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of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationMon, 24 Feb 2014 16:45:47 -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/2014/Feb/24/t1393278449n15k5kqeeejaelw.htm/, Retrieved Thu, 16 May 2024 14:07:59 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=234031, Retrieved Thu, 16 May 2024 14:07:59 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact87
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [] [2014-02-24 21:45:47] [921fe14319b38fdaec959b1bea4c8145] [Current]
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Dataseries X:
-65
-75
-77
-75
-71
-71
-72
-64
-63
-68
-64
-52
-47
-52
-47
-36
-33
-44
-32
-23
-26
-24
-17
-29
-14
-12
-13
-15
-17
-22
-22
-39
-56
-66
-66
-71
-69
-71
-72
-67
-72
-77
-64
-64
-57
-63
-69
-76
-70
-78
-78
-76
-69
-73
-73
-62
-63
-61
-46
-40




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 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 & 3 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=234031&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]3 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=234031&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=234031&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 time3 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean-54.16666666666672.70719554544562-20.0084056572096
Geometric MeanNaN
Harmonic Mean-40.7726456099376
Quadratic Mean58.0209732194603
Winsorized Mean ( 1 / 20 )-54.18333333333332.70284341454337-20.046789629686
Winsorized Mean ( 2 / 20 )-54.18333333333332.68943230800846-20.1467548270276
Winsorized Mean ( 3 / 20 )-54.23333333333332.67689071115589-20.259823498702
Winsorized Mean ( 4 / 20 )-54.32.63487046605357-20.6082237057099
Winsorized Mean ( 5 / 20 )-54.32.63487046605357-20.6082237057099
Winsorized Mean ( 6 / 20 )-54.72.50562079996562-21.8309171127373
Winsorized Mean ( 7 / 20 )-54.72.50562079996562-21.8309171127373
Winsorized Mean ( 8 / 20 )-54.56666666666672.44086752507237-22.3554396566642
Winsorized Mean ( 9 / 20 )-54.71666666666672.40821236964803-22.7208643873313
Winsorized Mean ( 10 / 20 )-54.88333333333332.31576416188782-23.6998802540377
Winsorized Mean ( 11 / 20 )-55.43333333333332.20161300224996-25.1785092460313
Winsorized Mean ( 12 / 20 )-56.03333333333332.0817971737643-26.9158465769333
Winsorized Mean ( 13 / 20 )-56.03333333333332.01182474254765-27.8519953295614
Winsorized Mean ( 14 / 20 )-56.73333333333331.87834322156622-30.2039226281698
Winsorized Mean ( 15 / 20 )-57.48333333333331.74059079305023-33.0251852203578
Winsorized Mean ( 16 / 20 )-57.751.69289392181214-34.1131829088159
Winsorized Mean ( 17 / 20 )-58.61.45811580298523-40.188851859384
Winsorized Mean ( 18 / 20 )-58.91.31799796815769-44.6889915030226
Winsorized Mean ( 19 / 20 )-59.21666666666671.26582450445663-46.7811031135681
Winsorized Mean ( 20 / 20 )-59.21666666666671.26582450445663-46.7811031135681
Trimmed Mean ( 1 / 20 )-54.48275862068972.67137832914794-20.3949991007329
Trimmed Mean ( 2 / 20 )-54.80357142857142.63054234233975-20.8335636900739
Trimmed Mean ( 3 / 20 )-55.14814814814812.58664086732679-21.3203730153471
Trimmed Mean ( 4 / 20 )-55.52.53579205127316-21.8866527214386
Trimmed Mean ( 5 / 20 )-55.862.48620848945965-22.4679467698787
Trimmed Mean ( 6 / 20 )-56.252.42082059236647-23.2359226360566
Trimmed Mean ( 7 / 20 )-56.58695652173912.37653100146499-23.810737788338
Trimmed Mean ( 8 / 20 )-56.95454545454552.31617041620137-24.589963267018
Trimmed Mean ( 9 / 20 )-57.38095238095242.25184203368268-25.4817840339854
Trimmed Mean ( 10 / 20 )-57.8252.17293594959116-26.6114608720426
Trimmed Mean ( 11 / 20 )-58.28947368421052.0903857324174-27.8845539271847
Trimmed Mean ( 12 / 20 )-58.72222222222222.01013744737001-29.2130382920094
