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of Irreproducible Research!

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationTue, 20 Oct 2009 11:54:15 -0600
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2009/Oct/20/t1256061331b6xjcu2uk3f106c.htm/, Retrieved Fri, 03 May 2024 00:13:36 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=48901, Retrieved Fri, 03 May 2024 00:13:36 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsws3p3.2
Estimated Impact138
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [] [2009-10-20 17:54:15] [9ea4b07b6662a0f40f92decdf1e3b5d5] [Current]
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Dataseries X:
48.01
-313.75
-164.34
3.59
53.09
-101.35
-293.94
-200.85
-76.01
-208.37
-272.69
-256.30
-267.18
51.94
49.60
-41.13
139.83
336.20
995.04
629.32
320.19
669.47
1103.92
1125.64
2082.23
2160.87
1569.79
1399.70
1402.43
1151.57
1212.68
1328.74
2300.47
2227.09
1757.53
2526.15
1627.24
522.67
90.23
-65.83
-234.57
-300.55
-431.27
-394.08
-637.38
-787.14
-794.43
-760.40
-907.47
-883.21
-716.74
-585.51
-529.40
-444.68
1697.16
2110.03
-6795.41
-3192.57
-2675.13




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

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 1 seconds \tabularnewline
R Server & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=48901&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=48901&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=48901&T=0

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

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







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean158.656610169492189.3863441082640.837740497692877
Geometric MeanNaN
Harmonic Mean215.110626702008
Quadratic Mean1451.02335796593
Winsorized Mean ( 1 / 19 )215.896610169492157.0459170393001.37473558204932
Winsorized Mean ( 2 / 19 )230.949491525424150.2623270143891.53697534248426
Winsorized Mean ( 3 / 19 )317.463389830509126.3097336908372.51337233128485
Winsorized Mean ( 4 / 19 )315.661355932203125.1768045819402.52172402855652
Winsorized Mean ( 5 / 19 )320.829152542373123.3880504240632.60016388491219
Winsorized Mean ( 6 / 19 )288.550169491525115.5746436637662.49665636288688
Winsorized Mean ( 7 / 19 )284.560169491525113.5149701112702.50680742119382
Winsorized Mean ( 8 / 19 )280.999491525424110.5721133606242.54132333176053
Winsorized Mean ( 9 / 19 )284.341694915254106.9014731668092.65984823681118
Winsorized Mean ( 10 / 19 )264.76711864406899.871197828512.65108584257398
Winsorized Mean ( 11 / 19 )274.71932203389898.26497079906212.79569942167551
Winsorized Mean ( 12 / 19 )277.51796610169593.06466648534882.98199065856411
Winsorized Mean ( 13 / 19 )254.90016949152587.76960528604692.90419637482462
Winsorized Mean ( 14 / 19 )249.22423728813683.88188058609942.97113316423948
Winsorized Mean ( 15 / 19 )263.05474576271280.03712816051133.28665897700835
Winsorized Mean ( 16 / 19 )260.74423728813678.50141654966563.3215227030097
Winsorized Mean ( 17 / 19 )231.27661016949272.50931385007973.18961244961825
Winsorized Mean ( 18 / 19 )138.43322033898354.18082806899512.5550222333756
Winsorized Mean ( 19 / 19 )127.27796610169551.77468026710492.45830520719915
Trimmed Mean ( 1 / 19 )239.122807017544146.3897015930541.63346741208802
Trimmed Mean ( 2 / 19 )264.038181818182132.7570540521751.98888250197546
Trimmed Mean ( 3 / 19 )282.455471698113120.2234157524192.34942144947691
Trimmed Mean ( 4 / 19 )268.95568627451116.9559250937282.29963284082417
Trimmed Mean ( 5 / 19 )254.896326530612113.2278597945202.25118029249325
Trimmed Mean ( 6 / 19 )238.342978723404109.0299009424922.18603315845549
Trimmed Mean ( 7 / 19 )227.371777777778106.2108053769342.14075937915028
Trimmed Mean ( 8 / 19 )216.162093023256103.0930347244652.09676719286603
Trimmed Mean ( 9 / 19 )204.49926829268399.77858977499442.04953055313609
