Free Statistics

of Irreproducible Research!

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationFri, 16 Oct 2009 07:44:32 -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/2009/Oct/16/t1255700707tt88jkod1zf5ft2.htm/, Retrieved Tue, 30 Apr 2024 02:40:40 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=47012, Retrieved Tue, 30 Apr 2024 02:40:40 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact136
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Bivariate Data Series] [Bivariate dataset] [2008-01-05 23:51:08] [74be16979710d4c4e7c6647856088456]
F RMPD  [Univariate Explorative Data Analysis] [Colombia Coffee] [2008-01-07 14:21:11] [74be16979710d4c4e7c6647856088456]
F RMPD    [Univariate Data Series] [] [2009-10-14 08:30:28] [74be16979710d4c4e7c6647856088456]
- RMPD      [Central Tendency] [WS3] [2009-10-16 12:59:56] [eaf42bcf5162b5692bb3c7f9d4636222]
- RMP         [Histogram] [WS3] [2009-10-16 13:03:45] [eaf42bcf5162b5692bb3c7f9d4636222]
- RMPD            [Central Tendency] [WS3] [2009-10-16 13:44:32] [78d370e6d5f4594e9982a5085e7604c6] [Current]
Feedback Forum

Post a new message
Dataseries X:
8.9
8.6
8.3
8.3
8.3
8.4
8.5
8.4
8.6
8.5
8.5
8.5
8.5
8.5
8.5
8.5
8.5
8.5
8.5
8.5
8.6
8.4
8.1
8
8
8
8
7.9
7.8
7.8
7.9
8.1
8
7.6
7.3
7
6.8
7
7.1
7.2
7.1
6.9
6.7
6.7
6.6
6.9
7.3
7.5
7.3
7.1
6.9
7.1
7.5
7.7
7.8
7.8
7.7
7.7
7.8
7.9




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=47012&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=47012&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=47012&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 Mean7.840.080682120198802597.1714672430778
Geometric Mean7.81491257476545
Harmonic Mean7.78927561225514
Quadratic Mean7.8644559040449
Winsorized Mean ( 1 / 20 )7.836666666666670.079296577916724898.8272996458502
Winsorized Mean ( 2 / 20 )7.836666666666670.079296577916724898.8272996458502
Winsorized Mean ( 3 / 20 )7.841666666666670.0781238935891523100.374754846519
Winsorized Mean ( 4 / 20 )7.841666666666670.0756251410482568103.69126666042
Winsorized Mean ( 5 / 20 )7.841666666666670.0756251410482568103.69126666042
Winsorized Mean ( 6 / 20 )7.841666666666670.0756251410482568103.69126666042
Winsorized Mean ( 7 / 20 )7.853333333333330.073240825061873107.226172379939
Winsorized Mean ( 8 / 20 )7.853333333333330.073240825061873107.226172379939
Winsorized Mean ( 9 / 20 )7.868333333333330.0703699532481773111.813820674055
Winsorized Mean ( 10 / 20 )7.868333333333330.0703699532481773111.813820674055
Winsorized Mean ( 11 / 20 )7.868333333333330.0703699532481773111.813820674055
Winsorized Mean ( 12 / 20 )7.868333333333330.0703699532481773111.813820674055
Winsorized Mean ( 13 / 20 )7.890.0664558814612443118.725383314662
Winsorized Mean ( 14 / 20 )7.913333333333330.0624575185192759126.699451418184
Winsorized Mean ( 15 / 20 )7.913333333333330.0624575185192759126.699451418184
Winsorized Mean ( 16 / 20 )7.886666666666670.0583418072941073135.180362632737
Winsorized Mean ( 17 / 20 )7.943333333333330.0491375715885471161.654983682278
Winsorized Mean ( 18 / 20 )7.943333333333330.0491375715885471161.654983682278
Winsorized Mean ( 19 / 20 )7.943333333333330.0394429192564736201.388068709687
Winsorized Mean ( 20 / 20 )7.976666666666670.0347197550912588229.744324108868
Trimmed Mean ( 1 / 20 )7.843103448275860.078518961260757699.8880184141676
Trimmed Mean ( 2 / 20 )7.850.0775015709937128101.288269377621
Trimmed Mean ( 3 / 20 )7.85740740740740.0761862558174678103.134185071816
Trimmed Mean ( 4 / 20 )7.863461538461540.0750579889521048104.765150895254
Trimmed Mean ( 5 / 20 )7.870.0745188648899713105.610841115471
Trimmed Mean ( 6 / 20 )7.877083333333330.0737327683519452106.832871047701
Trimmed Mean ( 7 / 20 )7.884782608695650.0726295205751711108.561677762074
Trimmed Mean ( 8 / 20 )7.890909090909090.0718097514253417109.886316750630
Trimmed Mean ( 9 / 20 )7.897619047619050.0706275253102706111.820696151031
Trimmed Mean ( 10 / 20 )7.90250.0697511602697357113.295606401960
Trimmed Mean ( 11 / 20 )7.90789473684210.0684497696601998115.528434589316
Trimmed Mean ( 12 / 20 )7.913888888888890.0665657304674345118.888335383934
Trimmed Mean ( 13 / 20 )7.920588235294120.0638597242464493124.031043490366
Trimmed Mean ( 14 / 20 )7.9250.0612372435695795129.414708077045
Trimmed Mean ( 15 / 20 )7.926666666666670.0587089711630102135.016276211989
Trimmed Mean ( 16 / 20 )7.928571428571430.054882544824192144.464354813892
Trimmed Mean ( 17 / 20 )7.934615384615380.050518026544167157.065030592165
Trimmed Mean ( 18 / 20 )7.933333333333330.0476500933993438166.491454000856
Trimmed Mean ( 19 / 20 )7.931818181818180.0428358204861971185.167882668993
Trimmed Mean ( 20 / 20 )7.930.0398021422327466199.235507315878
Median7.9
Midrange7.75
Midmean - Weighted Average at Xnp8.06190476190476
Midmean - Weighted Average at X(n+1)p8.06190476190476
Midmean - Empirical Distribution Function8.06190476190476
Midmean - Empirical Distribution Function - Averaging8.06190476190476
Midmean - Empirical Distribution Function - Interpolation8.06190476190476
