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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 computationThu, 11 Dec 2008 15:59:27 -0700
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/Dec/12/t1229036409yx3i7kfvl3ag8bc.htm/, Retrieved Fri, 17 May 2024 19:45:29 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=32470, Retrieved Fri, 17 May 2024 19:45:29 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact220
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Central Tendency] [Paper central ten...] [2007-11-09 08:56:17] [74be16979710d4c4e7c6647856088456]
-    D  [Central Tendency] [central tendency ...] [2008-12-11 22:56:40] [4ddbf81f78ea7c738951638c7e93f6ee]
-    D      [Central Tendency] [central tendency ...] [2008-12-11 22:59:27] [e8f764b122b426f433a1e1038b457077] [Current]
-    D        [Central Tendency] [central tendency ...] [2008-12-11 23:02:29] [4ddbf81f78ea7c738951638c7e93f6ee]
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Dataseries X:
9,4
9,5
9,1
9
9,3
9,9
9,8
9,4
8,3
8
8,5
10,4
11,1
10,9
9,9
9,2
9,2
9,5
9,6
9,5
9,1
8,9
9
10,1
10,3
10,2
9,6
9,2
9,3
9,4
9,4
9,2
9
9
9
9,8
10
9,9
9,3
9
9
9,1
9,1
9,1
9,2
8,8
8,3
8,4
8,1
7,8
7,9
7,9
8
7,9
7,5
7,2
6,9
6,6
6,7
7,3




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'George Udny Yule' @ 72.249.76.132

\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 & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=32470&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]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=32470&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=32470&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'George Udny Yule' @ 72.249.76.132







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean8.983333333333330.12465016960849972.0683602882226
Geometric Mean8.92961665839094
Harmonic Mean8.87292342944235
Quadratic Mean9.03421274932133
Winsorized Mean ( 1 / 20 )8.981666666666670.12319869731744672.9039093938114
Winsorized Mean ( 2 / 20 )8.971666666666670.11722043714780576.5367105341382
Winsorized Mean ( 3 / 20 )8.981666666666670.11192944879070680.243999802601
Winsorized Mean ( 4 / 20 )8.981666666666670.10885878653051682.507503095755
Winsorized Mean ( 5 / 20 )8.990.10307969600660287.214071716162
Winsorized Mean ( 6 / 20 )9.010.094321843543749395.5240023040993
Winsorized Mean ( 7 / 20 )9.010.0898114786367269100.321252213695
Winsorized Mean ( 8 / 20 )9.010.0898114786367269100.321252213695
Winsorized Mean ( 9 / 20 )9.010.0898114786367269100.321252213695
Winsorized Mean ( 10 / 20 )9.010.083622098557927107.746638213804
Winsorized Mean ( 11 / 20 )9.010.083622098557927107.746638213804
Winsorized Mean ( 12 / 20 )8.990.073480848037081122.344804668876
Winsorized Mean ( 13 / 20 )9.033333333333330.0648625956067996139.268761122263
Winsorized Mean ( 14 / 20 )9.010.0615570104595988146.368381647017
Winsorized Mean ( 15 / 20 )9.0350.0567393186642726159.237019631135
Winsorized Mean ( 16 / 20 )9.061666666666670.0517540722307631175.090891906286
Winsorized Mean ( 17 / 20 )9.118333333333330.0326331835779647279.419055500623
Winsorized Mean ( 18 / 20 )9.148333333333340.0278709360663184328.239184775317
Winsorized Mean ( 19 / 20 )9.180.0233857361519203392.546975659186
Winsorized Mean ( 20 / 20 )9.180.0233857361519203392.546975659186
Trimmed Mean ( 1 / 20 )8.987931034482760.11646324637776377.173969591482
Trimmed Mean ( 2 / 20 )8.994642857142860.10803497638472983.2567670039706
Trimmed Mean ( 3 / 20 )9.00740740740740.10165822392864288.604807946773
Trimmed Mean ( 4 / 20 )9.01730769230770.0963794487618493.5604821167846
Trimmed Mean ( 5 / 20 )9.0280.090982842069372799.2275004238307
Trimmed Mean ( 6 / 20 )9.03750.0862756283231434104.751482842295
Trimmed Mean ( 7 / 20 )9.043478260869560.0832116313586192108.680458647598
Trimmed Mean ( 8 / 20 )9.050.0805963502287186112.287963094081
Trimmed Mean ( 9 / 20 )9.057142857142860.0771247881793997117.434913870688
Trimmed Mean ( 10 / 20 )9.0650.0724613070931033125.101248703017
Trimmed Mean ( 11 / 20 )9.073684210526320.0680645048548983133.310074463479
Trimmed Mean ( 12 / 20 )9.083333333333330.061913918736689146.70906831085
Trimmed Mean ( 13 / 20 )9.097058823529410.0565630741457782160.830346668992
Trimmed Mean ( 14 / 20 )9.106250.0521585478412046174.58787441176
Trimmed Mean ( 15 / 20 )9.120.0465844925112288195.773303697613
Trimmed Mean ( 16 / 20 )9.132142857142860.0401892255127753227.228635053939
Trimmed Mean ( 17 / 20 )9.14230769230770.0324265213974739281.939205881637
Trimmed Mean ( 18 / 20 )9.145833333333330.0300839204647832304.010687172226
Trimmed Mean ( 19 / 20 )9.145454545454540.0284728721253773321.198876782908
Trimmed Mean ( 20 / 20 )9.140.0275298880644674332.002802866348
Median9.1
Midrange8.85
Midmean - Weighted Average at Xnp9.08181818181818
Midmean - Weighted Average at X(n+1)p9.13225806451613
Midmean - Empirical Distribution Function9.08181818181818
