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Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationMon, 20 Oct 2008 07:22:34 -0600
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2008/Oct/20/t1224509193xcw2ou2pcbnq4rl.htm/, Retrieved Sun, 19 May 2024 15:36:40 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=17240, Retrieved Sun, 19 May 2024 15:36:40 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact151
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
F     [Univariate Data Series] [Werkloosheid mannen] [2008-10-13 15:28:04] [7d3039e6253bb5fb3b26df1537d500b4]
- RMPD    [Central Tendency] [Central tendency ...] [2008-10-20 13:22:34] [35348cd8592af0baf5f138bd59921307] [Current]
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Dataseries X:
7.8
7.6
7.5
7.6
7.5
7.3
7.6
7.5
7.6
7.9
7.9
8.1
8.2
8.0
7.5
6.8
6.5
6.6
7.6
8.0
8.0
7.7
7.5
7.6
7.7
7.9
7.8
7.5
7.5
7.1
7.5
7.5
7.6
7.7
7.7
7.9
8.1
8.2
8.2
8.1
7.9
7.3
6.9
6.6
6.7
6.9
7.0
7.1
7.2
7.1
6.9
7.0
6.8
6.4
6.7
6.7
6.4
6.3
6.2
6.5




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\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 & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=17240&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]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=17240&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=17240&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'Gwilym Jenkins' @ 72.249.127.135







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean7.3750.0710544074182547103.793702149788
Geometric Mean7.35429033739278
Harmonic Mean7.33308580491526
Quadratic Mean7.39516734090582
Winsorized Mean ( 1 / 20 )7.376666666666670.070605399301655104.477373396765
Winsorized Mean ( 2 / 20 )7.380.0697776938116495105.764458480396
Winsorized Mean ( 3 / 20 )7.3750.0688330905181693107.143235099306
Winsorized Mean ( 4 / 20 )7.381666666666670.0672919126388256109.696193453233
Winsorized Mean ( 5 / 20 )7.381666666666670.0672919126388256109.696193453233
Winsorized Mean ( 6 / 20 )7.381666666666670.0634013164715067116.427656040613
Winsorized Mean ( 7 / 20 )7.381666666666670.0634013164715067116.427656040613
Winsorized Mean ( 8 / 20 )7.3950.0607125765319883121.803428917297
Winsorized Mean ( 9 / 20 )7.380.058309518948453126.565955835172
Winsorized Mean ( 10 / 20 )7.380.058309518948453126.565955835172
Winsorized Mean ( 11 / 20 )7.398333333333330.0547976074092453135.011977404055
Winsorized Mean ( 12 / 20 )7.398333333333330.0547976074092453135.011977404055
Winsorized Mean ( 13 / 20 )7.420.0509125760051505145.740023039678
Winsorized Mean ( 14 / 20 )7.396666666666670.0473576765603023156.187279526862
Winsorized Mean ( 15 / 20 )7.396666666666670.0473576765603023156.187279526862
Winsorized Mean ( 16 / 20 )7.396666666666670.0389818635699189.746358672755
Winsorized Mean ( 17 / 20 )7.396666666666670.0389818635699189.746358672755
Winsorized Mean ( 18 / 20 )7.426666666666670.0339380181686086218.830299099081
Winsorized Mean ( 19 / 20 )7.426666666666670.0339380181686086218.830299099081
Winsorized Mean ( 20 / 20 )7.393333333333330.0296749496467111249.143921770824
Trimmed Mean ( 1 / 20 )7.381034482758620.0691516695182923106.736894917716
Trimmed Mean ( 2 / 20 )7.385714285714290.0673442682328785109.671015507575
Trimmed Mean ( 3 / 20 )7.388888888888890.065645569441724112.557312728444
Trimmed Mean ( 4 / 20 )7.394230769230770.0639577927812902115.611099878259
Trimmed Mean ( 5 / 20 )7.3980.0624329844795234118.495056125763
Trimmed Mean ( 6 / 20 )7.402083333333330.0604716673102481122.405808580689
Trimmed Mean ( 7 / 20 )7.406521739130430.0591732226547877125.16677995281
Trimmed Mean ( 8 / 20 )7.411363636363640.0574489302659225129.007861452903
Trimmed Mean ( 9 / 20 )7.414285714285710.055954543166268132.505517778142
Trimmed Mean ( 10 / 20 )7.420.0545611865424779135.994109919572
Trimmed Mean ( 11 / 20 )7.426315789473680.0526244660912041141.119071433486
Trimmed Mean ( 12 / 20 )7.430555555555560.0509932215296828145.716535113011
Trimmed Mean ( 13 / 20 )7.435294117647060.0486689777259688152.772761316491
Trimmed Mean ( 14 / 20 )7.43750.046608787071303159.572914622772
Trimmed Mean ( 15 / 20 )7.443333333333330.0446398959061668166.741726929185
Trimmed Mean ( 16 / 20 )7.450.0416269652125186178.970529366372
Trimmed Mean ( 17 / 20 )7.457692307692310.0400665127480167186.132802587404
Trimmed Mean ( 18 / 20 )7.466666666666670.0374294828120144199.486236669825
Trimmed Mean ( 19 / 20 )7.472727272727270.0355426809958546210.246584201086
Trimmed Mean ( 20 / 20 )7.480.0321182027418786232.889743554888
Median7.5
Midrange7.2
Midmean - Weighted Average at Xnp7.42121212121212
Midmean - Weighted Average at X(n+1)p7.42121212121212
Midmean - Empirical Distribution Function7.42121212121212
Midmean - Empirical Distribution Function - Averaging7.42121212121212
Midmean - Empirical Distribution Function - Interpolation7.42121212121212
Midmean - Closest Observation7.42121212121212