Midmean - Closest Observation8.06190476190476
Midmean - True Basic - Statistics Graphics Toolkit8.06190476190476
Midmean - MS Excel (old versions)8.06190476190476
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 7.84 & 0.0806821201988025 & 97.1714672430778 \tabularnewline
Geometric Mean & 7.81491257476545 &  &  \tabularnewline
Harmonic Mean & 7.78927561225514 &  &  \tabularnewline
Quadratic Mean & 7.8644559040449 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 7.83666666666667 & 0.0792965779167248 & 98.8272996458502 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 7.83666666666667 & 0.0792965779167248 & 98.8272996458502 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 7.84166666666667 & 0.0781238935891523 & 100.374754846519 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 7.84166666666667 & 0.0756251410482568 & 103.69126666042 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 7.84166666666667 & 0.0756251410482568 & 103.69126666042 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 7.84166666666667 & 0.0756251410482568 & 103.69126666042 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 7.85333333333333 & 0.073240825061873 & 107.226172379939 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 7.85333333333333 & 0.073240825061873 & 107.226172379939 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 7.86833333333333 & 0.0703699532481773 & 111.813820674055 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 7.86833333333333 & 0.0703699532481773 & 111.813820674055 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 7.86833333333333 & 0.0703699532481773 & 111.813820674055 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 7.86833333333333 & 0.0703699532481773 & 111.813820674055 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 7.89 & 0.0664558814612443 & 118.725383314662 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 7.91333333333333 & 0.0624575185192759 & 126.699451418184 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 7.91333333333333 & 0.0624575185192759 & 126.699451418184 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 7.88666666666667 & 0.0583418072941073 & 135.180362632737 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 7.94333333333333 & 0.0491375715885471 & 161.654983682278 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 7.94333333333333 & 0.0491375715885471 & 161.654983682278 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 7.94333333333333 & 0.0394429192564736 & 201.388068709687 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 7.97666666666667 & 0.0347197550912588 & 229.744324108868 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 7.84310344827586 & 0.0785189612607576 & 99.8880184141676 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 7.85 & 0.0775015709937128 & 101.288269377621 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 7.8574074074074 & 0.0761862558174678 & 103.134185071816 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 7.86346153846154 & 0.0750579889521048 & 104.765150895254 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 7.87 & 0.0745188648899713 & 105.610841115471 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 7.87708333333333 & 0.0737327683519452 & 106.832871047701 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 7.88478260869565 & 0.0726295205751711 & 108.561677762074 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 7.89090909090909 & 0.0718097514253417 & 109.886316750630 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 7.89761904761905 & 0.0706275253102706 & 111.820696151031 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 7.9025 & 0.0697511602697357 & 113.295606401960 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 7.9078947368421 & 0.0684497696601998 & 115.528434589316 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 7.91388888888889 & 0.0665657304674345 & 118.888335383934 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 7.92058823529412 & 0.0638597242464493 & 124.031043490366 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 7.925 & 0.0612372435695795 & 129.414708077045 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 7.92666666666667 & 0.0587089711630102 & 135.016276211989 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 7.92857142857143 & 0.054882544824192 & 144.464354813892 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 7.93461538461538 & 0.050518026544167 & 157.065030592165 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 7.93333333333333 & 0.0476500933993438 & 166.491454000856 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 7.93181818181818 & 0.0428358204861971 & 185.167882668993 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 7.93 & 0.0398021422327466 & 199.235507315878 \tabularnewline
Median & 7.9 &  &  \tabularnewline
