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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 computationSun, 25 Oct 2009 11:50:32 -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/25/t12564931393u19l8ajth36bql.htm/, Retrieved Thu, 31 Oct 2024 22:58:17 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=50354, Retrieved Thu, 31 Oct 2024 22:58:17 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsWS 3 Part 2
Estimated Impact211
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Bivariate Data Series] [Bivariate dataset] [2008-01-05 23:51:08] [74be16979710d4c4e7c6647856088456]
F RMPD  [Univariate Explorative Data Analysis] [Colombia Coffee] [2008-01-07 14:21:11] [74be16979710d4c4e7c6647856088456]
F RMPD    [Univariate Data Series] [] [2009-10-14 08:30:28] [74be16979710d4c4e7c6647856088456]
-           [Univariate Data Series] [WS 3 Part 1/1] [2009-10-21 21:03:12] [9717cb857c153ca3061376906953b329]
- RMPD        [Central Tendency] [WS 3 Part 2] [2009-10-22 15:25:33] [9717cb857c153ca3061376906953b329]
-    D            [Central Tendency] [WS 3 Part 2] [2009-10-25 17:50:32] [52b85b290d6f50b0921ad6729b8a5af2] [Current]
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Dataseries X:
3147
3009
2947
2721
2591
2845
2795
2689
2634
2388
2464
2738
2804
2869
2600
2543
2377
2367
2455
2152
2263
2078
2244
2140
2462
2355
2082
1983
1886
1995
1930
1794
1784
1751
1890
1880
1951
1983
1940
1865
1793
1664
1714
1641
1437
1409
1353
1411
1595
1670
1549
1525
1614
1624
1720
1796
1590
1600
1686
1735




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=50354&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=50354&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=50354&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 Mean2091.9561.56453334133833.9797913906275
Geometric Mean2040.13549897273
Harmonic Mean1990.68691011102
Quadratic Mean2144.73217830727
Winsorized Mean ( 1 / 20 )2090.5833333333360.751858410888534.4118416788817
Winsorized Mean ( 2 / 20 )2088.5833333333360.224688950078534.6798525612080
Winsorized Mean ( 3 / 20 )2085.9833333333359.070146425091435.313664508664
Winsorized Mean ( 4 / 20 )2090.2557.678789220897336.2394916438830
Winsorized Mean ( 5 / 20 )2088.8333333333356.606183241476436.9011513180914
Winsorized Mean ( 6 / 20 )2092.0333333333355.76940500704637.5122046410397
Winsorized Mean ( 7 / 20 )2085.9666666666754.292579253140738.4208430574054
Winsorized Mean ( 8 / 20 )2084.3666666666753.732256126085438.7917205965742
Winsorized Mean ( 9 / 20 )2081.6666666666752.460131036809739.6809276973789
Winsorized Mean ( 10 / 20 )2074.1666666666750.445994878153641.1165776723518
Winsorized Mean ( 11 / 20 )2071.0548.818761010022342.4232396962066
Winsorized Mean ( 12 / 20 )2073.8547.810801943555343.3761810238689
Winsorized Mean ( 13 / 20 )2064.7545.745862861318445.1352290863859
Winsorized Mean ( 14 / 20 )2050.0542.022851094663948.7841721015526
Winsorized Mean ( 15 / 20 )2056.5540.928499215370750.2473835939644
Winsorized Mean ( 16 / 20 )2056.2833333333340.389236775028450.9116660160481
Winsorized Mean ( 17 / 20 )2041.5536.677325813280955.6624550653787
Winsorized Mean ( 18 / 20 )2043.0535.474924899288657.5913833729065
Winsorized Mean ( 19 / 20 )2050.3333333333333.535803168583361.1386381004917
Winsorized Mean ( 20 / 20 )2049.3333333333332.494333853458863.0674056152469
Trimmed Mean ( 1 / 20 )2086.559.632821092768734.9891211209697
Trimmed Mean ( 2 / 20 )2082.12558.235120514717235.7537682003046
Trimmed Mean ( 3 / 20 )2078.5370370370456.838995045354836.5688562118043
Trimmed Mean ( 4 / 20 )2075.6730769230855.637514072903737.3070779942334
Trimmed Mean ( 5 / 20 )2071.354.635312270900237.91137844568
Trimmed Mean ( 6 / 20 )2066.9166666666753.688108299820438.4985936759776
Trimmed Mean ( 7 / 20 )2061.4565217391352.676193474454939.1345005355944
Trimmed Mean ( 8 / 20 )2056.6818181818251.753101169729239.7402623552304
Trimmed Mean ( 9 / 20 )2051.7380952381050.64392628995640.5130140086514
Trimmed Mean ( 10 / 20 )2046.7549.470824735393341.3728699884738
Trimmed Mean ( 11 / 20 )2042.4210526315848.399661302480342.1990773833559
Trimmed Mean ( 12 / 20 )2038.0833333333347.315915222399943.0739492991669
Trimmed Mean ( 13 / 20 )2032.8235294117646.001307246949344.1905600312386
Trimmed Mean ( 14 / 20 )2028.2187544.695288558241145.3788042414603
Trimmed Mean ( 15 / 20 )2025.143.869931838791746.1614576343909
Trimmed Mean ( 16 / 20 )2020.6071428571442.819707525947847.1887189241706
Trimmed Mean ( 17 / 20 )2015.4615384615441.257101235628148.8512638576038
Trimmed Mean ( 18 / 20 )2011.62540.122087798964650.137595283661
Trimmed Mean ( 19 / 20 )2006.8636363636438.552729700187252.0550335078839
Trimmed Mean ( 20 / 20 )200036.504073312728454.7884062928021
Median1967
Midrange2250
Midmean - Weighted Average at Xnp2014.16129032258
Midmean - Weighted Average at X(n+1)p2025.1