Trimmed Mean ( 13 / 20 )-59.11764705882351.93373499387281-30.5717418602562
Trimmed Mean ( 14 / 20 )-59.56251.84201497095594-32.3355135214179
Trimmed Mean ( 15 / 20 )-59.96666666666671.75347492981848-34.198759073718
Trimmed Mean ( 16 / 20 )-60.32142857142861.67067262333507-36.1060735232568
Trimmed Mean ( 17 / 20 )-60.69230769230771.55886470599524-38.9336595144473
Trimmed Mean ( 18 / 20 )-611.48177332069148-41.1668904738642
Trimmed Mean ( 19 / 20 )-61.31818181818181.41174167651039-43.4344206439742
Trimmed Mean ( 20 / 20 )-61.651.31244047484067-46.9735589398707
Median-63.5
Midrange-45
Midmean - Weighted Average at Xnp-60.65625
Midmean - Weighted Average at X(n+1)p-60.65625
Midmean - Empirical Distribution Function-60.65625
Midmean - Empirical Distribution Function - Averaging-60.65625
Midmean - Empirical Distribution Function - Interpolation-60.65625
Midmean - Closest Observation-60.65625
Midmean - True Basic - Statistics Graphics Toolkit-60.65625
Midmean - MS Excel (old versions)-59.9090909090909
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & -54.1666666666667 & 2.70719554544562 & -20.0084056572096 \tabularnewline
Geometric Mean & NaN &  &  \tabularnewline
Harmonic Mean & -40.7726456099376 &  &  \tabularnewline
Quadratic Mean & 58.0209732194603 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & -54.1833333333333 & 2.70284341454337 & -20.046789629686 \tabularnewline
Winsorized Mean ( 2 / 20 ) & -54.1833333333333 & 2.68943230800846 & -20.1467548270276 \tabularnewline
Winsorized Mean ( 3 / 20 ) & -54.2333333333333 & 2.67689071115589 & -20.259823498702 \tabularnewline
Winsorized Mean ( 4 / 20 ) & -54.3 & 2.63487046605357 & -20.6082237057099 \tabularnewline
Winsorized Mean ( 5 / 20 ) & -54.3 & 2.63487046605357 & -20.6082237057099 \tabularnewline
Winsorized Mean ( 6 / 20 ) & -54.7 & 2.50562079996562 & -21.8309171127373 \tabularnewline
Winsorized Mean ( 7 / 20 ) & -54.7 & 2.50562079996562 & -21.8309171127373 \tabularnewline
Winsorized Mean ( 8 / 20 ) & -54.5666666666667 & 2.44086752507237 & -22.3554396566642 \tabularnewline
Winsorized Mean ( 9 / 20 ) & -54.7166666666667 & 2.40821236964803 & -22.7208643873313 \tabularnewline
Winsorized Mean ( 10 / 20 ) & -54.8833333333333 & 2.31576416188782 & -23.6998802540377 \tabularnewline
Winsorized Mean ( 11 / 20 ) & -55.4333333333333 & 2.20161300224996 & -25.1785092460313 \tabularnewline
Winsorized Mean ( 12 / 20 ) & -56.0333333333333 & 2.0817971737643 & -26.9158465769333 \tabularnewline
Winsorized Mean ( 13 / 20 ) & -56.0333333333333 & 2.01182474254765 & -27.8519953295614 \tabularnewline
Winsorized Mean ( 14 / 20 ) & -56.7333333333333 & 1.87834322156622 & -30.2039226281698 \tabularnewline
Winsorized Mean ( 15 / 20 ) & -57.4833333333333 & 1.74059079305023 & -33.0251852203578 \tabularnewline
Winsorized Mean ( 16 / 20 ) & -57.75 & 1.69289392181214 & -34.1131829088159 \tabularnewline
Winsorized Mean ( 17 / 20 ) & -58.6 & 1.45811580298523 & -40.188851859384 \tabularnewline
Winsorized Mean ( 18 / 20 ) & -58.9 & 1.31799796815769 & -44.6889915030226 \tabularnewline
Winsorized Mean ( 19 / 20 ) & -59.2166666666667 & 1.26582450445663 & -46.7811031135681 \tabularnewline
Winsorized Mean ( 20 / 20 ) & -59.2166666666667 & 1.26582450445663 & -46.7811031135681 \tabularnewline
Trimmed Mean ( 1 / 20 ) & -54.4827586206897 & 2.67137832914794 & -20.3949991007329 \tabularnewline
Trimmed Mean ( 2 / 20 ) & -54.8035714285714 & 2.63054234233975 & -20.8335636900739 \tabularnewline
Trimmed Mean ( 3 / 20 ) & -55.1481481481481 & 2.58664086732679 & -21.3203730153471 \tabularnewline
Trimmed Mean ( 4 / 20 ) & -55.5 & 2.53579205127316 & -21.8866527214386 \tabularnewline
Trimmed Mean ( 5 / 20 ) & -55.86 & 2.48620848945965 & -22.4679467698787 \tabularnewline