Trimmed Mean ( 10 / 19 )191.07846153846296.31417101057661.98390807431109
Trimmed Mean ( 11 / 19 )179.32810810810893.60996226262721.91569469502610
Trimmed Mean ( 12 / 19 )164.70971428571490.15859252989921.82688870426956
Trimmed Mean ( 13 / 19 )147.90242424242486.69738009505621.70596186505592
Trimmed Mean ( 14 / 19 )132.23774193548483.34768015517521.58657975470086
Trimmed Mean ( 15 / 19 )115.23724137931079.53162746335321.44894861396379
Trimmed Mean ( 16 / 19 )93.703333333333374.71372939312471.25416485155346
Trimmed Mean ( 17 / 19 )69.064867.4229609384421.02435133430371
Trimmed Mean ( 18 / 19 )44.587826086956558.37948346556460.763758489114704
Trimmed Mean ( 19 / 19 )29.9454.0916846043210.553504669322285
Median3.59
Midrange-2134.63
Midmean - Weighted Average at Xnp98.26
Midmean - Weighted Average at X(n+1)p132.237741935484
Midmean - Empirical Distribution Function132.237741935484
Midmean - Empirical Distribution Function - Averaging132.237741935484
Midmean - Empirical Distribution Function - Interpolation115.237241379310
Midmean - Closest Observation98.26
Midmean - True Basic - Statistics Graphics Toolkit132.237741935484
Midmean - MS Excel (old versions)132.237741935484
Number of observations59

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 158.656610169492 & 189.386344108264 & 0.837740497692877 \tabularnewline
Geometric Mean & NaN &  &  \tabularnewline
Harmonic Mean & 215.110626702008 &  &  \tabularnewline
Quadratic Mean & 1451.02335796593 &  &  \tabularnewline
Winsorized Mean ( 1 / 19 ) & 215.896610169492 & 157.045917039300 & 1.37473558204932 \tabularnewline
Winsorized Mean ( 2 / 19 ) & 230.949491525424 & 150.262327014389 & 1.53697534248426 \tabularnewline
Winsorized Mean ( 3 / 19 ) & 317.463389830509 & 126.309733690837 & 2.51337233128485 \tabularnewline
Winsorized Mean ( 4 / 19 ) & 315.661355932203 & 125.176804581940 & 2.52172402855652 \tabularnewline
Winsorized Mean ( 5 / 19 ) & 320.829152542373 & 123.388050424063 & 2.60016388491219 \tabularnewline
Winsorized Mean ( 6 / 19 ) & 288.550169491525 & 115.574643663766 & 2.49665636288688 \tabularnewline
Winsorized Mean ( 7 / 19 ) & 284.560169491525 & 113.514970111270 & 2.50680742119382 \tabularnewline
Winsorized Mean ( 8 / 19 ) & 280.999491525424 & 110.572113360624 & 2.54132333176053 \tabularnewline
Winsorized Mean ( 9 / 19 ) & 284.341694915254 & 106.901473166809 & 2.65984823681118 \tabularnewline
Winsorized Mean ( 10 / 19 ) & 264.767118644068 & 99.87119782851 & 2.65108584257398 \tabularnewline
Winsorized Mean ( 11 / 19 ) & 274.719322033898 & 98.2649707990621 & 2.79569942167551 \tabularnewline
Winsorized Mean ( 12 / 19 ) & 277.517966101695 & 93.0646664853488 & 2.98199065856411 \tabularnewline
Winsorized Mean ( 13 / 19 ) & 254.900169491525 & 87.7696052860469 & 2.90419637482462 \tabularnewline
Winsorized Mean ( 14 / 19 ) & 249.224237288136 & 83.8818805860994 & 2.97113316423948 \tabularnewline
Winsorized Mean ( 15 / 19 ) & 263.054745762712 & 80.0371281605113 & 3.28665897700835 \tabularnewline
Winsorized Mean ( 16 / 19 ) & 260.744237288136 & 78.5014165496656 & 3.3215227030097 \tabularnewline
Winsorized Mean ( 17 / 19 ) & 231.276610169492 & 72.5093138500797 & 3.18961244961825 \tabularnewline
Winsorized Mean ( 18 / 19 ) & 138.433220338983 & 54.1808280689951 & 2.5550222333756 \tabularnewline
Winsorized Mean ( 19 / 19 ) & 127.277966101695 & 51.7746802671049 & 2.45830520719915 \tabularnewline
Trimmed Mean ( 1 / 19 ) & 239.122807017544 & 146.389701593054 & 1.63346741208802 \tabularnewline
Trimmed Mean ( 2 / 19 ) & 264.038181818182 & 132.757054052175 & 1.98888250197546 \tabularnewline
Trimmed Mean ( 3 / 19 ) & 282.455471698113 & 120.223415752419 & 2.34942144947691 \tabularnewline
Trimmed Mean ( 4 / 19 ) & 268.95568627451 & 116.955925093728 & 2.29963284082417 \tabularnewline
Trimmed Mean ( 5 / 19 ) & 254.896326530612 & 113.227859794520 & 2.25118029249325 \tabularnewline
