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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 computationFri, 20 Nov 2009 07:28:45 -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/2009/Nov/20/t12587274665muzug5eqg4uc0m.htm/, Retrieved Thu, 28 Mar 2024 14:07:17 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=58210, Retrieved Thu, 28 Mar 2024 14:07:17 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsETSHWP(2)
Estimated Impact135
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Multiple Regression] [invoer-textiel] [2008-12-19 19:19:44] [5e74953d94072114d25d7276793b561e]
-   PD  [Multiple Regression] [invoer-textiel] [2008-12-19 19:31:41] [5e74953d94072114d25d7276793b561e]
-   PD    [Multiple Regression] [werkloosheid/invoer] [2008-12-19 20:08:51] [5e74953d94072114d25d7276793b561e]
- RM D        [Central Tendency] [Paper statistiek:...] [2009-11-20 14:28:45] [af31b947d6acaef3c71f428c4bb503e9] [Current]
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Dataseries X:
1.43
1.43
1.43
1.43
1.43
1.43
1.44
1.48
1.48
1.48
1.48
1.48
1.48
1.48
1.48
1.48
1.48
1.48
1.48
1.48
1.48
1.48
1.48
1.48
1.48
1.48
1.48
1.48
1.48
1.48
1.48
1.48
1.48
1.48
1.48
1.48
1.48
1.57
1.58
1.58
1.58
1.58
1.59
1.6
1.6
1.61
1.61
1.61
1.62
1.63
1.63
1.64
1.64
1.64
1.64
1.64
1.65
1.65
1.65
1.65




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 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 & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58210&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]2 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=58210&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58210&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 time2 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean1.526833333333330.00969737475881004157.448110577165
Geometric Mean1.52504257777793
Harmonic Mean1.52327980010142
Quadratic Mean1.52864918582824
Winsorized Mean ( 1 / 20 )1.526833333333330.00969737475881004157.448110577165
Winsorized Mean ( 2 / 20 )1.526833333333330.00969737475881004157.448110577165
Winsorized Mean ( 3 / 20 )1.526833333333330.00969737475881004157.448110577165
Winsorized Mean ( 4 / 20 )1.526166666666670.0095583006392931159.669247103692
Winsorized Mean ( 5 / 20 )1.526166666666670.0095583006392931159.669247103692
Winsorized Mean ( 6 / 20 )1.527166666666670.0093943475813035162.56229114899
Winsorized Mean ( 7 / 20 )1.531833333333330.00878973356796762174.275286217524
Winsorized Mean ( 8 / 20 )1.531833333333330.00878973356796762174.275286217524
Winsorized Mean ( 9 / 20 )1.530333333333330.0084838386294632180.382183133316
Winsorized Mean ( 10 / 20 )1.530333333333330.0084838386294632180.382183133316
Winsorized Mean ( 11 / 20 )1.52850.00812621133951508188.095034221841
Winsorized Mean ( 12 / 20 )1.52650.00775261938602901196.901192228127
Winsorized Mean ( 13 / 20 )1.52650.00775261938602901196.901192228127
Winsorized Mean ( 14 / 20 )1.52650.00775261938602901196.901192228127
Winsorized Mean ( 15 / 20 )1.5240.00730374101186246208.660191746227
Winsorized Mean ( 16 / 20 )1.5240.00730374101186246208.660191746227
Winsorized Mean ( 17 / 20 )1.521166666666670.00681097347658041223.340565324063
Winsorized Mean ( 18 / 20 )1.518166666666670.00630438671894988240.811158062897
Winsorized Mean ( 19 / 20 )1.518166666666670.00630438671894988240.811158062897
Winsorized Mean ( 20 / 20 )1.518166666666670.00630438671894988240.811158062897
Trimmed Mean ( 1 / 20 )1.526379310344830.00965746775067031158.051711872285
Trimmed Mean ( 2 / 20 )1.525892857142860.0095983520829734158.974461860974
Trimmed Mean ( 3 / 20 )1.525370370370370.00951556510369693160.30265714621
Trimmed Mean ( 4 / 20 )1.524807692307690.00940335609922128162.155689545137
Trimmed Mean ( 5 / 20 )1.52440.00930727167984523163.785914114989
Trimmed Mean ( 6 / 20 )1.523958333333330.00917587987999538166.083073586846
Trimmed Mean ( 7 / 20 )1.523260869565220.00904660156025234168.379347694266
Trimmed Mean ( 8 / 20 )1.521590909090910.00901574369875655168.770426481929
Trimmed Mean ( 9 / 20 )1.519761904761900.00894873835499286169.829739620666
Trimmed Mean ( 10 / 20 )1.5180.00891699615974015170.236699983533
Trimmed Mean ( 11 / 20 )1.516052631578950.00884141516645902171.471716126427
Trimmed Mean ( 12 / 20 )1.514166666666670.00880453526711327171.975762573453
Trimmed Mean ( 13 / 20 )1.512352941176470.00881639640379871171.538673161842
Trimmed Mean ( 14 / 20 )1.51031250.00878144551211577171.989053273316
Trimmed Mean ( 15 / 20 )1.5080.00867550389407394173.822756396903
Trimmed Mean ( 16 / 20 )1.505714285714290.0086132138461135174.814455163412
Trimmed Mean ( 17 / 20 )1.503076923076920.00844473856714675177.989751976984
Trimmed Mean ( 18 / 20 )1.500416666666670.00830747800606515180.610368823274
Trimmed Mean ( 19 / 20 )1.497727272727270.00821601798889589182.293572719958
Trimmed Mean ( 20 / 20 )1.49450.0079297905992131188.466515137021
Median1.48
Midrange1.54
Midmean - Weighted Average at Xnp1.50210526315789
Midmean - Weighted Average at X(n+1)p1.50210526315789
Midmean - Empirical Distribution Function1.50210526315789