Trimmed Mean ( 6 / 20 ) & -56.25 & 2.42082059236647 & -23.2359226360566 \tabularnewline
Trimmed Mean ( 7 / 20 ) & -56.5869565217391 & 2.37653100146499 & -23.810737788338 \tabularnewline
Trimmed Mean ( 8 / 20 ) & -56.9545454545455 & 2.31617041620137 & -24.589963267018 \tabularnewline
Trimmed Mean ( 9 / 20 ) & -57.3809523809524 & 2.25184203368268 & -25.4817840339854 \tabularnewline
Trimmed Mean ( 10 / 20 ) & -57.825 & 2.17293594959116 & -26.6114608720426 \tabularnewline
Trimmed Mean ( 11 / 20 ) & -58.2894736842105 & 2.0903857324174 & -27.8845539271847 \tabularnewline
Trimmed Mean ( 12 / 20 ) & -58.7222222222222 & 2.01013744737001 & -29.2130382920094 \tabularnewline
Trimmed Mean ( 13 / 20 ) & -59.1176470588235 & 1.93373499387281 & -30.5717418602562 \tabularnewline
Trimmed Mean ( 14 / 20 ) & -59.5625 & 1.84201497095594 & -32.3355135214179 \tabularnewline
Trimmed Mean ( 15 / 20 ) & -59.9666666666667 & 1.75347492981848 & -34.198759073718 \tabularnewline
Trimmed Mean ( 16 / 20 ) & -60.3214285714286 & 1.67067262333507 & -36.1060735232568 \tabularnewline
Trimmed Mean ( 17 / 20 ) & -60.6923076923077 & 1.55886470599524 & -38.9336595144473 \tabularnewline
Trimmed Mean ( 18 / 20 ) & -61 & 1.48177332069148 & -41.1668904738642 \tabularnewline
Trimmed Mean ( 19 / 20 ) & -61.3181818181818 & 1.41174167651039 & -43.4344206439742 \tabularnewline
Trimmed Mean ( 20 / 20 ) & -61.65 & 1.31244047484067 & -46.9735589398707 \tabularnewline
Median & -63.5 &  &  \tabularnewline
Midrange & -45 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & -60.65625 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & -60.65625 &  &  \tabularnewline
Midmean - Empirical Distribution Function & -60.65625 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & -60.65625 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & -60.65625 &  &  \tabularnewline
Midmean - Closest Observation & -60.65625 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & -60.65625 &  &  \tabularnewline
Midmean - MS Excel (old versions) & -59.9090909090909 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=234031&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]-54.1666666666667[/C][C]2.70719554544562[/C][C]-20.0084056572096[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]NaN[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]-40.7726456099376[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]58.0209732194603[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]-54.1833333333333[/C][C]2.70284341454337[/C][C]-20.046789629686[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]-54.1833333333333[/C][C]2.68943230800846[/C][C]-20.1467548270276[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]-54.2333333333333[/C][C]2.67689071115589[/C][C]-20.259823498702[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]-54.3[/C][C]2.63487046605357[/C][C]-20.6082237057099[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]-54.3[/C][C]2.63487046605357[/C][C]-20.6082237057099[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]-54.7[/C][C]2.50562079996562[/C][C]-21.8309171127373[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]-54.7[/C][C]2.50562079996562[/C][C]-21.8309171127373[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]-54.5666666666667[/C][C]2.44086752507237[/C][C]-22.3554396566642[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]-54.7166666666667[/C][C]2.40821236964803[/C][C]-22.7208643873313[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]-54.8833333333333[/C][C]2.31576416188782[/C][C]-23.6998802540377[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]-55.4333333333333[/C][C]2.20161300224996[/C][C]-25.1785092460313[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]-56.0333333333333[/C][C]2.0817971737643[/C][C]-26.9158