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Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationWed, 07 Mar 2012 13:55:03 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2012/Mar/07/t1331146593fzjot6r9s7zevam.htm/, Retrieved Mon, 29 Apr 2024 01:13:57 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=163686, Retrieved Mon, 29 Apr 2024 01:13:57 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDG2011W52a
Estimated Impact128
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [Opgave 5: Oefenin...] [2012-03-07 18:55:03] [aa59cfa385e119596867d158cdccc7ef] [Current]
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Dataseries X:
16,41
16,38
16,12
16,03
16,02
16,01
16,01
15,94
15,88
15,75
15,8
15,84
15,84
15,79
15,79
15,75
15,63
15,63
15,63
15,62
15,59
15,55
15,61
15,58
15,58
15,64
15,56
15,57
15,46
15,5
15,5
15,58
15,69
15,78
15,8
15,79
15,79
15,79
15,75
15,71
15,76
15,76
15,76
15,76
15,78
15,84
15,82
15,86
15,86
15,87
15,84
15,84
15,89
15,89
15,89
15,91
15,95
16,08
16,08
16,09




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

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=163686&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' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=163686&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=163686&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' @ jenkins.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean15.80366666666670.025042299431734631.078895520274
Geometric Mean15.8025033300958
Harmonic Mean15.8013471341404
Quadratic Mean15.8048372342141
Winsorized Mean ( 1 / 20 )15.80383333333330.0246937075022597639.994352078851
Winsorized Mean ( 2 / 20 )15.79516666666670.0218501466292856722.886071871779
Winsorized Mean ( 3 / 20 )15.79616666666670.0209466522636581754.114140428664
Winsorized Mean ( 4 / 20 )15.79616666666670.0206587715008581764.622749518794
Winsorized Mean ( 5 / 20 )15.7970.0204998277517911770.591840637284
Winsorized Mean ( 6 / 20 )15.7930.0192020184908851822.465617742044
Winsorized Mean ( 7 / 20 )15.79183333333330.0189609942566709832.858927098584
Winsorized Mean ( 8 / 20 )15.79050.0186923123869917844.759047093012
Winsorized Mean ( 9 / 20 )15.7920.0184096511166641857.810932967947
Winsorized Mean ( 10 / 20 )15.78533333333330.0158977429138598992.929211326695
Winsorized Mean ( 11 / 20 )15.78533333333330.01523908642861861035.84512150865
Winsorized Mean ( 12 / 20 )15.78133333333330.01388098456810741136.90302412641
Winsorized Mean ( 13 / 20 )15.7770.01322619383609021192.86018302177
Winsorized Mean ( 14 / 20 )15.7770.01322619383609021192.86018302177
Winsorized Mean ( 15 / 20 )15.77950.01275901143824851236.73374511577
Winsorized Mean ( 16 / 20 )15.79016666666670.009978767477832561582.37645097392
Winsorized Mean ( 17 / 20 )15.7930.008600683194515891836.2494749336
Winsorized Mean ( 18 / 20 )15.8020.006296802165712692509.52778634923
Winsorized Mean ( 19 / 20 )15.8020.006296802165712692509.52778634923
Winsorized Mean ( 20 / 20 )15.79533333333330.005296127284956032982.43083737828
Trimmed Mean ( 1 / 20 )15.79913793103450.0228957558772467690.046575257875
Trimmed Mean ( 2 / 20 )15.79410714285710.0205820764064811767.371903151799
Trimmed Mean ( 3 / 20 )15.79351851851850.0197116839133021801.226246726722
Trimmed Mean ( 4 / 20 )15.79250.0190733184876076827.989110036661
Trimmed Mean ( 5 / 20 )15.79140.0183836884220768858.989754256076
Trimmed Mean ( 6 / 20 )15.790.0175594229214212899.232285175917
Trimmed Mean ( 7 / 20 )15.7893478260870.0169380861009898932.180160848529
Trimmed Mean ( 8 / 20 )15.78886363636360.0162050024546454974.32034833401
Trimmed Mean ( 9 / 20 )15.78857142857140.01532297065085451030.3858036621
Trimmed Mean ( 10 / 20 )15.7880.0142288980058731109.57292641239
Trimmed Mean ( 11 / 20 )15.78842105263160.01354370364275061165.73881628623
Trimmed Mean ( 12 / 20 )15.78888888888890.01280363153951441233.15708048623
Trimmed Mean ( 13 / 20 )15.790.01218543591689881295.80920269765
Trimmed Mean ( 14 / 20 )15.7918750.01148664634934141374.80292504221
Trimmed Mean ( 15 / 20 )15.7940.01044525960787291512.0734757129
Trimmed Mean ( 16 / 20 )15.79607142857140.009046313606740821746.13352081903
Trimmed Mean ( 17 / 20 )15.79692307692310.008185714211952611929.81610008529
Trimmed Mean ( 18 / 20 )15.79750.007451534225838372120.03320674846
Trimmed Mean ( 19 / 20 )15.79681818181820.007278812389345652170.24664695861
Trimmed Mean ( 20 / 20 )15.7960.006935795784039142277.46036530519
Median15.79
Midrange15.935
Midmean - Weighted Average at Xnp15.7854285714286
Midmean - Weighted Average at X(n+1)p15.8
Midmean - Empirical Distribution Function15.7854285714286
Midmean - Empirical Distribution Function - Averaging15.8
Midmean - Empirical Distribution Function - Interpolation15.8
Midmean - Closest Observation15.7854285714286
Midmean - True Basic - Statistics Graphics Toolkit15.8