Midmean - Empirical Distribution Function2014.16129032258
Midmean - Empirical Distribution Function - Averaging2025.1
Midmean - Empirical Distribution Function - Interpolation2025.1
Midmean - Closest Observation2014.16129032258
Midmean - True Basic - Statistics Graphics Toolkit2025.1
Midmean - MS Excel (old versions)2028.21875
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 2091.95 & 61.564533341338 & 33.9797913906275 \tabularnewline
Geometric Mean & 2040.13549897273 &  &  \tabularnewline
Harmonic Mean & 1990.68691011102 &  &  \tabularnewline
Quadratic Mean & 2144.73217830727 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 2090.58333333333 & 60.7518584108885 & 34.4118416788817 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 2088.58333333333 & 60.2246889500785 & 34.6798525612080 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 2085.98333333333 & 59.0701464250914 & 35.313664508664 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 2090.25 & 57.6787892208973 & 36.2394916438830 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 2088.83333333333 & 56.6061832414764 & 36.9011513180914 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 2092.03333333333 & 55.769405007046 & 37.5122046410397 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 2085.96666666667 & 54.2925792531407 & 38.4208430574054 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 2084.36666666667 & 53.7322561260854 & 38.7917205965742 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 2081.66666666667 & 52.4601310368097 & 39.6809276973789 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 2074.16666666667 & 50.4459948781536 & 41.1165776723518 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 2071.05 & 48.8187610100223 & 42.4232396962066 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 2073.85 & 47.8108019435553 & 43.3761810238689 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 2064.75 & 45.7458628613184 & 45.1352290863859 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 2050.05 & 42.0228510946639 & 48.7841721015526 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 2056.55 & 40.9284992153707 & 50.2473835939644 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 2056.28333333333 & 40.3892367750284 & 50.9116660160481 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 2041.55 & 36.6773258132809 & 55.6624550653787 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 2043.05 & 35.4749248992886 & 57.5913833729065 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 2050.33333333333 & 33.5358031685833 & 61.1386381004917 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 2049.33333333333 & 32.4943338534588 & 63.0674056152469 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 2086.5 & 59.6328210927687 & 34.9891211209697 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 2082.125 & 58.2351205147172 & 35.7537682003046 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 2078.53703703704 & 56.8389950453548 & 36.5688562118043 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 2075.67307692308 & 55.6375140729037 & 37.3070779942334 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 2071.3 & 54.6353122709002 & 37.91137844568 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 2066.91666666667 & 53.6881082998204 & 38.4985936759776 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 2061.45652173913 & 52.6761934744549 & 39.1345005355944 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 2056.68181818182 & 51.7531011697292 & 39.7402623552304 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 2051.73809523810 & 50.643926289956 & 40.5130140086514 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 2046.75 & 49.4708247353933 & 41.3728699884738 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 2042.42105263158 & 48.3996613024803 & 42.1990773833559 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 2038.08333333333 & 47.3159152223999 & 43.0739492991669 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 2032.82352941176 & 46.0013072469493 & 44.1905600312386 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 2028.21875 & 44.6952885582411 & 45.3788042414603 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 2025.1 & 43.8699318387917 & 46.1614576343909 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 2020.60714285714 & 42.8197075259478 & 47.1887189241706 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 2015.46153846154 & 41.2571012356281 & 48.8512638576038 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 2011.625 & 40.1220877989646 & 50.137595283661 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 2006.86363636364 & 38.5527297001872 & 52.0550335078839 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 2000 & 36.5040733127284 & 54.7884062928021 \tabularnewline
Median & 1967 &  &  \tabularnewline
