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Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationThu, 25 Nov 2010 10:41:20 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2010/Nov/25/t12906816230x8opea2wyaxmki.htm/, Retrieved Fri, 29 Mar 2024 06:08:01 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=100738, Retrieved Fri, 29 Mar 2024 06:08:01 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact114
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
F     [Central Tendency] [Time needed to su...] [2010-09-25 09:42:08] [b98453cac15ba1066b407e146608df68]
-    D    [Central Tendency] [Measures of centr...] [2010-11-25 10:41:20] [85c2b01fe80f9fc86b9396d4d142e465] [Current]
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Dataseries X:
16896,2
16698
19691,6
15930,7
17444,6
17699,4
15189,8
15672,7
17180,8
17664,9
17862,9
16162,3
17463,6
16772,1
19106,9
16721,3
18161,3
18509,9
17802,7
16409,9
17967,7
20286,6
19537,3
18021,9
20194,3
19049,6
20244,7
21473,3
19673,6
21053,2
20159,5
18203,6
21289,5
20432,3
17180,4
15816,8
15071,8
14521,1
15668,8
14346,9
13881
15465,9
14238,2
13557,7
16127,6
16793,9
16014
16867,9
16014,6
15878,6
18664,9
17962,5
17332,7
19542,1
17203,6




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24

\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 & 2 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=100738&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]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=100738&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=100738&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 time2 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean17468.7218181818265.1525953474165.8817681769014
Geometric Mean17360.0033640646
Harmonic Mean17251.3161550907
Quadratic Mean17577.0520991796
Winsorized Mean ( 1 / 18 )17471.2581818182262.68845814968166.509424528515
Winsorized Mean ( 2 / 18 )17475.6545454545257.26648678824267.9282201254564
Winsorized Mean ( 3 / 18 )17447.7163636364247.73884255983470.4278593673592
Winsorized Mean ( 4 / 18 )17449.7890909091242.52341910135471.9509445956499
Winsorized Mean ( 5 / 18 )17496.0436363636231.21611045898675.6696564163817
Winsorized Mean ( 6 / 18 )17503.4181818182227.54695375290976.9222259104598
Winsorized Mean ( 7 / 18 )17534.1290909091220.20474449811479.6264818493013
Winsorized Mean ( 8 / 18 )17495.5836363636200.71075987530387.1681400998794
Winsorized Mean ( 9 / 18 )17493.2763636364200.00748613874387.4631080133743
Winsorized Mean ( 10 / 18 )17495.5672727273190.87607999124891.6592968250893
Winsorized Mean ( 11 / 18 )17506.9672727273188.69084226116992.7812238417788
Winsorized Mean ( 12 / 18 )17424.4290909091168.791258304306103.230636858547
Winsorized Mean ( 13 / 18 )17430.5745454545163.099089424700106.871072100632
Winsorized Mean ( 14 / 18 )17332.8036363636145.746396019308118.924406433126
Winsorized Mean ( 15 / 18 )17321.3490909091133.548451109535129.700860975934
Winsorized Mean ( 16 / 18 )17242.3381818182117.740086130823146.444076511545
Winsorized Mean ( 17 / 18 )17305.7945454545103.065420739989167.910773770702
Winsorized Mean ( 18 / 18 )17354.4681.3960544134302213.210088929526
Trimmed Mean ( 1 / 18 )17466.9566037736253.76384135799468.8315423911491
Trimmed Mean ( 2 / 18 )17462.3176470588242.53853219167771.998117120864
Trimmed Mean ( 3 / 18 )17454.8326530612232.10757979918775.201476264423
Trimmed Mean ( 4 / 18 )17457.6085106383223.69630605684278.0415591941079
Trimmed Mean ( 5 / 18 )17459.9977777778215.04055146091681.1939778760804
Trimmed Mean ( 6 / 18 )17450.7767441860207.95145620488583.9175500987722
Trimmed Mean ( 7 / 18 )17450.7767441860199.77686105271687.3513411524733
Trimmed Mean ( 8 / 18 )17419.8435897436191.14179772968891.1357107479896
Trimmed Mean ( 9 / 18 )17405.7702702703185.65440603835593.7536072624872
Trimmed Mean ( 10 / 18 )17390.4914285714178.12287598009197.6319932680357
Trimmed Mean ( 11 / 18 )17372.9787878788170.338311249993101.991023982748