Midrange & 7.75 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 8.06190476190476 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 8.06190476190476 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 8.06190476190476 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 8.06190476190476 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 8.06190476190476 &  &  \tabularnewline
Midmean - Closest Observation & 8.06190476190476 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 8.06190476190476 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 8.06190476190476 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=47012&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]7.84[/C][C]0.0806821201988025[/C][C]97.1714672430778[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]7.81491257476545[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]7.78927561225514[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]7.8644559040449[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]7.83666666666667[/C][C]0.0792965779167248[/C][C]98.8272996458502[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]7.83666666666667[/C][C]0.0792965779167248[/C][C]98.8272996458502[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]7.84166666666667[/C][C]0.0781238935891523[/C][C]100.374754846519[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]7.84166666666667[/C][C]0.0756251410482568[/C][C]103.69126666042[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]7.84166666666667[/C][C]0.0756251410482568[/C][C]103.69126666042[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]7.84166666666667[/C][C]0.0756251410482568[/C][C]103.69126666042[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]7.85333333333333[/C][C]0.073240825061873[/C][C]107.226172379939[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]7.85333333333333[/C][C]0.073240825061873[/C][C]107.226172379939[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]7.86833333333333[/C][C]0.0703699532481773[/C][C]111.813820674055[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]7.86833333333333[/C][C]0.0703699532481773[/C][C]111.813820674055[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]7.86833333333333[/C][C]0.0703699532481773[/C][C]111.813820674055[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]7.86833333333333[/C][C]0.0703699532481773[/C][C]111.813820674055[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]7.89[/C][C]0.0664558814612443[/C][C]118.725383314662[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]7.91333333333333[/C][C]0.0624575185192759[/C][C]126.699451418184[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]7.91333333333333[/C][C]0.0624575185192759[/C][C]126.699451418184[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]7.88666666666667[/C][C]0.0583418072941073[/C][C]135.180362632737[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]7.94333333333333[/C][C]0.0491375715885471[/C][C]161.654983682278[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]7.94333333333333[/C][C]0.0491375715885471[/C][C]161.654983682278[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]7.94333333333333[/C][C]0.0394429192564736[/C][C]201.388068709687[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]7.97666666666667[/C][C]0.0347197550912588[/C][C]229.744324108868[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]7.84310344827586[/C][C]0.0785189612607576[/C][C]99.8880184141676[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]7.85[/C][C]0.0775015709937128[/C][C]101.288269377621[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]7.8574074074074[/C][C]0.0761862558174678[/C][C]103.134185071816[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]7.86346153846154[/C][C]0.0750579889521048[/C][C]104.765150895254[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]7.87[/C][C]0.0745188648899713[/C][C]105.610841115471[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]7.87708333333333[/C][C]0.0737327683519452[/C][C]106.832871047701[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]7.88478260869565[/C][C]0.0726295205751711[/C][C]108.561677762074[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]7.89090909090909[/C][C]0.0718097514253417[/C][C]109.886316750630[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]7.89761904761905[/C][C]0.0706275253102706[/C][C]111.820696151031[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]7.9025[/C][C]0.0697511602697357[/C][C]113.295606401960[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]7.9078947368421[/C][C]0.0684497696601998[/C][C]115.528434589316[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]7.91388888888889[/C][C]0.0665657304674345[/C][C]118.888335383934[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]7.92058823529412[/C][C]0.0638597242464493[/C][C]124.031043490366[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]7.925[/C][C]0.0612372435695795[/C][C]129.414708077045[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]7.92666666666667[/C][C]0.0587089711630102[/C][C]135.016276211989[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]7.92857142857143[/C][C]0.054882544824192[/C][C]144.464354813892[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]7.93461538461538[/C][C]0.050518026544167[/C][C]157.065030592165[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]7.93333333333333[/C][C]0.0476500933993438[/C][C]166.491454000856[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]7.93181818181818[/C][C]0.0428358204861971[/C][C]185.167882668993[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]7.93[/C][C]0.0398021422327466[/C][C]199.235507315878[/C][/ROW]