Midmean - Empirical Distribution Function - Averaging1.50210526315789
Midmean - Empirical Distribution Function - Interpolation1.50210526315789
Midmean - Closest Observation1.50210526315789
Midmean - True Basic - Statistics Graphics Toolkit1.50210526315789
Midmean - MS Excel (old versions)1.51
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 1.52683333333333 & 0.00969737475881004 & 157.448110577165 \tabularnewline
Geometric Mean & 1.52504257777793 &  &  \tabularnewline
Harmonic Mean & 1.52327980010142 &  &  \tabularnewline
Quadratic Mean & 1.52864918582824 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 1.52683333333333 & 0.00969737475881004 & 157.448110577165 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 1.52683333333333 & 0.00969737475881004 & 157.448110577165 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 1.52683333333333 & 0.00969737475881004 & 157.448110577165 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 1.52616666666667 & 0.0095583006392931 & 159.669247103692 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 1.52616666666667 & 0.0095583006392931 & 159.669247103692 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 1.52716666666667 & 0.0093943475813035 & 162.56229114899 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 1.53183333333333 & 0.00878973356796762 & 174.275286217524 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 1.53183333333333 & 0.00878973356796762 & 174.275286217524 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 1.53033333333333 & 0.0084838386294632 & 180.382183133316 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 1.53033333333333 & 0.0084838386294632 & 180.382183133316 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 1.5285 & 0.00812621133951508 & 188.095034221841 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 1.5265 & 0.00775261938602901 & 196.901192228127 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 1.5265 & 0.00775261938602901 & 196.901192228127 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 1.5265 & 0.00775261938602901 & 196.901192228127 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 1.524 & 0.00730374101186246 & 208.660191746227 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 1.524 & 0.00730374101186246 & 208.660191746227 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 1.52116666666667 & 0.00681097347658041 & 223.340565324063 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 1.51816666666667 & 0.00630438671894988 & 240.811158062897 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 1.51816666666667 & 0.00630438671894988 & 240.811158062897 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 1.51816666666667 & 0.00630438671894988 & 240.811158062897 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 1.52637931034483 & 0.00965746775067031 & 158.051711872285 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 1.52589285714286 & 0.0095983520829734 & 158.974461860974 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 1.52537037037037 & 0.00951556510369693 & 160.30265714621 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 1.52480769230769 & 0.00940335609922128 & 162.155689545137 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 1.5244 & 0.00930727167984523 & 163.785914114989 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 1.52395833333333 & 0.00917587987999538 & 166.083073586846 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 1.52326086956522 & 0.00904660156025234 & 168.379347694266 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 1.52159090909091 & 0.00901574369875655 & 168.770426481929 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 1.51976190476190 & 0.00894873835499286 & 169.829739620666 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 1.518 & 0.00891699615974015 & 170.236699983533 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 1.51605263157895 & 0.00884141516645902 & 171.471716126427 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 1.51416666666667 & 0.00880453526711327 & 171.975762573453 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 1.51235294117647 & 0.00881639640379871 & 171.538673161842 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 1.5103125 & 0.00878144551211577 & 171.989053273316 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 1.508 & 0.00867550389407394 & 173.822756396903 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 1.50571428571429 & 0.0086132138461135 & 174.814455163412 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 1.50307692307692 & 0.00844473856714675 & 177.989751976984 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 1.50041666666667 & 0.00830747800606515 & 180.610368823274 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 1.49772727272727 & 0.00821601798889589 & 182.293572719958 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 1.4945 & 0.0079297905992131 & 188.466515137021 \tabularnewline
Median & 1.48 &  &  \tabularnewline