Midmean - Empirical Distribution Function - Averaging9.13225806451613
Midmean - Empirical Distribution Function - Interpolation9.13225806451613
Midmean - Closest Observation9.08181818181818
Midmean - True Basic - Statistics Graphics Toolkit9.13225806451613
Midmean - MS Excel (old versions)9.08181818181818
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 8.98333333333333 & 0.124650169608499 & 72.0683602882226 \tabularnewline
Geometric Mean & 8.92961665839094 &  &  \tabularnewline
Harmonic Mean & 8.87292342944235 &  &  \tabularnewline
Quadratic Mean & 9.03421274932133 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 8.98166666666667 & 0.123198697317446 & 72.9039093938114 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 8.97166666666667 & 0.117220437147805 & 76.5367105341382 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 8.98166666666667 & 0.111929448790706 & 80.243999802601 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 8.98166666666667 & 0.108858786530516 & 82.507503095755 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 8.99 & 0.103079696006602 & 87.214071716162 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 9.01 & 0.0943218435437493 & 95.5240023040993 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 9.01 & 0.0898114786367269 & 100.321252213695 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 9.01 & 0.0898114786367269 & 100.321252213695 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 9.01 & 0.0898114786367269 & 100.321252213695 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 9.01 & 0.083622098557927 & 107.746638213804 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 9.01 & 0.083622098557927 & 107.746638213804 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 8.99 & 0.073480848037081 & 122.344804668876 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 9.03333333333333 & 0.0648625956067996 & 139.268761122263 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 9.01 & 0.0615570104595988 & 146.368381647017 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 9.035 & 0.0567393186642726 & 159.237019631135 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 9.06166666666667 & 0.0517540722307631 & 175.090891906286 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 9.11833333333333 & 0.0326331835779647 & 279.419055500623 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 9.14833333333334 & 0.0278709360663184 & 328.239184775317 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 9.18 & 0.0233857361519203 & 392.546975659186 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 9.18 & 0.0233857361519203 & 392.546975659186 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 8.98793103448276 & 0.116463246377763 & 77.173969591482 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 8.99464285714286 & 0.108034976384729 & 83.2567670039706 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 9.0074074074074 & 0.101658223928642 & 88.604807946773 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 9.0173076923077 & 0.09637944876184 & 93.5604821167846 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 9.028 & 0.0909828420693727 & 99.2275004238307 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 9.0375 & 0.0862756283231434 & 104.751482842295 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 9.04347826086956 & 0.0832116313586192 & 108.680458647598 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 9.05 & 0.0805963502287186 & 112.287963094081 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 9.05714285714286 & 0.0771247881793997 & 117.434913870688 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 9.065 & 0.0724613070931033 & 125.101248703017 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 9.07368421052632 & 0.0680645048548983 & 133.310074463479 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 9.08333333333333 & 0.061913918736689 & 146.70906831085 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 9.09705882352941 & 0.0565630741457782 & 160.830346668992 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 9.10625 & 0.0521585478412046 & 174.58787441176 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 9.12 & 0.0465844925112288 & 195.773303697613 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 9.13214285714286 & 0.0401892255127753 & 227.228635053939 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 9.1423076923077 & 0.0324265213974739 & 281.939205881637 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 9.14583333333333 & 0.0300839204647832 & 304.010687172226 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 9.14545454545454 & 0.0284728721253773 & 321.198876782908 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 9.14 & 0.0275298880644674 & 332.002802866348 \tabularnewline
Median & 9.1 &  &  \tabularnewline