Midmean - True Basic - Statistics Graphics Toolkit7.42121212121212
Midmean - MS Excel (old versions)7.42121212121212
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 7.375 & 0.0710544074182547 & 103.793702149788 \tabularnewline
Geometric Mean & 7.35429033739278 &  &  \tabularnewline
Harmonic Mean & 7.33308580491526 &  &  \tabularnewline
Quadratic Mean & 7.39516734090582 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 7.37666666666667 & 0.070605399301655 & 104.477373396765 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 7.38 & 0.0697776938116495 & 105.764458480396 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 7.375 & 0.0688330905181693 & 107.143235099306 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 7.38166666666667 & 0.0672919126388256 & 109.696193453233 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 7.38166666666667 & 0.0672919126388256 & 109.696193453233 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 7.38166666666667 & 0.0634013164715067 & 116.427656040613 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 7.38166666666667 & 0.0634013164715067 & 116.427656040613 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 7.395 & 0.0607125765319883 & 121.803428917297 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 7.38 & 0.058309518948453 & 126.565955835172 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 7.38 & 0.058309518948453 & 126.565955835172 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 7.39833333333333 & 0.0547976074092453 & 135.011977404055 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 7.39833333333333 & 0.0547976074092453 & 135.011977404055 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 7.42 & 0.0509125760051505 & 145.740023039678 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 7.39666666666667 & 0.0473576765603023 & 156.187279526862 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 7.39666666666667 & 0.0473576765603023 & 156.187279526862 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 7.39666666666667 & 0.0389818635699 & 189.746358672755 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 7.39666666666667 & 0.0389818635699 & 189.746358672755 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 7.42666666666667 & 0.0339380181686086 & 218.830299099081 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 7.42666666666667 & 0.0339380181686086 & 218.830299099081 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 7.39333333333333 & 0.0296749496467111 & 249.143921770824 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 7.38103448275862 & 0.0691516695182923 & 106.736894917716 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 7.38571428571429 & 0.0673442682328785 & 109.671015507575 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 7.38888888888889 & 0.065645569441724 & 112.557312728444 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 7.39423076923077 & 0.0639577927812902 & 115.611099878259 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 7.398 & 0.0624329844795234 & 118.495056125763 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 7.40208333333333 & 0.0604716673102481 & 122.405808580689 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 7.40652173913043 & 0.0591732226547877 & 125.16677995281 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 7.41136363636364 & 0.0574489302659225 & 129.007861452903 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 7.41428571428571 & 0.055954543166268 & 132.505517778142 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 7.42 & 0.0545611865424779 & 135.994109919572 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 7.42631578947368 & 0.0526244660912041 & 141.119071433486 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 7.43055555555556 & 0.0509932215296828 & 145.716535113011 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 7.43529411764706 & 0.0486689777259688 & 152.772761316491 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 7.4375 & 0.046608787071303 & 159.572914622772 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 7.44333333333333 & 0.0446398959061668 & 166.741726929185 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 7.45 & 0.0416269652125186 & 178.970529366372 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 7.45769230769231 & 0.0400665127480167 & 186.132802587404 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 7.46666666666667 & 0.0374294828120144 & 199.486236669825 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 7.47272727272727 & 0.0355426809958546 & 210.246584201086 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 7.48 & 0.0321182027418786 & 232.889743554888 \tabularnewline
Median & 7.5 &  &  \tabularnewline