Midrange & 1.54 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 1.50210526315789 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 1.50210526315789 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 1.50210526315789 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 1.50210526315789 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 1.50210526315789 &  &  \tabularnewline
Midmean - Closest Observation & 1.50210526315789 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 1.50210526315789 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 1.51 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58210&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]1.52683333333333[/C][C]0.00969737475881004[/C][C]157.448110577165[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]1.52504257777793[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]1.52327980010142[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]1.52864918582824[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]1.52683333333333[/C][C]0.00969737475881004[/C][C]157.448110577165[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]1.52683333333333[/C][C]0.00969737475881004[/C][C]157.448110577165[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]1.52683333333333[/C][C]0.00969737475881004[/C][C]157.448110577165[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]1.52616666666667[/C][C]0.0095583006392931[/C][C]159.669247103692[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]1.52616666666667[/C][C]0.0095583006392931[/C][C]159.669247103692[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]1.52716666666667[/C][C]0.0093943475813035[/C][C]162.56229114899[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]1.53183333333333[/C][C]0.00878973356796762[/C][C]174.275286217524[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]1.53183333333333[/C][C]0.00878973356796762[/C][C]174.275286217524[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]1.53033333333333[/C][C]0.0084838386294632[/C][C]180.382183133316[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]1.53033333333333[/C][C]0.0084838386294632[/C][C]180.382183133316[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]1.5285[/C][C]0.00812621133951508[/C][C]188.095034221841[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]1.5265[/C][C]0.00775261938602901[/C][C]196.901192228127[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]1.5265[/C][C]0.00775261938602901[/C][C]196.901192228127[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]1.5265[/C][C]0.00775261938602901[/C][C]196.901192228127[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]1.524[/C][C]0.00730374101186246[/C][C]208.660191746227[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]1.524[/C][C]0.00730374101186246[/C][C]208.660191746227[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]1.52116666666667[/C][C]0.00681097347658041[/C][C]223.340565324063[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]1.51816666666667[/C][C]0.00630438671894988[/C][C]240.811158062897[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]1.51816666666667[/C][C]0.00630438671894988[/C][C]240.811158062897[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]1.51816666666667[/C][C]0.00630438671894988[/C][C]240.811158062897[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]1.52637931034483[/C][C]0.00965746775067031[/C][C]158.051711872285[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]1.52589285714286[/C][C]0.0095983520829734[/C][C]158.974461860974[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]1.52537037037037[/C][C]0.00951556510369693[/C][C]160.30265714621[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]1.52480769230769[/C][C]0.00940335609922128[/C][C]162.155689545137[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]1.5244[/C][C]0.00930727167984523[/C][C]163.785914114989[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]1.52395833333333[/C][C]0.00917587987999538[/C][C]166.083073586846[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]1.52326086956522[/C][C]0.00904660156025234[/C][C]168.379347694266[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]1.52159090909091[/C][C]0.00901574369875655[/C][C]168.770426481929[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]1.51976190476190[/C][C]0.00894873835499286[/C][C]169.829739620666[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]1.518[/C][C]0.00891699615974015[/C][C]170.236699983533[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]1.51605263157895[/C][C]0.00884141516645902[/C][C]171.471716126427[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]1.51416666666667[/C][C]0.00880453526711327[/C][C]171.975762573453[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]1.51235294117647[/C][C]0.00881639640379871[/C][C]171.538673161842[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]1.5103125[/C][C]0.00878144551211577[/C][C]171.989053273316[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]1.508[/C][C]0.00867550389407394[/C][C]173.822756396903[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]1.50571428571429[/C][C]0.0086132138461135[/C][C]174.814455163412[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]1.50307692307692[/C][C]0.00844473856714675[/C][C]177.989751976984[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]1.50041666666667[/C][C]0.00830747800606515[/C][C]180.610368823274[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]1.49772727272727[/C][C]0.00821601798889589[/C][C]182.293572719958[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]1.4945[/C][C]0.0079297905992131[/C][C]188.466515137021[/C][/ROW]