Midrange & 8.85 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 9.08181818181818 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 9.13225806451613 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 9.08181818181818 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 9.13225806451613 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 9.13225806451613 &  &  \tabularnewline
Midmean - Closest Observation & 9.08181818181818 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 9.13225806451613 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 9.08181818181818 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=32470&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]8.98333333333333[/C][C]0.124650169608499[/C][C]72.0683602882226[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]8.92961665839094[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]8.87292342944235[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]9.03421274932133[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]8.98166666666667[/C][C]0.123198697317446[/C][C]72.9039093938114[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]8.97166666666667[/C][C]0.117220437147805[/C][C]76.5367105341382[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]8.98166666666667[/C][C]0.111929448790706[/C][C]80.243999802601[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]8.98166666666667[/C][C]0.108858786530516[/C][C]82.507503095755[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]8.99[/C][C]0.103079696006602[/C][C]87.214071716162[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]9.01[/C][C]0.0943218435437493[/C][C]95.5240023040993[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]9.01[/C][C]0.0898114786367269[/C][C]100.321252213695[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]9.01[/C][C]0.0898114786367269[/C][C]100.321252213695[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]9.01[/C][C]0.0898114786367269[/C][C]100.321252213695[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]9.01[/C][C]0.083622098557927[/C][C]107.746638213804[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]9.01[/C][C]0.083622098557927[/C][C]107.746638213804[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]8.99[/C][C]0.073480848037081[/C][C]122.344804668876[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]9.03333333333333[/C][C]0.0648625956067996[/C][C]139.268761122263[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]9.01[/C][C]0.0615570104595988[/C][C]146.368381647017[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]9.035[/C][C]0.0567393186642726[/C][C]159.237019631135[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]9.06166666666667[/C][C]0.0517540722307631[/C][C]175.090891906286[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]9.11833333333333[/C][C]0.0326331835779647[/C][C]279.419055500623[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]9.14833333333334[/C][C]0.0278709360663184[/C][C]328.239184775317[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]9.18[/C][C]0.0233857361519203[/C][C]392.546975659186[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]9.18[/C][C]0.0233857361519203[/C][C]392.546975659186[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]8.98793103448276[/C][C]0.116463246377763[/C][C]77.173969591482[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]8.99464285714286[/C][C]0.108034976384729[/C][C]83.2567670039706[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]9.0074074074074[/C][C]0.101658223928642[/C][C]88.604807946773[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]9.0173076923077[/C][C]0.09637944876184[/C][C]93.5604821167846[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]9.028[/C][C]0.0909828420693727[/C][C]99.2275004238307[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]9.0375[/C][C]0.0862756283231434[/C][C]104.751482842295[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]9.04347826086956[/C][C]0.0832116313586192[/C][C]108.680458647598[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]9.05[/C][C]0.0805963502287186[/C][C]112.287963094081[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]9.05714285714286[/C][C]0.0771247881793997[/C][C]117.434913870688[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]9.065[/C][C]0.0724613070931033[/C][C]125.101248703017[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]9.07368421052632[/C][C]0.0680645048548983[/C][C]133.310074463479[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]9.08333333333333[/C][C]0.061913918736689[/C][C]146.70906831085[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]9.09705882352941[/C][C]0.0565630741457782[/C][C]160.830346668992[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]9.10625[/C][C]0.0521585478412046[/C][C]174.58787441176[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]9.12[/C][C]0.0465844925112288[/C][C]195.773303697613[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]9.13214285714286[/C][C]0.0401892255127753[/C][C]227.228635053939[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]9.1423076923077[/C][C]0.0324265213974739[/C][C]281.939205881637[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]9.14583333333333[/C][C]0.0300839204647832[/C][C]304.010687172226[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]9.14545454545454[/C][C]0.0284728721253773[/C][C]321.198876782908[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]9.14[/C][C]0.0275298880644674[/C][C]332.002802866348[/C][/ROW]