[ROW][C]Median[/C][C]7.9[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]7.75[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]8.06190476190476[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]8.06190476190476[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]8.06190476190476[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]8.06190476190476[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]8.06190476190476[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]8.06190476190476[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]8.06190476190476[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]8.06190476190476[/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=47012&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=47012&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 Mean7.840.080682120198802597.1714672430778
Geometric Mean7.81491257476545
Harmonic Mean7.78927561225514
Quadratic Mean7.8644559040449
Winsorized Mean ( 1 / 20 )7.836666666666670.079296577916724898.8272996458502
Winsorized Mean ( 2 / 20 )7.836666666666670.079296577916724898.8272996458502
Winsorized Mean ( 3 / 20 )7.841666666666670.0781238935891523100.374754846519
Winsorized Mean ( 4 / 20 )7.841666666666670.0756251410482568103.69126666042
Winsorized Mean ( 5 / 20 )7.841666666666670.0756251410482568103.69126666042
Winsorized Mean ( 6 / 20 )7.841666666666670.0756251410482568103.69126666042
Winsorized Mean ( 7 / 20 )7.853333333333330.073240825061873107.226172379939
Winsorized Mean ( 8 / 20 )7.853333333333330.073240825061873107.226172379939
Winsorized Mean ( 9 / 20 )7.868333333333330.0703699532481773111.813820674055
Winsorized Mean ( 10 / 20 )7.868333333333330.0703699532481773111.813820674055
Winsorized Mean ( 11 / 20 )7.868333333333330.0703699532481773111.813820674055
Winsorized Mean ( 12 / 20 )7.868333333333330.0703699532481773111.813820674055
Winsorized Mean ( 13 / 20 )7.890.0664558814612443118.725383314662
Winsorized Mean ( 14 / 20 )7.913333333333330.0624575185192759126.699451418184
Winsorized Mean ( 15 / 20 )7.913333333333330.0624575185192759126.699451418184
Winsorized Mean ( 16 / 20 )7.886666666666670.0583418072941073135.180362632737
Winsorized Mean ( 17 / 20 )7.943333333333330.0491375715885471161.654983682278
Winsorized Mean ( 18 / 20 )7.943333333333330.0491375715885471161.654983682278
Winsorized Mean ( 19 / 20 )7.943333333333330.0394429192564736201.388068709687
Winsorized Mean ( 20 / 20 )7.976666666666670.0347197550912588229.744324108868
Trimmed Mean ( 1 / 20 )7.843103448275860.078518961260757699.8880184141676
Trimmed Mean ( 2 / 20 )7.850.0775015709937128101.288269377621
Trimmed Mean ( 3 / 20 )7.85740740740740.0761862558174678103.134185071816
Trimmed Mean ( 4 / 20 )7.863461538461540.0750579889521048104.765150895254
Trimmed Mean ( 5 / 20 )7.870.0745188648899713105.610841115471
Trimmed Mean ( 6 / 20 )7.877083333333330.0737327683519452106.832871047701
Trimmed Mean ( 7 / 20 )7.884782608695650.0726295205751711108.561677762074
Trimmed Mean ( 8 / 20 )7.890909090909090.0718097514253417109.886316750630
Trimmed Mean ( 9 / 20 )7.897619047619050.0706275253102706111.820696151031
Trimmed Mean ( 10 / 20 )7.90250.0697511602697357113.295606401960
Trimmed Mean ( 11 / 20 )7.90789473684210.0684497696601998115.528434589316
Trimmed Mean ( 12 / 20 )7.913888888888890.0665657304674345118.888335383934
Trimmed Mean ( 13 / 20 )7.920588235294120.0638597242464493124.031043490366
Trimmed Mean ( 14 / 20 )7.9250.0612372435695795129.414708077045
Trimmed Mean ( 15 / 20 )7.926666666666670.0587089711630102135.016276211989
Trimmed Mean ( 16 / 20 )7.928571428571430.054882544824192144.464354813892
Trimmed Mean ( 17 / 20 )7.934615384615380.050518026544167157.065030592165
Trimmed Mean ( 18 / 20 )7.933333333333330.0476500933993438166.491454000856
Trimmed Mean ( 19 / 20 )7.931818181818180.0428358204861971185.167882668993
Trimmed Mean ( 20 / 20 )7.930.0398021422327466199.235507315878
Median7.9
Midrange7.75
Midmean - Weighted Average at Xnp8.06190476190476
Midmean - Weighted Average at X(n+1)p8.06190476190476
Midmean - Empirical Distribution Function8.06190476190476
Midmean - Empirical Distribution Function - Averaging8.06190476190476
Midmean - Empirical Distribution Function - Interpolation8.06190476190476
Midmean - Closest Observation8.06190476190476
Midmean - True Basic - Statistics Graphics Toolkit8.06190476190476
Midmean - MS Excel (old versions)8.06190476190476
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')