465769333[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]-56.0333333333333[/C][C]2.01182474254765[/C][C]-27.8519953295614[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]-56.7333333333333[/C][C]1.87834322156622[/C][C]-30.2039226281698[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]-57.4833333333333[/C][C]1.74059079305023[/C][C]-33.0251852203578[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]-57.75[/C][C]1.69289392181214[/C][C]-34.1131829088159[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]-58.6[/C][C]1.45811580298523[/C][C]-40.188851859384[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]-58.9[/C][C]1.31799796815769[/C][C]-44.6889915030226[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]-59.2166666666667[/C][C]1.26582450445663[/C][C]-46.7811031135681[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]-59.2166666666667[/C][C]1.26582450445663[/C][C]-46.7811031135681[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]-54.4827586206897[/C][C]2.67137832914794[/C][C]-20.3949991007329[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]-54.8035714285714[/C][C]2.63054234233975[/C][C]-20.8335636900739[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]-55.1481481481481[/C][C]2.58664086732679[/C][C]-21.3203730153471[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]-55.5[/C][C]2.53579205127316[/C][C]-21.8866527214386[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]-55.86[/C][C]2.48620848945965[/C][C]-22.4679467698787[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]-56.25[/C][C]2.42082059236647[/C][C]-23.2359226360566[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]-56.5869565217391[/C][C]2.37653100146499[/C][C]-23.810737788338[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]-56.9545454545455[/C][C]2.31617041620137[/C][C]-24.589963267018[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]-57.3809523809524[/C][C]2.25184203368268[/C][C]-25.4817840339854[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]-57.825[/C][C]2.17293594959116[/C][C]-26.6114608720426[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]-58.2894736842105[/C][C]2.0903857324174[/C][C]-27.8845539271847[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]-58.7222222222222[/C][C]2.01013744737001[/C][C]-29.2130382920094[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]-59.1176470588235[/C][C]1.93373499387281[/C][C]-30.5717418602562[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]-59.5625[/C][C]1.84201497095594[/C][C]-32.3355135214179[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]-59.9666666666667[/C][C]1.75347492981848[/C][C]-34.198759073718[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]-60.3214285714286[/C][C]1.67067262333507[/C][C]-36.1060735232568[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]-60.6923076923077[/C][C]1.55886470599524[/C][C]-38.9336595144473[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]-61[/C][C]1.48177332069148[/C][C]-41.1668904738642[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]-61.3181818181818[/C][C]1.41174167651039[/C][C]-43.4344206439742[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]-61.65[/C][C]1.31244047484067[/C][C]-46.9735589398707[/C][/ROW]
[ROW][C]Median[/C][C]-63.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]-45[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]-60.65625[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]-60.65625[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]-60.65625[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]-60.65625[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]-60.65625[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]-60.65625[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]-60.65625[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]-59.9090909090909[/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=234031&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=234031&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 Mean-54.16666666666672.70719554544562-20.0084056572096