Midrange & 2250 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 2014.16129032258 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 2025.1 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 2014.16129032258 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 2025.1 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 2025.1 &  &  \tabularnewline
Midmean - Closest Observation & 2014.16129032258 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 2025.1 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 2028.21875 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=50354&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]2091.95[/C][C]61.564533341338[/C][C]33.9797913906275[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]2040.13549897273[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]1990.68691011102[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]2144.73217830727[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]2090.58333333333[/C][C]60.7518584108885[/C][C]34.4118416788817[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]2088.58333333333[/C][C]60.2246889500785[/C][C]34.6798525612080[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]2085.98333333333[/C][C]59.0701464250914[/C][C]35.313664508664[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]2090.25[/C][C]57.6787892208973[/C][C]36.2394916438830[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]2088.83333333333[/C][C]56.6061832414764[/C][C]36.9011513180914[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]2092.03333333333[/C][C]55.769405007046[/C][C]37.5122046410397[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]2085.96666666667[/C][C]54.2925792531407[/C][C]38.4208430574054[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]2084.36666666667[/C][C]53.7322561260854[/C][C]38.7917205965742[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]2081.66666666667[/C][C]52.4601310368097[/C][C]39.6809276973789[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]2074.16666666667[/C][C]50.4459948781536[/C][C]41.1165776723518[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]2071.05[/C][C]48.8187610100223[/C][C]42.4232396962066[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]2073.85[/C][C]47.8108019435553[/C][C]43.3761810238689[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]2064.75[/C][C]45.7458628613184[/C][C]45.1352290863859[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]2050.05[/C][C]42.0228510946639[/C][C]48.7841721015526[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]2056.55[/C][C]40.9284992153707[/C][C]50.2473835939644[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]2056.28333333333[/C][C]40.3892367750284[/C][C]50.9116660160481[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]2041.55[/C][C]36.6773258132809[/C][C]55.6624550653787[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]2043.05[/C][C]35.4749248992886[/C][C]57.5913833729065[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]2050.33333333333[/C][C]33.5358031685833[/C][C]61.1386381004917[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]2049.33333333333[/C][C]32.4943338534588[/C][C]63.0674056152469[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]2086.5[/C][C]59.6328210927687[/C][C]34.9891211209697[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]2082.125[/C][C]58.2351205147172[/C][C]35.7537682003046[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]2078.53703703704[/C][C]56.8389950453548[/C][C]36.5688562118043[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]2075.67307692308[/C][C]55.6375140729037[/C][C]37.3070779942334[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]2071.3[/C][C]54.6353122709002[/C][C]37.91137844568[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]2066.91666666667[/C][C]53.6881082998204[/C][C]38.4985936759776[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]2061.45652173913[/C][C]52.6761934744549[/C][C]39.1345005355944[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]2056.68181818182[/C][C]51.7531011697292[/C][C]39.7402623552304[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]2051.73809523810[/C][C]50.643926289956[/C][C]40.5130140086514[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]2046.75[/C][C]49.4708247353933[/C][C]41.3728699884738[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]2042.42105263158[/C][C]48.3996613024803[/C][C]42.1990773833559[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]2038.08333333333[/C][C]47.3159152223999[/C][C]43.0739492991669[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]2032.82352941176[/C][C]46.0013072469493[/C][C]44.1905600312386[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]2028.21875[/C][C]44.6952885582411[/C][C]45.3788042414603[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]2025.1[/C][C]43.8699318387917[/C][C]46.1614576343909[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]2020.60714285714[/C][C]42.8197075259478[/C][C]47.1887189241706[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]2015.46153846154[/C][C]41.2571012356281[/C][C]48.8512638576038[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]2011.625[/C][C]40.1220877989646[/C][C]50.137595283661[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]2006.86363636364[/C][C]38.5527297001872[/C][C]52.0550335078839[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]2000[/C][C]36.5040733127284[/C][C]54.7884062928021[/C][/ROW]