Midrange & 7.2 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 7.42121212121212 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 7.42121212121212 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 7.42121212121212 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 7.42121212121212 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 7.42121212121212 &  &  \tabularnewline
Midmean - Closest Observation & 7.42121212121212 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 7.42121212121212 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 7.42121212121212 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=17240&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]7.375[/C][C]0.0710544074182547[/C][C]103.793702149788[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]7.35429033739278[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]7.33308580491526[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]7.39516734090582[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]7.37666666666667[/C][C]0.070605399301655[/C][C]104.477373396765[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]7.38[/C][C]0.0697776938116495[/C][C]105.764458480396[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]7.375[/C][C]0.0688330905181693[/C][C]107.143235099306[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]7.38166666666667[/C][C]0.0672919126388256[/C][C]109.696193453233[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]7.38166666666667[/C][C]0.0672919126388256[/C][C]109.696193453233[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]7.38166666666667[/C][C]0.0634013164715067[/C][C]116.427656040613[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]7.38166666666667[/C][C]0.0634013164715067[/C][C]116.427656040613[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]7.395[/C][C]0.0607125765319883[/C][C]121.803428917297[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]7.38[/C][C]0.058309518948453[/C][C]126.565955835172[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]7.38[/C][C]0.058309518948453[/C][C]126.565955835172[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]7.39833333333333[/C][C]0.0547976074092453[/C][C]135.011977404055[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]7.39833333333333[/C][C]0.0547976074092453[/C][C]135.011977404055[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]7.42[/C][C]0.0509125760051505[/C][C]145.740023039678[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]7.39666666666667[/C][C]0.0473576765603023[/C][C]156.187279526862[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]7.39666666666667[/C][C]0.0473576765603023[/C][C]156.187279526862[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]7.39666666666667[/C][C]0.0389818635699[/C][C]189.746358672755[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]7.39666666666667[/C][C]0.0389818635699[/C][C]189.746358672755[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]7.42666666666667[/C][C]0.0339380181686086[/C][C]218.830299099081[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]7.42666666666667[/C][C]0.0339380181686086[/C][C]218.830299099081[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]7.39333333333333[/C][C]0.0296749496467111[/C][C]249.143921770824[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]7.38103448275862[/C][C]0.0691516695182923[/C][C]106.736894917716[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]7.38571428571429[/C][C]0.0673442682328785[/C][C]109.671015507575[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]7.38888888888889[/C][C]0.065645569441724[/C][C]112.557312728444[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]7.39423076923077[/C][C]0.0639577927812902[/C][C]115.611099878259[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]7.398[/C][C]0.0624329844795234[/C][C]118.495056125763[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]7.40208333333333[/C][C]0.0604716673102481[/C][C]122.405808580689[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]7.40652173913043[/C][C]0.0591732226547877[/C][C]125.16677995281[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]7.41136363636364[/C][C]0.0574489302659225[/C][C]129.007861452903[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]7.41428571428571[/C][C]0.055954543166268[/C][C]132.505517778142[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]7.42[/C][C]0.0545611865424779[/C][C]135.994109919572[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]7.42631578947368[/C][C]0.0526244660912041[/C][C]141.119071433486[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]7.43055555555556[/C][C]0.0509932215296828[/C][C]145.716535113011[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]7.43529411764706[/C][C]0.0486689777259688[/C][C]152.772761316491[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]7.4375[/C][C]0.046608787071303[/C][C]159.572914622772[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]7.44333333333333[/C][C]0.0446398959061668[/C][C]166.741726929185[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]7.45[/C][C]0.0416269652125186[/C][C]178.970529366372[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]7.45769230769231[/C][C]0.0400665127480167[/C][C]186.132802587404[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]7.46666666666667[/C][C]0.0374294828120144[/C][C]199.486236669825[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]7.47272727272727[/C][C]0.0355426809958546[/C][C]210.246584201086[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]7.48[/C][C]0.0321182027418786[/C][C]232.889743554888[/C][/ROW]