Midmean - MS Excel (old versions)15.7854285714286
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 15.8036666666667 & 0.025042299431734 & 631.078895520274 \tabularnewline
Geometric Mean & 15.8025033300958 &  &  \tabularnewline
Harmonic Mean & 15.8013471341404 &  &  \tabularnewline
Quadratic Mean & 15.8048372342141 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 15.8038333333333 & 0.0246937075022597 & 639.994352078851 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 15.7951666666667 & 0.0218501466292856 & 722.886071871779 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 15.7961666666667 & 0.0209466522636581 & 754.114140428664 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 15.7961666666667 & 0.0206587715008581 & 764.622749518794 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 15.797 & 0.0204998277517911 & 770.591840637284 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 15.793 & 0.0192020184908851 & 822.465617742044 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 15.7918333333333 & 0.0189609942566709 & 832.858927098584 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 15.7905 & 0.0186923123869917 & 844.759047093012 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 15.792 & 0.0184096511166641 & 857.810932967947 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 15.7853333333333 & 0.0158977429138598 & 992.929211326695 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 15.7853333333333 & 0.0152390864286186 & 1035.84512150865 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 15.7813333333333 & 0.0138809845681074 & 1136.90302412641 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 15.777 & 0.0132261938360902 & 1192.86018302177 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 15.777 & 0.0132261938360902 & 1192.86018302177 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 15.7795 & 0.0127590114382485 & 1236.73374511577 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 15.7901666666667 & 0.00997876747783256 & 1582.37645097392 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 15.793 & 0.00860068319451589 & 1836.2494749336 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 15.802 & 0.00629680216571269 & 2509.52778634923 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 15.802 & 0.00629680216571269 & 2509.52778634923 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 15.7953333333333 & 0.00529612728495603 & 2982.43083737828 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 15.7991379310345 & 0.0228957558772467 & 690.046575257875 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 15.7941071428571 & 0.0205820764064811 & 767.371903151799 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 15.7935185185185 & 0.0197116839133021 & 801.226246726722 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 15.7925 & 0.0190733184876076 & 827.989110036661 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 15.7914 & 0.0183836884220768 & 858.989754256076 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 15.79 & 0.0175594229214212 & 899.232285175917 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 15.789347826087 & 0.0169380861009898 & 932.180160848529 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 15.7888636363636 & 0.0162050024546454 & 974.32034833401 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 15.7885714285714 & 0.0153229706508545 & 1030.3858036621 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 15.788 & 0.014228898005873 & 1109.57292641239 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 15.7884210526316 & 0.0135437036427506 & 1165.73881628623 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 15.7888888888889 & 0.0128036315395144 & 1233.15708048623 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 15.79 & 0.0121854359168988 & 1295.80920269765 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 15.791875 & 0.0114866463493414 & 1374.80292504221 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 15.794 & 0.0104452596078729 & 1512.0734757129 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 15.7960714285714 & 0.00904631360674082 & 1746.13352081903 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 15.7969230769231 & 0.00818571421195261 & 1929.81610008529 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 15.7975 & 0.00745153422583837 & 2120.03320674846 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 15.7968181818182 & 0.00727881238934565 & 2170.24664695861 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 15.796 & 0.00693579578403914 & 2277.46036530519 \tabularnewline
Median & 15.79 &  &  \tabularnewline
