Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationThu, 24 Nov 2011 10:06:40 -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/2011/Nov/24/t1322147501rgnv626z5pzqjy7.htm/, Retrieved Thu, 31 Oct 2024 22:55:13 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=146942, Retrieved Thu, 31 Oct 2024 22:55:13 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact122
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
F     [Univariate Data Series] [HPC Retail Sales] [2008-03-02 15:42:48] [74be16979710d4c4e7c6647856088456]
- RMPD    [Central Tendency] [WS8] [2011-11-24 15:06:40] [d41d8cd98f00b204e9800998ecf8427e] [Current]
Feedback Forum

Post a new message
Dataseries X:
89 924
31 795
27 922
59 954
52 150
39 964
34 604
51 106
52 593
68 794
47 124
32 315
42 248
36 088
52 744
72 586
92 334
80 761
71 078
63 713
57 122
55 243
62 143
62 708
62 474
64 250
71 866
69 886
58 724
55 298
52 594
54 854
54 694
49 298
44 659
43 657
47 002
47 042
48 959
49 750
54 048
60 067
68 929
74 617
75 940
72 762
75 621
73 008
74 196
78 878
83 812
91 624
89 388
110 410
113 857
112 060
117 236
132 810
137 699
146 409




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=146942&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=146942&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=146942&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 Mean67589.853370.9579918699620.0506355056967
Geometric Mean63233.5686849326
Harmonic Mean59332.0537074669
Quadratic Mean72379.7342646177
Winsorized Mean ( 1 / 20 )67509.23333333333303.6730149142620.4345990140569
Winsorized Mean ( 2 / 20 )67363.63243.2729290337920.7702532207391
Winsorized Mean ( 3 / 20 )66699.352976.204248867122.4108778909879
Winsorized Mean ( 4 / 20 )66573.01666666672894.7137672079222.998134537799
Winsorized Mean ( 5 / 20 )66746.26666666672798.3616855382623.8519084261362
Winsorized Mean ( 6 / 20 )66809.66666666672717.2427571909324.5873014068622
Winsorized Mean ( 7 / 20 )64865.18333333332171.5491694163929.870464941287
Winsorized Mean ( 8 / 20 )64904.11666666672129.509760709230.4784311695531
Winsorized Mean ( 9 / 20 )65000.56666666672020.8410280522232.1651063910343
Winsorized Mean ( 10 / 20 )64917.92001.238841275732.4388567026901
Winsorized Mean ( 11 / 20 )63910.66666666671796.4745415236935.5756038782829
Winsorized Mean ( 12 / 20 )63667.46666666671627.5121096109639.1195041134813
Winsorized Mean ( 13 / 20 )63332.93333333331545.0946808548740.9896779259458
Winsorized Mean ( 14 / 20 )62752.86666666671416.0297164575244.3160662077455
Winsorized Mean ( 15 / 20 )63012.11666666671351.7213861227146.6162016178579
Winsorized Mean ( 16 / 20 )63022.78333333331268.7927615663649.6714556091333
Winsorized Mean ( 17 / 20 )63029.01666666671232.2683223863551.1487762215681
Winsorized Mean ( 18 / 20 )62672.91666666671178.3436870444753.1872978620214
Winsorized Mean ( 19 / 20 )62642.51666666671159.9152366487754.0061158672709
Winsorized Mean ( 20 / 20 )63018.51666666671089.4104258652957.8464416811623
Trimmed Mean ( 1 / 20 )66914.82758620693131.2227489097221.3701908015028
Trimmed Mean ( 2 / 20 )66277.96428571432913.6572250869722.7473443736114
Trimmed Mean ( 3 / 20 )65674.83333333332679.4575975923924.5104954795123
Trimmed Mean ( 4 / 20 )65280.78846153852525.5619502712725.8480250126221
Trimmed Mean ( 5 / 20 )64893.122364.3873733241527.4460609679052
Trimmed Mean ( 6 / 20 )64429.83333333332192.0052081923329.3931023031037
Trimmed Mean ( 7 / 20 )63912.47826086961992.8983880908732.0701138817697
Trimmed Mean ( 8 / 20 )63726.88636363641923.7197769828933.1269071130433
Trimmed Mean ( 9 / 20 )63516.66666666671844.4175879853134.4372484194576
Trimmed Mean ( 10 / 20 )63269.351769.6701838702835.7520574040691
Trimmed Mean ( 11 / 20 )63009.05263157891673.4512484701237.6521590869062
Trimmed Mean ( 12 / 20 )62872.44444444441606.4473291522539.1375697811539
Trimmed Mean ( 13 / 20 )62755.52941176471562.026798355140.1757059980339
Trimmed Mean ( 14 / 20 )62672.251521.4653013810241.1920337211192
Trimmed Mean ( 15 / 20 )62660.73333333331498.3961141131141.8185369964215
Trimmed Mean ( 16 / 20 )62610.53571428571478.1321184104542.3578751415101
Trimmed Mean ( 17 / 20 )62551.07692307691466.6000743982242.6503980294309
Trimmed Mean ( 18 / 20 )62480.79166666671451.6414783990543.0414758715589
Trimmed Mean ( 19 / 20 )62451.68181818181437.4548807319543.4460118750869
Trimmed Mean ( 20 / 20 )62421.551408.6759861937544.3122127528156
Median62308.5
Midrange87165.5
Midmean - Weighted Average at Xnp62244.2580645161
Midmean - Weighted Average at X(n+1)p62660.7333333333
Midmean - Empirical Distribution Function62244.2580645161
Midmean - Empirical Distribution Function - Averaging62660.7333333333
Midmean - Empirical Distribution Function - Interpolation62660.7333333333
Midmean - Closest Observation62244.2580645161
Midmean - True Basic - Statistics Graphics Toolkit62660.7333333333
Midmean - MS Excel (old versions)62672.25