[ROW][C]Median[/C][C]9.1[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]8.85[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]9.08181818181818[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]9.13225806451613[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]9.08181818181818[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]9.13225806451613[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]9.13225806451613[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]9.08181818181818[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]9.13225806451613[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]9.08181818181818[/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=32470&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=32470&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 Mean8.983333333333330.12465016960849972.0683602882226
Geometric Mean8.92961665839094
Harmonic Mean8.87292342944235
Quadratic Mean9.03421274932133
Winsorized Mean ( 1 / 20 )8.981666666666670.12319869731744672.9039093938114
Winsorized Mean ( 2 / 20 )8.971666666666670.11722043714780576.5367105341382
Winsorized Mean ( 3 / 20 )8.981666666666670.11192944879070680.243999802601
Winsorized Mean ( 4 / 20 )8.981666666666670.10885878653051682.507503095755
Winsorized Mean ( 5 / 20 )8.990.10307969600660287.214071716162
Winsorized Mean ( 6 / 20 )9.010.094321843543749395.5240023040993
Winsorized Mean ( 7 / 20 )9.010.0898114786367269100.321252213695
Winsorized Mean ( 8 / 20 )9.010.0898114786367269100.321252213695
Winsorized Mean ( 9 / 20 )9.010.0898114786367269100.321252213695
Winsorized Mean ( 10 / 20 )9.010.083622098557927107.746638213804
Winsorized Mean ( 11 / 20 )9.010.083622098557927107.746638213804
Winsorized Mean ( 12 / 20 )8.990.073480848037081122.344804668876
Winsorized Mean ( 13 / 20 )9.033333333333330.0648625956067996139.268761122263
Winsorized Mean ( 14 / 20 )9.010.0615570104595988146.368381647017
Winsorized Mean ( 15 / 20 )9.0350.0567393186642726159.237019631135
Winsorized Mean ( 16 / 20 )9.061666666666670.0517540722307631175.090891906286
Winsorized Mean ( 17 / 20 )9.118333333333330.0326331835779647279.419055500623
Winsorized Mean ( 18 / 20 )9.148333333333340.0278709360663184328.239184775317
Winsorized Mean ( 19 / 20 )9.180.0233857361519203392.546975659186
Winsorized Mean ( 20 / 20 )9.180.0233857361519203392.546975659186
Trimmed Mean ( 1 / 20 )8.987931034482760.11646324637776377.173969591482
Trimmed Mean ( 2 / 20 )8.994642857142860.10803497638472983.2567670039706
Trimmed Mean ( 3 / 20 )9.00740740740740.10165822392864288.604807946773
Trimmed Mean ( 4 / 20 )9.01730769230770.0963794487618493.5604821167846
Trimmed Mean ( 5 / 20 )9.0280.090982842069372799.2275004238307
Trimmed Mean ( 6 / 20 )9.03750.0862756283231434104.751482842295
Trimmed Mean ( 7 / 20 )9.043478260869560.0832116313586192108.680458647598
Trimmed Mean ( 8 / 20 )9.050.0805963502287186112.287963094081
Trimmed Mean ( 9 / 20 )9.057142857142860.0771247881793997117.434913870688
Trimmed Mean ( 10 / 20 )9.0650.0724613070931033125.101248703017
Trimmed Mean ( 11 / 20 )9.073684210526320.0680645048548983133.310074463479
Trimmed Mean ( 12 / 20 )9.083333333333330.061913918736689146.70906831085
Trimmed Mean ( 13 / 20 )9.097058823529410.0565630741457782160.830346668992
Trimmed Mean ( 14 / 20 )9.106250.0521585478412046174.58787441176
Trimmed Mean ( 15 / 20 )9.120.0465844925112288195.773303697613
Trimmed Mean ( 16 / 20 )9.132142857142860.0401892255127753227.228635053939
Trimmed Mean ( 17 / 20 )9.14230769230770.0324265213974739281.939205881637
Trimmed Mean ( 18 / 20 )9.145833333333330.0300839204647832304.010687172226
Trimmed Mean ( 19 / 20 )9.145454545454540.0284728721253773321.198876782908
Trimmed Mean ( 20 / 20 )9.140.0275298880644674332.002802866348
Median9.1
Midrange8.85
Midmean - Weighted Average at Xnp9.08181818181818
Midmean - Weighted Average at X(n+1)p9.13225806451613
Midmean - Empirical Distribution Function9.08181818181818
Midmean - Empirical Distribution Function - Averaging9.13225806451613
Midmean - Empirical Distribution Function - Interpolation9.13225806451613
Midmean - Closest Observation9.08181818181818
Midmean - True Basic - Statistics Graphics Toolkit9.13225806451613
Midmean - MS Excel (old versions)9.08181818181818
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')