Trimmed Mean ( 12 / 18 )17351.3677419355159.663812490737108.674391969327
Trimmed Mean ( 13 / 18 )17339.8206896552151.364884991062114.556428927879
Trimmed Mean ( 14 / 18 )17339.8206896552140.802506209889123.149943537279
Trimmed Mean ( 15 / 18 )17325.6131.687225363738131.566292418602
Trimmed Mean ( 16 / 18 )17324.9652173913122.290132174355141.670999199594
Trimmed Mean ( 17 / 18 )17338.4904761905113.803678052697152.354394628281
Trimmed Mean ( 18 / 18 )17344.0578947368106.782443832612162.424245711446
Median17332.7
Midrange17515.5
Midmean - Weighted Average at Xnp17278.7571428571
Midmean - Weighted Average at X(n+1)p17339.8206896552
Midmean - Empirical Distribution Function17339.8206896552
Midmean - Empirical Distribution Function - Averaging17339.8206896552
Midmean - Empirical Distribution Function - Interpolation17325.6
Midmean - Closest Observation17278.7571428571
Midmean - True Basic - Statistics Graphics Toolkit17339.8206896552
Midmean - MS Excel (old versions)17339.8206896552
Number of observations55

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 17468.7218181818 & 265.15259534741 & 65.8817681769014 \tabularnewline
Geometric Mean & 17360.0033640646 &  &  \tabularnewline
Harmonic Mean & 17251.3161550907 &  &  \tabularnewline
Quadratic Mean & 17577.0520991796 &  &  \tabularnewline
Winsorized Mean ( 1 / 18 ) & 17471.2581818182 & 262.688458149681 & 66.509424528515 \tabularnewline
Winsorized Mean ( 2 / 18 ) & 17475.6545454545 & 257.266486788242 & 67.9282201254564 \tabularnewline
Winsorized Mean ( 3 / 18 ) & 17447.7163636364 & 247.738842559834 & 70.4278593673592 \tabularnewline
Winsorized Mean ( 4 / 18 ) & 17449.7890909091 & 242.523419101354 & 71.9509445956499 \tabularnewline
Winsorized Mean ( 5 / 18 ) & 17496.0436363636 & 231.216110458986 & 75.6696564163817 \tabularnewline
Winsorized Mean ( 6 / 18 ) & 17503.4181818182 & 227.546953752909 & 76.9222259104598 \tabularnewline
Winsorized Mean ( 7 / 18 ) & 17534.1290909091 & 220.204744498114 & 79.6264818493013 \tabularnewline
Winsorized Mean ( 8 / 18 ) & 17495.5836363636 & 200.710759875303 & 87.1681400998794 \tabularnewline
Winsorized Mean ( 9 / 18 ) & 17493.2763636364 & 200.007486138743 & 87.4631080133743 \tabularnewline
Winsorized Mean ( 10 / 18 ) & 17495.5672727273 & 190.876079991248 & 91.6592968250893 \tabularnewline
Winsorized Mean ( 11 / 18 ) & 17506.9672727273 & 188.690842261169 & 92.7812238417788 \tabularnewline
Winsorized Mean ( 12 / 18 ) & 17424.4290909091 & 168.791258304306 & 103.230636858547 \tabularnewline
Winsorized Mean ( 13 / 18 ) & 17430.5745454545 & 163.099089424700 & 106.871072100632 \tabularnewline
Winsorized Mean ( 14 / 18 ) & 17332.8036363636 & 145.746396019308 & 118.924406433126 \tabularnewline
Winsorized Mean ( 15 / 18 ) & 17321.3490909091 & 133.548451109535 & 129.700860975934 \tabularnewline
Winsorized Mean ( 16 / 18 ) & 17242.3381818182 & 117.740086130823 & 146.444076511545 \tabularnewline
Winsorized Mean ( 17 / 18 ) & 17305.7945454545 & 103.065420739989 & 167.910773770702 \tabularnewline
Winsorized Mean ( 18 / 18 ) & 17354.46 & 81.3960544134302 & 213.210088929526 \tabularnewline
Trimmed Mean ( 1 / 18 ) & 17466.9566037736 & 253.763841357994 & 68.8315423911491 \tabularnewline
Trimmed Mean ( 2 / 18 ) & 17462.3176470588 & 242.538532191677 & 71.998117120864 \tabularnewline
Trimmed Mean ( 3 / 18 ) & 17454.8326530612 & 232.107579799187 & 75.201476264423 \tabularnewline
Trimmed Mean ( 4 / 18 ) & 17457.6085106383 & 223.696306056842 & 78.0415591941079 \tabularnewline
Trimmed Mean ( 5 / 18 ) & 17459.9977777778 & 215.040551460916 & 81.1939778760804 \tabularnewline
Trimmed Mean ( 6 / 18 ) & 17450.7767441860 & 207.951456204885 & 83.9175500987722 \tabularnewline
Trimmed Mean ( 7 / 18 ) & 17450.7767441860 & 199.776861052716 & 87.3513411524733 \tabularnewline
Trimmed Mean ( 8 / 18 ) & 17419.8435897436 & 191.141797729688 & 91.1357107479896 \tabularnewline