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 67589.85 & 3370.95799186996 & 20.0506355056967 \tabularnewline
Geometric Mean & 63233.5686849326 &  &  \tabularnewline
Harmonic Mean & 59332.0537074669 &  &  \tabularnewline
Quadratic Mean & 72379.7342646177 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 67509.2333333333 & 3303.67301491426 & 20.4345990140569 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 67363.6 & 3243.27292903379 & 20.7702532207391 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 66699.35 & 2976.2042488671 & 22.4108778909879 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 66573.0166666667 & 2894.71376720792 & 22.998134537799 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 66746.2666666667 & 2798.36168553826 & 23.8519084261362 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 66809.6666666667 & 2717.24275719093 & 24.5873014068622 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 64865.1833333333 & 2171.54916941639 & 29.870464941287 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 64904.1166666667 & 2129.5097607092 & 30.4784311695531 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 65000.5666666667 & 2020.84102805222 & 32.1651063910343 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 64917.9 & 2001.2388412757 & 32.4388567026901 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 63910.6666666667 & 1796.47454152369 & 35.5756038782829 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 63667.4666666667 & 1627.51210961096 & 39.1195041134813 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 63332.9333333333 & 1545.09468085487 & 40.9896779259458 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 62752.8666666667 & 1416.02971645752 & 44.3160662077455 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 63012.1166666667 & 1351.72138612271 & 46.6162016178579 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 63022.7833333333 & 1268.79276156636 & 49.6714556091333 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 63029.0166666667 & 1232.26832238635 & 51.1487762215681 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 62672.9166666667 & 1178.34368704447 & 53.1872978620214 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 62642.5166666667 & 1159.91523664877 & 54.0061158672709 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 63018.5166666667 & 1089.41042586529 & 57.8464416811623 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 66914.8275862069 & 3131.22274890972 & 21.3701908015028 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 66277.9642857143 & 2913.65722508697 & 22.7473443736114 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 65674.8333333333 & 2679.45759759239 & 24.5104954795123 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 65280.7884615385 & 2525.56195027127 & 25.8480250126221 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 64893.12 & 2364.38737332415 & 27.4460609679052 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 64429.8333333333 & 2192.00520819233 & 29.3931023031037 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 63912.4782608696 & 1992.89838809087 & 32.0701138817697 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 63726.8863636364 & 1923.71977698289 & 33.1269071130433 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 63516.6666666667 & 1844.41758798531 & 34.4372484194576 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 63269.35 & 1769.67018387028 & 35.7520574040691 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 63009.0526315789 & 1673.45124847012 & 37.6521590869062 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 62872.4444444444 & 1606.44732915225 & 39.1375697811539 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 62755.5294117647 & 1562.0267983551 & 40.1757059980339 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 62672.25 & 1521.46530138102 & 41.1920337211192 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 62660.7333333333 & 1498.39611411311 & 41.8185369964215 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 62610.5357142857 & 1478.13211841045 & 42.3578751415101 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 62551.0769230769 & 1466.60007439822 & 42.6503980294309 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 62480.7916666667 & 1451.64147839905 & 43.0414758715589 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 62451.6818181818 & 1437.45488073195 & 43.4460118750869 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 62421.55 & 1408.67598619375 & 44.3122127528156 \tabularnewline
Median & 62308.5 &  &  \tabularnewline
Midrange & 87165.5 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 62244.2580645161 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 62660.7333333333 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 62244.2580645161 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 62660.7333333333 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 62660.7333333333 &  &  \tabularnewline