Geometric MeanNaN
Harmonic Mean-40.7726456099376
Quadratic Mean58.0209732194603
Winsorized Mean ( 1 / 20 )-54.18333333333332.70284341454337-20.046789629686
Winsorized Mean ( 2 / 20 )-54.18333333333332.68943230800846-20.1467548270276
Winsorized Mean ( 3 / 20 )-54.23333333333332.67689071115589-20.259823498702
Winsorized Mean ( 4 / 20 )-54.32.63487046605357-20.6082237057099
Winsorized Mean ( 5 / 20 )-54.32.63487046605357-20.6082237057099
Winsorized Mean ( 6 / 20 )-54.72.50562079996562-21.8309171127373
Winsorized Mean ( 7 / 20 )-54.72.50562079996562-21.8309171127373
Winsorized Mean ( 8 / 20 )-54.56666666666672.44086752507237-22.3554396566642
Winsorized Mean ( 9 / 20 )-54.71666666666672.40821236964803-22.7208643873313
Winsorized Mean ( 10 / 20 )-54.88333333333332.31576416188782-23.6998802540377
Winsorized Mean ( 11 / 20 )-55.43333333333332.20161300224996-25.1785092460313
Winsorized Mean ( 12 / 20 )-56.03333333333332.0817971737643-26.9158465769333
Winsorized Mean ( 13 / 20 )-56.03333333333332.01182474254765-27.8519953295614
Winsorized Mean ( 14 / 20 )-56.73333333333331.87834322156622-30.2039226281698
Winsorized Mean ( 15 / 20 )-57.48333333333331.74059079305023-33.0251852203578
Winsorized Mean ( 16 / 20 )-57.751.69289392181214-34.1131829088159
Winsorized Mean ( 17 / 20 )-58.61.45811580298523-40.188851859384
Winsorized Mean ( 18 / 20 )-58.91.31799796815769-44.6889915030226
Winsorized Mean ( 19 / 20 )-59.21666666666671.26582450445663-46.7811031135681
Winsorized Mean ( 20 / 20 )-59.21666666666671.26582450445663-46.7811031135681
Trimmed Mean ( 1 / 20 )-54.48275862068972.67137832914794-20.3949991007329
Trimmed Mean ( 2 / 20 )-54.80357142857142.63054234233975-20.8335636900739
Trimmed Mean ( 3 / 20 )-55.14814814814812.58664086732679-21.3203730153471
Trimmed Mean ( 4 / 20 )-55.52.53579205127316-21.8866527214386
Trimmed Mean ( 5 / 20 )-55.862.48620848945965-22.4679467698787
Trimmed Mean ( 6 / 20 )-56.252.42082059236647-23.2359226360566
Trimmed Mean ( 7 / 20 )-56.58695652173912.37653100146499-23.810737788338
Trimmed Mean ( 8 / 20 )-56.95454545454552.31617041620137-24.589963267018
Trimmed Mean ( 9 / 20 )-57.38095238095242.25184203368268-25.4817840339854
Trimmed Mean ( 10 / 20 )-57.8252.17293594959116-26.6114608720426
Trimmed Mean ( 11 / 20 )-58.28947368421052.0903857324174-27.8845539271847
Trimmed Mean ( 12 / 20 )-58.72222222222222.01013744737001-29.2130382920094
Trimmed Mean ( 13 / 20 )-59.11764705882351.93373499387281-30.5717418602562
Trimmed Mean ( 14 / 20 )-59.56251.84201497095594-32.3355135214179
Trimmed Mean ( 15 / 20 )-59.96666666666671.75347492981848-34.198759073718
Trimmed Mean ( 16 / 20 )-60.32142857142861.67067262333507-36.1060735232568
Trimmed Mean ( 17 / 20 )-60.69230769230771.55886470599524-38.9336595144473
Trimmed Mean ( 18 / 20 )-611.48177332069148-41.1668904738642
Trimmed Mean ( 19 / 20 )-61.31818181818181.41174167651039-43.4344206439742
Trimmed Mean ( 20 / 20 )-61.651.31244047484067-46.9735589398707
Median-63.5
Midrange-45
Midmean - Weighted Average at Xnp-60.65625
Midmean - Weighted Average at X(n+1)p-60.65625
Midmean - Empirical Distribution Function-60.65625
Midmean - Empirical Distribution Function - Averaging-60.65625
Midmean - Empirical Distribution Function - Interpolation-60.65625
Midmean - Closest Observation-60.65625
Midmean - True Basic - Statistics Graphics Toolkit-60.65625
Midmean - MS Excel (old versions)-59.9090909090909
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')