Trimmed Mean ( 9 / 18 ) & 17405.7702702703 & 185.654406038355 & 93.7536072624872 \tabularnewline
Trimmed Mean ( 10 / 18 ) & 17390.4914285714 & 178.122875980091 & 97.6319932680357 \tabularnewline
Trimmed Mean ( 11 / 18 ) & 17372.9787878788 & 170.338311249993 & 101.991023982748 \tabularnewline
Trimmed Mean ( 12 / 18 ) & 17351.3677419355 & 159.663812490737 & 108.674391969327 \tabularnewline
Trimmed Mean ( 13 / 18 ) & 17339.8206896552 & 151.364884991062 & 114.556428927879 \tabularnewline
Trimmed Mean ( 14 / 18 ) & 17339.8206896552 & 140.802506209889 & 123.149943537279 \tabularnewline
Trimmed Mean ( 15 / 18 ) & 17325.6 & 131.687225363738 & 131.566292418602 \tabularnewline
Trimmed Mean ( 16 / 18 ) & 17324.9652173913 & 122.290132174355 & 141.670999199594 \tabularnewline
Trimmed Mean ( 17 / 18 ) & 17338.4904761905 & 113.803678052697 & 152.354394628281 \tabularnewline
Trimmed Mean ( 18 / 18 ) & 17344.0578947368 & 106.782443832612 & 162.424245711446 \tabularnewline
Median & 17332.7 &  &  \tabularnewline
Midrange & 17515.5 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 17278.7571428571 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 17339.8206896552 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 17339.8206896552 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 17339.8206896552 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 17325.6 &  &  \tabularnewline
Midmean - Closest Observation & 17278.7571428571 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 17339.8206896552 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 17339.8206896552 &  &  \tabularnewline
Number of observations & 55 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=100738&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]17468.7218181818[/C][C]265.15259534741[/C][C]65.8817681769014[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]17360.0033640646[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]17251.3161550907[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]17577.0520991796[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 18 )[/C][C]17471.2581818182[/C][C]262.688458149681[/C][C]66.509424528515[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 18 )[/C][C]17475.6545454545[/C][C]257.266486788242[/C][C]67.9282201254564[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 18 )[/C][C]17447.7163636364[/C][C]247.738842559834[/C][C]70.4278593673592[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 18 )[/C][C]17449.7890909091[/C][C]242.523419101354[/C][C]71.9509445956499[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 18 )[/C][C]17496.0436363636[/C][C]231.216110458986[/C][C]75.6696564163817[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 18 )[/C][C]17503.4181818182[/C][C]227.546953752909[/C][C]76.9222259104598[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 18 )[/C][C]17534.1290909091[/C][C]220.204744498114[/C][C]79.6264818493013[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 18 )[/C][C]17495.5836363636[/C][C]200.710759875303[/C][C]87.1681400998794[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 18 )[/C][C]17493.2763636364[/C][C]200.007486138743[/C][C]87.4631080133743[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 18 )[/C][C]17495.5672727273[/C][C]190.876079991248[/C][C]91.6592968250893[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 18 )[/C][C]17506.9672727273[/C][C]188.690842261169[/C][C]92.7812238417788[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 18 )[/C][C]17424.4290909091[/C][C]168.791258304306[/C][C]103.230636858547[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 18 )[/C][C]17430.5745454545[/C][C]163.099089424700[/C][C]106.871072100632[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 18 )[/C][C]17332.8036363636[/C][C]145.746396019308[/C][C]118.924406433126[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 18 )[/C][C]17321.3490909091[/C][C]133.548451109535[/C][C]129.700860975934[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 