Midmean - Closest Observation & 62244.2580645161 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 62660.7333333333 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 62672.25 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=146942&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]67589.85[/C][C]3370.95799186996[/C][C]20.0506355056967[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]63233.5686849326[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]59332.0537074669[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]72379.7342646177[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]67509.2333333333[/C][C]3303.67301491426[/C][C]20.4345990140569[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]67363.6[/C][C]3243.27292903379[/C][C]20.7702532207391[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]66699.35[/C][C]2976.2042488671[/C][C]22.4108778909879[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]66573.0166666667[/C][C]2894.71376720792[/C][C]22.998134537799[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]66746.2666666667[/C][C]2798.36168553826[/C][C]23.8519084261362[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]66809.6666666667[/C][C]2717.24275719093[/C][C]24.5873014068622[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]64865.1833333333[/C][C]2171.54916941639[/C][C]29.870464941287[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]64904.1166666667[/C][C]2129.5097607092[/C][C]30.4784311695531[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]65000.5666666667[/C][C]2020.84102805222[/C][C]32.1651063910343[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]64917.9[/C][C]2001.2388412757[/C][C]32.4388567026901[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]63910.6666666667[/C][C]1796.47454152369[/C][C]35.5756038782829[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]63667.4666666667[/C][C]1627.51210961096[/C][C]39.1195041134813[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]63332.9333333333[/C][C]1545.09468085487[/C][C]40.9896779259458[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]62752.8666666667[/C][C]1416.02971645752[/C][C]44.3160662077455[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]63012.1166666667[/C][C]1351.72138612271[/C][C]46.6162016178579[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]63022.7833333333[/C][C]1268.79276156636[/C][C]49.6714556091333[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]63029.0166666667[/C][C]1232.26832238635[/C][C]51.1487762215681[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]62672.9166666667[/C][C]1178.34368704447[/C][C]53.1872978620214[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]62642.5166666667[/C][C]1159.91523664877[/C][C]54.0061158672709[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]63018.5166666667[/C][C]1089.41042586529[/C][C]57.8464416811623[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]66914.8275862069[/C][C]3131.22274890972[/C][C]21.3701908015028[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]66277.9642857143[/C][C]2913.65722508697[/C][C]22.7473443736114[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]65674.8333333333[/C][C]2679.45759759239[/C][C]24.5104954795123[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]65280.7884615385[/C][C]2525.56195027127[/C][C]25.8480250126221[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]64893.12[/C][C]2364.38737332415[/C][C]27.4460609679052[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]64429.8333333333[/C][C]2192.00520819233[/C][C]29.3931023031037[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]63912.4782608696[/C][C]1992.89838809087[/C][C]32.0701138817697[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]63726.8863636364[/C][C]1923.71977698289[/C][C]33.1269071130433[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]63516.6666666667[/C][C]1844.41758798531[/C][C]34.4372484194576[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]63269.35[/C][C]1769.67018387028[/C][C]35.7520574040691[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]63009.0526315789[/C][C]1673.45124847012[/C][C]37.6521590869062[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]62872.4444444444[/C][C]1606.44732915225[/C][C]39.1375697811539[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]62755.5294117647[/C][C]1562.0267983551[/C][C]40.1757059980339[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]62672.25[/C][C]1521.46530138102[/C][C]41.1920337211192[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]62660.7333333333[/C][C]1498.39611411311[/C][C]41.8185369964215[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]62610.5357142857[/C][C]1478.13211841045[/C][C]42.3578751415101[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]62551.0769230769[/C][C]1466.60007439822[/C][C]42.6503980294309[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]62480.7916666667[/C][C]1451.64147839905[/C][C]43.0414758715589[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]62451.6818181818[/C][C]1437.45488073195[/C][C]43.4460118750869[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]62421.55[/C][C]1408.67598619375[/C][C]44.3122127528156[/C][/ROW]