[ROW][C]Median[/C][C]1967[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]2250[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]2014.16129032258[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]2025.1[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]2014.16129032258[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]2025.1[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]2025.1[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]2014.16129032258[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]2025.1[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]2028.21875[/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=50354&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=50354&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 Mean2091.9561.56453334133833.9797913906275
Geometric Mean2040.13549897273
Harmonic Mean1990.68691011102
Quadratic Mean2144.73217830727
Winsorized Mean ( 1 / 20 )2090.5833333333360.751858410888534.4118416788817
Winsorized Mean ( 2 / 20 )2088.5833333333360.224688950078534.6798525612080
Winsorized Mean ( 3 / 20 )2085.9833333333359.070146425091435.313664508664
Winsorized Mean ( 4 / 20 )2090.2557.678789220897336.2394916438830
Winsorized Mean ( 5 / 20 )2088.8333333333356.606183241476436.9011513180914
Winsorized Mean ( 6 / 20 )2092.0333333333355.76940500704637.5122046410397
Winsorized Mean ( 7 / 20 )2085.9666666666754.292579253140738.4208430574054
Winsorized Mean ( 8 / 20 )2084.3666666666753.732256126085438.7917205965742
Winsorized Mean ( 9 / 20 )2081.6666666666752.460131036809739.6809276973789
Winsorized Mean ( 10 / 20 )2074.1666666666750.445994878153641.1165776723518
Winsorized Mean ( 11 / 20 )2071.0548.818761010022342.4232396962066
Winsorized Mean ( 12 / 20 )2073.8547.810801943555343.3761810238689
Winsorized Mean ( 13 / 20 )2064.7545.745862861318445.1352290863859
Winsorized Mean ( 14 / 20 )2050.0542.022851094663948.7841721015526
Winsorized Mean ( 15 / 20 )2056.5540.928499215370750.2473835939644
Winsorized Mean ( 16 / 20 )2056.2833333333340.389236775028450.9116660160481
Winsorized Mean ( 17 / 20 )2041.5536.677325813280955.6624550653787
Winsorized Mean ( 18 / 20 )2043.0535.474924899288657.5913833729065
Winsorized Mean ( 19 / 20 )2050.3333333333333.535803168583361.1386381004917
Winsorized Mean ( 20 / 20 )2049.3333333333332.494333853458863.0674056152469
Trimmed Mean ( 1 / 20 )2086.559.632821092768734.9891211209697
Trimmed Mean ( 2 / 20 )2082.12558.235120514717235.7537682003046
Trimmed Mean ( 3 / 20 )2078.5370370370456.838995045354836.5688562118043
Trimmed Mean ( 4 / 20 )2075.6730769230855.637514072903737.3070779942334
Trimmed Mean ( 5 / 20 )2071.354.635312270900237.91137844568
Trimmed Mean ( 6 / 20 )2066.9166666666753.688108299820438.4985936759776
Trimmed Mean ( 7 / 20 )2061.4565217391352.676193474454939.1345005355944
Trimmed Mean ( 8 / 20 )2056.6818181818251.753101169729239.7402623552304
Trimmed Mean ( 9 / 20 )2051.7380952381050.64392628995640.5130140086514
Trimmed Mean ( 10 / 20 )2046.7549.470824735393341.3728699884738
Trimmed Mean ( 11 / 20 )2042.4210526315848.399661302480342.1990773833559
Trimmed Mean ( 12 / 20 )2038.0833333333347.315915222399943.0739492991669
Trimmed Mean ( 13 / 20 )2032.8235294117646.001307246949344.1905600312386
Trimmed Mean ( 14 / 20 )2028.2187544.695288558241145.3788042414603
Trimmed Mean ( 15 / 20 )2025.143.869931838791746.1614576343909
Trimmed Mean ( 16 / 20 )2020.6071428571442.819707525947847.1887189241706
Trimmed Mean ( 17 / 20 )2015.4615384615441.257101235628148.8512638576038
Trimmed Mean ( 18 / 20 )2011.62540.122087798964650.137595283661
Trimmed Mean ( 19 / 20 )2006.8636363636438.552729700187252.0550335078839
Trimmed Mean ( 20 / 20 )200036.504073312728454.7884062928021
Median1967
Midrange2250
Midmean - Weighted Average at Xnp2014.16129032258
Midmean - Weighted Average at X(n+1)p2025.1
Midmean - Empirical Distribution Function2014.16129032258
Midmean - Empirical Distribution Function - Averaging2025.1
Midmean - Empirical Distribution Function - Interpolation2025.1
Midmean - Closest Observation2014.16129032258
Midmean - True Basic - Statistics Graphics Toolkit2025.1
Midmean - MS Excel (old versions)2028.21875
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')