[ROW][C]Median[/C][C]7.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]7.2[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]7.42121212121212[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]7.42121212121212[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]7.42121212121212[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]7.42121212121212[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]7.42121212121212[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]7.42121212121212[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]7.42121212121212[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]7.42121212121212[/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=17240&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=17240&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 Mean7.3750.0710544074182547103.793702149788
Geometric Mean7.35429033739278
Harmonic Mean7.33308580491526
Quadratic Mean7.39516734090582
Winsorized Mean ( 1 / 20 )7.376666666666670.070605399301655104.477373396765
Winsorized Mean ( 2 / 20 )7.380.0697776938116495105.764458480396
Winsorized Mean ( 3 / 20 )7.3750.0688330905181693107.143235099306
Winsorized Mean ( 4 / 20 )7.381666666666670.0672919126388256109.696193453233
Winsorized Mean ( 5 / 20 )7.381666666666670.0672919126388256109.696193453233
Winsorized Mean ( 6 / 20 )7.381666666666670.0634013164715067116.427656040613
Winsorized Mean ( 7 / 20 )7.381666666666670.0634013164715067116.427656040613
Winsorized Mean ( 8 / 20 )7.3950.0607125765319883121.803428917297
Winsorized Mean ( 9 / 20 )7.380.058309518948453126.565955835172
Winsorized Mean ( 10 / 20 )7.380.058309518948453126.565955835172
Winsorized Mean ( 11 / 20 )7.398333333333330.0547976074092453135.011977404055
Winsorized Mean ( 12 / 20 )7.398333333333330.0547976074092453135.011977404055
Winsorized Mean ( 13 / 20 )7.420.0509125760051505145.740023039678
Winsorized Mean ( 14 / 20 )7.396666666666670.0473576765603023156.187279526862
Winsorized Mean ( 15 / 20 )7.396666666666670.0473576765603023156.187279526862
Winsorized Mean ( 16 / 20 )7.396666666666670.0389818635699189.746358672755
Winsorized Mean ( 17 / 20 )7.396666666666670.0389818635699189.746358672755
Winsorized Mean ( 18 / 20 )7.426666666666670.0339380181686086218.830299099081
Winsorized Mean ( 19 / 20 )7.426666666666670.0339380181686086218.830299099081
Winsorized Mean ( 20 / 20 )7.393333333333330.0296749496467111249.143921770824
Trimmed Mean ( 1 / 20 )7.381034482758620.0691516695182923106.736894917716
Trimmed Mean ( 2 / 20 )7.385714285714290.0673442682328785109.671015507575
Trimmed Mean ( 3 / 20 )7.388888888888890.065645569441724112.557312728444
Trimmed Mean ( 4 / 20 )7.394230769230770.0639577927812902115.611099878259
Trimmed Mean ( 5 / 20 )7.3980.0624329844795234118.495056125763
Trimmed Mean ( 6 / 20 )7.402083333333330.0604716673102481122.405808580689
Trimmed Mean ( 7 / 20 )7.406521739130430.0591732226547877125.16677995281
Trimmed Mean ( 8 / 20 )7.411363636363640.0574489302659225129.007861452903
Trimmed Mean ( 9 / 20 )7.414285714285710.055954543166268132.505517778142
Trimmed Mean ( 10 / 20 )7.420.0545611865424779135.994109919572
Trimmed Mean ( 11 / 20 )7.426315789473680.0526244660912041141.119071433486
Trimmed Mean ( 12 / 20 )7.430555555555560.0509932215296828145.716535113011
Trimmed Mean ( 13 / 20 )7.435294117647060.0486689777259688152.772761316491
Trimmed Mean ( 14 / 20 )7.43750.046608787071303159.572914622772
Trimmed Mean ( 15 / 20 )7.443333333333330.0446398959061668166.741726929185
Trimmed Mean ( 16 / 20 )7.450.0416269652125186178.970529366372
Trimmed Mean ( 17 / 20 )7.457692307692310.0400665127480167186.132802587404
Trimmed Mean ( 18 / 20 )7.466666666666670.0374294828120144199.486236669825
Trimmed Mean ( 19 / 20 )7.472727272727270.0355426809958546210.246584201086
Trimmed Mean ( 20 / 20 )7.480.0321182027418786232.889743554888
Median7.5
Midrange7.2
Midmean - Weighted Average at Xnp7.42121212121212
Midmean - Weighted Average at X(n+1)p7.42121212121212
Midmean - Empirical Distribution Function7.42121212121212
Midmean - Empirical Distribution Function - Averaging7.42121212121212
Midmean - Empirical Distribution Function - Interpolation7.42121212121212
Midmean - Closest Observation7.42121212121212
Midmean - True Basic - Statistics Graphics Toolkit7.42121212121212
Midmean - MS Excel (old versions)7.42121212121212
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')