[ROW][C]Median[/C][C]62308.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]87165.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]62244.2580645161[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]62660.7333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]62244.2580645161[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]62660.7333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]62660.7333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]62244.2580645161[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]62660.7333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]62672.25[/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=146942&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=146942&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 Mean67589.853370.9579918699620.0506355056967
Geometric Mean63233.5686849326
Harmonic Mean59332.0537074669
Quadratic Mean72379.7342646177
Winsorized Mean ( 1 / 20 )67509.23333333333303.6730149142620.4345990140569
Winsorized Mean ( 2 / 20 )67363.63243.2729290337920.7702532207391
Winsorized Mean ( 3 / 20 )66699.352976.204248867122.4108778909879
Winsorized Mean ( 4 / 20 )66573.01666666672894.7137672079222.998134537799
Winsorized Mean ( 5 / 20 )66746.26666666672798.3616855382623.8519084261362
Winsorized Mean ( 6 / 20 )66809.66666666672717.2427571909324.5873014068622
Winsorized Mean ( 7 / 20 )64865.18333333332171.5491694163929.870464941287
Winsorized Mean ( 8 / 20 )64904.11666666672129.509760709230.4784311695531
Winsorized Mean ( 9 / 20 )65000.56666666672020.8410280522232.1651063910343
Winsorized Mean ( 10 / 20 )64917.92001.238841275732.4388567026901
Winsorized Mean ( 11 / 20 )63910.66666666671796.4745415236935.5756038782829
Winsorized Mean ( 12 / 20 )63667.46666666671627.5121096109639.1195041134813
Winsorized Mean ( 13 / 20 )63332.93333333331545.0946808548740.9896779259458
Winsorized Mean ( 14 / 20 )62752.86666666671416.0297164575244.3160662077455
Winsorized Mean ( 15 / 20 )63012.11666666671351.7213861227146.6162016178579
Winsorized Mean ( 16 / 20 )63022.78333333331268.7927615663649.6714556091333
Winsorized Mean ( 17 / 20 )63029.01666666671232.2683223863551.1487762215681
Winsorized Mean ( 18 / 20 )62672.91666666671178.3436870444753.1872978620214
Winsorized Mean ( 19 / 20 )62642.51666666671159.9152366487754.0061158672709
Winsorized Mean ( 20 / 20 )63018.51666666671089.4104258652957.8464416811623
Trimmed Mean ( 1 / 20 )66914.82758620693131.2227489097221.3701908015028
Trimmed Mean ( 2 / 20 )66277.96428571432913.6572250869722.7473443736114
Trimmed Mean ( 3 / 20 )65674.83333333332679.4575975923924.5104954795123
Trimmed Mean ( 4 / 20 )65280.78846153852525.5619502712725.8480250126221
Trimmed Mean ( 5 / 20 )64893.122364.3873733241527.4460609679052
Trimmed Mean ( 6 / 20 )64429.83333333332192.0052081923329.3931023031037
Trimmed Mean ( 7 / 20 )63912.47826086961992.8983880908732.0701138817697
Trimmed Mean ( 8 / 20 )63726.88636363641923.7197769828933.1269071130433
Trimmed Mean ( 9 / 20 )63516.66666666671844.4175879853134.4372484194576
Trimmed Mean ( 10 / 20 )63269.351769.6701838702835.7520574040691
Trimmed Mean ( 11 / 20 )63009.05263157891673.4512484701237.6521590869062
Trimmed Mean ( 12 / 20 )62872.44444444441606.4473291522539.1375697811539
Trimmed Mean ( 13 / 20 )62755.52941176471562.026798355140.1757059980339
Trimmed Mean ( 14 / 20 )62672.251521.4653013810241.1920337211192
Trimmed Mean ( 15 / 20 )62660.73333333331498.3961141131141.8185369964215
Trimmed Mean ( 16 / 20 )62610.53571428571478.1321184104542.3578751415101
Trimmed Mean ( 17 / 20 )62551.07692307691466.6000743982242.6503980294309
Trimmed Mean ( 18 / 20 )62480.79166666671451.6414783990543.0414758715589
Trimmed Mean ( 19 / 20 )62451.68181818181437.4548807319543.4460118750869
Trimmed Mean ( 20 / 20 )62421.551408.6759861937544.3122127528156
Median62308.5
Midrange87165.5
Midmean - Weighted Average at Xnp62244.2580645161
Midmean - Weighted Average at X(n+1)p62660.7333333333
Midmean - Empirical Distribution Function62244.2580645161
Midmean - Empirical Distribution Function - Averaging62660.7333333333
Midmean - Empirical Distribution Function - Interpolation62660.7333333333
Midmean - Closest Observation62244.2580645161
Midmean - True Basic - Statistics Graphics Toolkit62660.7333333333
Midmean - MS Excel (old versions)62672.25
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')