed Mean ( 11 / 20 )102.5894736842110.312262187718694328.536331707987
Trimmed Mean ( 12 / 20 )102.5805555555560.311061149616446329.776173212381
Trimmed Mean ( 13 / 20 )102.5588235294120.311145249453905329.61719232228
Trimmed Mean ( 14 / 20 )102.5343750.309936562675436330.823747011009
Trimmed Mean ( 15 / 20 )102.5066666666670.306854015735789334.056787299561
Trimmed Mean ( 16 / 20 )102.4750.300995921855338340.453117664666
Trimmed Mean ( 17 / 20 )102.4384615384620.290891305265884352.153741566216
Trimmed Mean ( 18 / 20 )102.3958333333330.273959108253712373.763201326036
Trimmed Mean ( 19 / 20 )102.3454545454550.245101557953305417.563459816737
Trimmed Mean ( 20 / 20 )102.3150.214141492820444477.791569734644
Median102.5
Midrange103.9
Midmean - Weighted Average at Xnp102.659459459459
Midmean - Weighted Average at X(n+1)p102.659459459459
Midmean - Empirical Distribution Function102.659459459459
Midmean - Empirical Distribution Function - Averaging102.659459459459
Midmean - Empirical Distribution Function - Interpolation102.659459459459
Midmean - Closest Observation102.659459459459
Midmean - True Basic - Statistics Graphics Toolkit102.659459459459
Midmean - MS Excel (old versions)102.659459459459
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')