Trimmed Mean ( 6 / 19 ) & 238.342978723404 & 109.029900942492 & 2.18603315845549 \tabularnewline
Trimmed Mean ( 7 / 19 ) & 227.371777777778 & 106.210805376934 & 2.14075937915028 \tabularnewline
Trimmed Mean ( 8 / 19 ) & 216.162093023256 & 103.093034724465 & 2.09676719286603 \tabularnewline
Trimmed Mean ( 9 / 19 ) & 204.499268292683 & 99.7785897749944 & 2.04953055313609 \tabularnewline
Trimmed Mean ( 10 / 19 ) & 191.078461538462 & 96.3141710105766 & 1.98390807431109 \tabularnewline
Trimmed Mean ( 11 / 19 ) & 179.328108108108 & 93.6099622626272 & 1.91569469502610 \tabularnewline
Trimmed Mean ( 12 / 19 ) & 164.709714285714 & 90.1585925298992 & 1.82688870426956 \tabularnewline
Trimmed Mean ( 13 / 19 ) & 147.902424242424 & 86.6973800950562 & 1.70596186505592 \tabularnewline
Trimmed Mean ( 14 / 19 ) & 132.237741935484 & 83.3476801551752 & 1.58657975470086 \tabularnewline
Trimmed Mean ( 15 / 19 ) & 115.237241379310 & 79.5316274633532 & 1.44894861396379 \tabularnewline
Trimmed Mean ( 16 / 19 ) & 93.7033333333333 & 74.7137293931247 & 1.25416485155346 \tabularnewline
Trimmed Mean ( 17 / 19 ) & 69.0648 & 67.422960938442 & 1.02435133430371 \tabularnewline
Trimmed Mean ( 18 / 19 ) & 44.5878260869565 & 58.3794834655646 & 0.763758489114704 \tabularnewline
Trimmed Mean ( 19 / 19 ) & 29.94 & 54.091684604321 & 0.553504669322285 \tabularnewline
Median & 3.59 &  &  \tabularnewline
Midrange & -2134.63 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 98.26 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 132.237741935484 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 132.237741935484 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 132.237741935484 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 115.237241379310 &  &  \tabularnewline
Midmean - Closest Observation & 98.26 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 132.237741935484 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 132.237741935484 &  &  \tabularnewline
Number of observations & 59 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=48901&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]158.656610169492[/C][C]189.386344108264[/C][C]0.837740497692877[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]NaN[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]215.110626702008[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]1451.02335796593[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 19 )[/C][C]215.896610169492[/C][C]157.045917039300[/C][C]1.37473558204932[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 19 )[/C][C]230.949491525424[/C][C]150.262327014389[/C][C]1.53697534248426[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 19 )[/C][C]317.463389830509[/C][C]126.309733690837[/C][C]2.51337233128485[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 19 )[/C][C]315.661355932203[/C][C]125.176804581940[/C][C]2.52172402855652[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 19 )[/C][C]320.829152542373[/C][C]123.388050424063[/C][C]2.60016388491219[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 19 )[/C][C]288.550169491525[/C][C]115.574643663766[/C][C]2.49665636288688[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 19 )[/C][C]284.560169491525[/C][C]113.514970111270[/C][C]2.50680742119382[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 19 )[/C][C]280.999491525424[/C][C]110.572113360624[/C][C]2.54132333176053[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 19 )[/C][C]284.341694915254[/C][C]106.901473166809[/C][C]2.65984823681118[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 19 )[/C][C]264.767118644068[/C][C]99.87119782851[/C][C]2.65108584257398[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 19 )[/C][C]274.719322033898[/C][C]98.2649707990621[/C][C]2.79569942167551[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 19 )[/C][C]277.517966101695[/C][C]93.0646664853488[/C][C]2.98199065856411[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 19 )[/C][C]254.900169491525[/C][C]87.7696052860469[/C][C]2.90419637482462[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 19 )[/C][C]249.224237288136[/C][C]83.8818805860994[/C][C]2.97113316423948[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 19 )[/C][C]263.054745762712[/C][C]80.0371281605113[/C][C]3.28665897700835[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 19 )[/C][C]260.744237288136[/C][C]78.5014165496656[/C][C]3.3215227030097[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 19 )[/C][C]231.276610169492[/C][C]72.5093138500797[/C][C]3.18961244961825[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 19 )[/C][C]138.433220338983[/C][C]54.1808280689951[/C][C]2.5550222333756[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 19 )[/C][C]127.277966101695[/C][C]51.7746802671049[/C][C]2.45830520719915[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 19 )[/C][C]239.122807017544[/C][C]146.389701593054[/C][C]1.63346741208802[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 19 )[/C][C]264.038181818182[/C][C]132.757054052175[/C][C]1.98888250197546[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 19 )[/C][C]282.455471698113[/C][C]120.223415752419[/C][C]2.34942144947691[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 19 )[/C][C]268.95568627451[/C][C]116.955925093728[/C][C]2.29963284082417[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 19 )[/C][C]254.896326530612[/C][C]113.227859794520[/C][C]2.25118029249325[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 19 )[/C][C]238.342978723404[/C][C]109.029900942492[/C][C]2.18603315845549[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 19 )[/C][C]227.371777777778[/C][C]106.210805376934[/C][C]2.14075937915028[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 19 )[/C][C]216.162093023256[/C][C]103.093034724465[/C][C]2.09676719286603[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 19 )[/C][C]204.499268292683[/C][C]99.7785897749944[/C][C]2.04953055313609[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 19 )[/C][C]191.078461538462[/C][C]96.3141710105766[/C][C]1.98390807431109[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 19 )[/C][C]179.328108108108[/C][C]93.6099622626272[/C][C]1.91569469502610[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 19 )[/C][C]164.709714285714[/C][C]90.1585925298992[/C][C]1.82688870426956[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 19 )[/C][C]147.902424242424[/C][C]86.6973800950562[/C][C]1.70596186505592[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 19 )[/C][C]132.237741935484[/C][C]83.3476801551752[/C][C]1.58657975470086[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 19 )[/C][C]115.237241379310[/C][C]79.5316274633532[/C][C]1.44894861396379[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 19 )[/C][C]93.7033333333333[/C][C]74.7137293931247[/C][C]1.25416485155346[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 19 )[/C][C]69.0648[/C][C]67.422960938442[/C][C]1.02435133430371[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 19 )[/C][C]44.5878260869565[/C][C]58.3794834655646[/C][C]0.763758489114704[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 19 )[/C][C]29.94[/C][C]54.091684604321[/C][C]0.553504669322285[/C][/ROW]
[ROW][C]Median[/C][C]3.59[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]-2134.63[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]98.26[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]132.237741935484[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]132.237741935484[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]132.237741935484[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]115.237241379310[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]98.26[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]132.237741935484[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]132.237741935484[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]59[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=48901&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=48901&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 Mean158.656610169492189.3863441082640.837740497692877