[ROW][C]Median[/C][C]1.48[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]1.54[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]1.50210526315789[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]1.50210526315789[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]1.50210526315789[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]1.50210526315789[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]1.50210526315789[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]1.50210526315789[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]1.50210526315789[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]1.51[/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=58210&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58210&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 Mean1.526833333333330.00969737475881004157.448110577165
Geometric Mean1.52504257777793
Harmonic Mean1.52327980010142
Quadratic Mean1.52864918582824
Winsorized Mean ( 1 / 20 )1.526833333333330.00969737475881004157.448110577165
Winsorized Mean ( 2 / 20 )1.526833333333330.00969737475881004157.448110577165
Winsorized Mean ( 3 / 20 )1.526833333333330.00969737475881004157.448110577165
Winsorized Mean ( 4 / 20 )1.526166666666670.0095583006392931159.669247103692
Winsorized Mean ( 5 / 20 )1.526166666666670.0095583006392931159.669247103692
Winsorized Mean ( 6 / 20 )1.527166666666670.0093943475813035162.56229114899
Winsorized Mean ( 7 / 20 )1.531833333333330.00878973356796762174.275286217524
Winsorized Mean ( 8 / 20 )1.531833333333330.00878973356796762174.275286217524
Winsorized Mean ( 9 / 20 )1.530333333333330.0084838386294632180.382183133316
Winsorized Mean ( 10 / 20 )1.530333333333330.0084838386294632180.382183133316
Winsorized Mean ( 11 / 20 )1.52850.00812621133951508188.095034221841
Winsorized Mean ( 12 / 20 )1.52650.00775261938602901196.901192228127
Winsorized Mean ( 13 / 20 )1.52650.00775261938602901196.901192228127
Winsorized Mean ( 14 / 20 )1.52650.00775261938602901196.901192228127
Winsorized Mean ( 15 / 20 )1.5240.00730374101186246208.660191746227
Winsorized Mean ( 16 / 20 )1.5240.00730374101186246208.660191746227
Winsorized Mean ( 17 / 20 )1.521166666666670.00681097347658041223.340565324063
Winsorized Mean ( 18 / 20 )1.518166666666670.00630438671894988240.811158062897
Winsorized Mean ( 19 / 20 )1.518166666666670.00630438671894988240.811158062897
Winsorized Mean ( 20 / 20 )1.518166666666670.00630438671894988240.811158062897
Trimmed Mean ( 1 / 20 )1.526379310344830.00965746775067031158.051711872285
Trimmed Mean ( 2 / 20 )1.525892857142860.0095983520829734158.974461860974
Trimmed Mean ( 3 / 20 )1.525370370370370.00951556510369693160.30265714621
Trimmed Mean ( 4 / 20 )1.524807692307690.00940335609922128162.155689545137
Trimmed Mean ( 5 / 20 )1.52440.00930727167984523163.785914114989
Trimmed Mean ( 6 / 20 )1.523958333333330.00917587987999538166.083073586846
Trimmed Mean ( 7 / 20 )1.523260869565220.00904660156025234168.379347694266
Trimmed Mean ( 8 / 20 )1.521590909090910.00901574369875655168.770426481929
Trimmed Mean ( 9 / 20 )1.519761904761900.00894873835499286169.829739620666
Trimmed Mean ( 10 / 20 )1.5180.00891699615974015170.236699983533
Trimmed Mean ( 11 / 20 )1.516052631578950.00884141516645902171.471716126427
Trimmed Mean ( 12 / 20 )1.514166666666670.00880453526711327171.975762573453
Trimmed Mean ( 13 / 20 )1.512352941176470.00881639640379871171.538673161842
Trimmed Mean ( 14 / 20 )1.51031250.00878144551211577171.989053273316
Trimmed Mean ( 15 / 20 )1.5080.00867550389407394173.822756396903
Trimmed Mean ( 16 / 20 )1.505714285714290.0086132138461135174.814455163412
Trimmed Mean ( 17 / 20 )1.503076923076920.00844473856714675177.989751976984
Trimmed Mean ( 18 / 20 )1.500416666666670.00830747800606515180.610368823274
Trimmed Mean ( 19 / 20 )1.497727272727270.00821601798889589182.293572719958
Trimmed Mean ( 20 / 20 )1.49450.0079297905992131188.466515137021
Median1.48
Midrange1.54
Midmean - Weighted Average at Xnp1.50210526315789
Midmean - Weighted Average at X(n+1)p1.50210526315789
Midmean - Empirical Distribution Function1.50210526315789
Midmean - Empirical Distribution Function - Averaging1.50210526315789
Midmean - Empirical Distribution Function - Interpolation1.50210526315789
Midmean - Closest Observation1.50210526315789
Midmean - True Basic - Statistics Graphics Toolkit1.50210526315789
Midmean - MS Excel (old versions)1.51
Number of observations60



Parameters (Session):
par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;
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')