Midrange & 15.935 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 15.7854285714286 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 15.8 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 15.7854285714286 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 15.8 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 15.8 &  &  \tabularnewline
Midmean - Closest Observation & 15.7854285714286 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 15.8 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 15.7854285714286 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=163686&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]15.8036666666667[/C][C]0.025042299431734[/C][C]631.078895520274[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]15.8025033300958[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]15.8013471341404[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]15.8048372342141[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]15.8038333333333[/C][C]0.0246937075022597[/C][C]639.994352078851[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]15.7951666666667[/C][C]0.0218501466292856[/C][C]722.886071871779[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]15.7961666666667[/C][C]0.0209466522636581[/C][C]754.114140428664[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]15.7961666666667[/C][C]0.0206587715008581[/C][C]764.622749518794[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]15.797[/C][C]0.0204998277517911[/C][C]770.591840637284[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]15.793[/C][C]0.0192020184908851[/C][C]822.465617742044[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]15.7918333333333[/C][C]0.0189609942566709[/C][C]832.858927098584[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]15.7905[/C][C]0.0186923123869917[/C][C]844.759047093012[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]15.792[/C][C]0.0184096511166641[/C][C]857.810932967947[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]15.7853333333333[/C][C]0.0158977429138598[/C][C]992.929211326695[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]15.7853333333333[/C][C]0.0152390864286186[/C][C]1035.84512150865[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]15.7813333333333[/C][C]0.0138809845681074[/C][C]1136.90302412641[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]15.777[/C][C]0.0132261938360902[/C][C]1192.86018302177[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]15.777[/C][C]0.0132261938360902[/C][C]1192.86018302177[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]15.7795[/C][C]0.0127590114382485[/C][C]1236.73374511577[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]15.7901666666667[/C][C]0.00997876747783256[/C][C]1582.37645097392[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]15.793[/C][C]0.00860068319451589[/C][C]1836.2494749336[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]15.802[/C][C]0.00629680216571269[/C][C]2509.52778634923[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]15.802[/C][C]0.00629680216571269[/C][C]2509.52778634923[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]15.7953333333333[/C][C]0.00529612728495603[/C][C]2982.43083737828[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]15.7991379310345[/C][C]0.0228957558772467[/C][C]690.046575257875[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]15.7941071428571[/C][C]0.0205820764064811[/C][C]767.371903151799[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]15.7935185185185[/C][C]0.0197116839133021[/C][C]801.226246726722[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]15.7925[/C][C]0.0190733184876076[/C][C]827.989110036661[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]15.7914[/C][C]0.0183836884220768[/C][C]858.989754256076[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]15.79[/C][C]0.0175594229214212[/C][C]899.232285175917[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]15.789347826087[/C][C]0.0169380861009898[/C][C]932.180160848529[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]15.7888636363636[/C][C]0.0162050024546454[/C][C]974.32034833401[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]15.7885714285714[/C][C]0.0153229706508545[/C][C]1030.3858036621[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]15.788[/C][C]0.014228898005873[/C][C]1109.57292641239[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]15.7884210526316[/C][C]0.0135437036427506[/C][C]1165.73881628623[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]15.7888888888889[/C][C]0.0128036315395144[/C][C]1233.15708048623[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]15.79[/C][C]0.0121854359168988[/C][C]1295.80920269765[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]15.791875[/C][C]0.0114866463493414[/C][C]1374.80292504221[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]15.794[/C][C]0.0104452596078729[/C][C]1512.0734757129[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]15.7960714285714[/C][C]0.00904631360674082[/C][C]1746.13352081903[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]15.7969230769231[/C][C]0.00818571421195261[/C][C]1929.81610008529[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]15.7975[/C][C]0.00745153422583837[/C][C]2120.03320674846[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]15.7968181818182[/C][C]0.00727881238934565[/C][C]2170.24664695861[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]15.796[/C][C]0.00693579578403914[/C][C]2277.46036530519[/C][/ROW]