Geometric MeanNaN
Harmonic Mean215.110626702008
Quadratic Mean1451.02335796593
Winsorized Mean ( 1 / 19 )215.896610169492157.0459170393001.37473558204932
Winsorized Mean ( 2 / 19 )230.949491525424150.2623270143891.53697534248426
Winsorized Mean ( 3 / 19 )317.463389830509126.3097336908372.51337233128485
Winsorized Mean ( 4 / 19 )315.661355932203125.1768045819402.52172402855652
Winsorized Mean ( 5 / 19 )320.829152542373123.3880504240632.60016388491219
Winsorized Mean ( 6 / 19 )288.550169491525115.5746436637662.49665636288688
Winsorized Mean ( 7 / 19 )284.560169491525113.5149701112702.50680742119382
Winsorized Mean ( 8 / 19 )280.999491525424110.5721133606242.54132333176053
Winsorized Mean ( 9 / 19 )284.341694915254106.9014731668092.65984823681118
Winsorized Mean ( 10 / 19 )264.76711864406899.871197828512.65108584257398
Winsorized Mean ( 11 / 19 )274.71932203389898.26497079906212.79569942167551
Winsorized Mean ( 12 / 19 )277.51796610169593.06466648534882.98199065856411
Winsorized Mean ( 13 / 19 )254.90016949152587.76960528604692.90419637482462
Winsorized Mean ( 14 / 19 )249.22423728813683.88188058609942.97113316423948
Winsorized Mean ( 15 / 19 )263.05474576271280.03712816051133.28665897700835
Winsorized Mean ( 16 / 19 )260.74423728813678.50141654966563.3215227030097
Winsorized Mean ( 17 / 19 )231.27661016949272.50931385007973.18961244961825
Winsorized Mean ( 18 / 19 )138.43322033898354.18082806899512.5550222333756
Winsorized Mean ( 19 / 19 )127.27796610169551.77468026710492.45830520719915
Trimmed Mean ( 1 / 19 )239.122807017544146.3897015930541.63346741208802
Trimmed Mean ( 2 / 19 )264.038181818182132.7570540521751.98888250197546
Trimmed Mean ( 3 / 19 )282.455471698113120.2234157524192.34942144947691
Trimmed Mean ( 4 / 19 )268.95568627451116.9559250937282.29963284082417
Trimmed Mean ( 5 / 19 )254.896326530612113.2278597945202.25118029249325
Trimmed Mean ( 6 / 19 )238.342978723404109.0299009424922.18603315845549
Trimmed Mean ( 7 / 19 )227.371777777778106.2108053769342.14075937915028
Trimmed Mean ( 8 / 19 )216.162093023256103.0930347244652.09676719286603
Trimmed Mean ( 9 / 19 )204.49926829268399.77858977499442.04953055313609
Trimmed Mean ( 10 / 19 )191.07846153846296.31417101057661.98390807431109
Trimmed Mean ( 11 / 19 )179.32810810810893.60996226262721.91569469502610
Trimmed Mean ( 12 / 19 )164.70971428571490.15859252989921.82688870426956
Trimmed Mean ( 13 / 19 )147.90242424242486.69738009505621.70596186505592
Trimmed Mean ( 14 / 19 )132.23774193548483.34768015517521.58657975470086
Trimmed Mean ( 15 / 19 )115.23724137931079.53162746335321.44894861396379
Trimmed Mean ( 16 / 19 )93.703333333333374.71372939312471.25416485155346
Trimmed Mean ( 17 / 19 )69.064867.4229609384421.02435133430371
Trimmed Mean ( 18 / 19 )44.587826086956558.37948346556460.763758489114704
Trimmed Mean ( 19 / 19 )29.9454.0916846043210.553504669322285
Median3.59
Midrange-2134.63
Midmean - Weighted Average at Xnp98.26
Midmean - Weighted Average at X(n+1)p132.237741935484
Midmean - Empirical Distribution Function132.237741935484
Midmean - Empirical Distribution Function - Averaging132.237741935484
Midmean - Empirical Distribution Function - Interpolation115.237241379310
Midmean - Closest Observation98.26
Midmean - True Basic - Statistics Graphics Toolkit132.237741935484
Midmean - MS Excel (old versions)132.237741935484
Number of observations59



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')