[ROW][C]Median[/C][C]15.79[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]15.935[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]15.7854285714286[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]15.8[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]15.7854285714286[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]15.8[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]15.8[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]15.7854285714286[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]15.8[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]15.7854285714286[/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=163686&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=163686&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 Mean15.80366666666670.025042299431734631.078895520274
Geometric Mean15.8025033300958
Harmonic Mean15.8013471341404
Quadratic Mean15.8048372342141
Winsorized Mean ( 1 / 20 )15.80383333333330.0246937075022597639.994352078851
Winsorized Mean ( 2 / 20 )15.79516666666670.0218501466292856722.886071871779
Winsorized Mean ( 3 / 20 )15.79616666666670.0209466522636581754.114140428664
Winsorized Mean ( 4 / 20 )15.79616666666670.0206587715008581764.622749518794
Winsorized Mean ( 5 / 20 )15.7970.0204998277517911770.591840637284
Winsorized Mean ( 6 / 20 )15.7930.0192020184908851822.465617742044
Winsorized Mean ( 7 / 20 )15.79183333333330.0189609942566709832.858927098584
Winsorized Mean ( 8 / 20 )15.79050.0186923123869917844.759047093012
Winsorized Mean ( 9 / 20 )15.7920.0184096511166641857.810932967947
Winsorized Mean ( 10 / 20 )15.78533333333330.0158977429138598992.929211326695
Winsorized Mean ( 11 / 20 )15.78533333333330.01523908642861861035.84512150865
Winsorized Mean ( 12 / 20 )15.78133333333330.01388098456810741136.90302412641
Winsorized Mean ( 13 / 20 )15.7770.01322619383609021192.86018302177
Winsorized Mean ( 14 / 20 )15.7770.01322619383609021192.86018302177
Winsorized Mean ( 15 / 20 )15.77950.01275901143824851236.73374511577
Winsorized Mean ( 16 / 20 )15.79016666666670.009978767477832561582.37645097392
Winsorized Mean ( 17 / 20 )15.7930.008600683194515891836.2494749336
Winsorized Mean ( 18 / 20 )15.8020.006296802165712692509.52778634923
Winsorized Mean ( 19 / 20 )15.8020.006296802165712692509.52778634923
Winsorized Mean ( 20 / 20 )15.79533333333330.005296127284956032982.43083737828
Trimmed Mean ( 1 / 20 )15.79913793103450.0228957558772467690.046575257875
Trimmed Mean ( 2 / 20 )15.79410714285710.0205820764064811767.371903151799
Trimmed Mean ( 3 / 20 )15.79351851851850.0197116839133021801.226246726722
Trimmed Mean ( 4 / 20 )15.79250.0190733184876076827.989110036661
Trimmed Mean ( 5 / 20 )15.79140.0183836884220768858.989754256076
Trimmed Mean ( 6 / 20 )15.790.0175594229214212899.232285175917
Trimmed Mean ( 7 / 20 )15.7893478260870.0169380861009898932.180160848529
Trimmed Mean ( 8 / 20 )15.78886363636360.0162050024546454974.32034833401
Trimmed Mean ( 9 / 20 )15.78857142857140.01532297065085451030.3858036621
Trimmed Mean ( 10 / 20 )15.7880.0142288980058731109.57292641239
Trimmed Mean ( 11 / 20 )15.78842105263160.01354370364275061165.73881628623
Trimmed Mean ( 12 / 20 )15.78888888888890.01280363153951441233.15708048623
Trimmed Mean ( 13 / 20 )15.790.01218543591689881295.80920269765
Trimmed Mean ( 14 / 20 )15.7918750.01148664634934141374.80292504221
Trimmed Mean ( 15 / 20 )15.7940.01044525960787291512.0734757129
Trimmed Mean ( 16 / 20 )15.79607142857140.009046313606740821746.13352081903
Trimmed Mean ( 17 / 20 )15.79692307692310.008185714211952611929.81610008529
Trimmed Mean ( 18 / 20 )15.79750.007451534225838372120.03320674846
Trimmed Mean ( 19 / 20 )15.79681818181820.007278812389345652170.24664695861
Trimmed Mean ( 20 / 20 )15.7960.006935795784039142277.46036530519
Median15.79
Midrange15.935
Midmean - Weighted Average at Xnp15.7854285714286
Midmean - Weighted Average at X(n+1)p15.8
Midmean - Empirical Distribution Function15.7854285714286
Midmean - Empirical Distribution Function - Averaging15.8
Midmean - Empirical Distribution Function - Interpolation15.8
Midmean - Closest Observation15.7854285714286
Midmean - True Basic - Statistics Graphics Toolkit15.8
Midmean - MS Excel (old versions)15.7854285714286
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')