18 )[/C][C]17242.3381818182[/C][C]117.740086130823[/C][C]146.444076511545[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 18 )[/C][C]17305.7945454545[/C][C]103.065420739989[/C][C]167.910773770702[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 18 )[/C][C]17354.46[/C][C]81.3960544134302[/C][C]213.210088929526[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 18 )[/C][C]17466.9566037736[/C][C]253.763841357994[/C][C]68.8315423911491[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 18 )[/C][C]17462.3176470588[/C][C]242.538532191677[/C][C]71.998117120864[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 18 )[/C][C]17454.8326530612[/C][C]232.107579799187[/C][C]75.201476264423[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 18 )[/C][C]17457.6085106383[/C][C]223.696306056842[/C][C]78.0415591941079[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 18 )[/C][C]17459.9977777778[/C][C]215.040551460916[/C][C]81.1939778760804[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 18 )[/C][C]17450.7767441860[/C][C]207.951456204885[/C][C]83.9175500987722[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 18 )[/C][C]17450.7767441860[/C][C]199.776861052716[/C][C]87.3513411524733[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 18 )[/C][C]17419.8435897436[/C][C]191.141797729688[/C][C]91.1357107479896[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 18 )[/C][C]17405.7702702703[/C][C]185.654406038355[/C][C]93.7536072624872[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 18 )[/C][C]17390.4914285714[/C][C]178.122875980091[/C][C]97.6319932680357[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 18 )[/C][C]17372.9787878788[/C][C]170.338311249993[/C][C]101.991023982748[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 18 )[/C][C]17351.3677419355[/C][C]159.663812490737[/C][C]108.674391969327[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 18 )[/C][C]17339.8206896552[/C][C]151.364884991062[/C][C]114.556428927879[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 18 )[/C][C]17339.8206896552[/C][C]140.802506209889[/C][C]123.149943537279[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 18 )[/C][C]17325.6[/C][C]131.687225363738[/C][C]131.566292418602[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 18 )[/C][C]17324.9652173913[/C][C]122.290132174355[/C][C]141.670999199594[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 18 )[/C][C]17338.4904761905[/C][C]113.803678052697[/C][C]152.354394628281[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 18 )[/C][C]17344.0578947368[/C][C]106.782443832612[/C][C]162.424245711446[/C][/ROW]
[ROW][C]Median[/C][C]17332.7[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]17515.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]17278.7571428571[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]17339.8206896552[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]17339.8206896552[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]17339.8206896552[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]17325.6[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]17278.7571428571[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]17339.8206896552[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]17339.8206896552[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]55[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=100738&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=100738&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 Mean17468.7218181818265.1525953474165.8817681769014
Geometric Mean17360.0033640646
Harmonic Mean17251.3161550907
Quadratic Mean17577.0520991796
Winsorized Mean ( 1 / 18 )17471.2581818182262.68845814968166.509424528515
Winsorized Mean ( 2 / 18 )17475.6545454545257.26648678824267.9282201254564
Winsorized Mean ( 3 / 18 )17447.7163636364247.73884255983470.4278593673592
Winsorized Mean ( 4 / 18 )17449.7890909091242.52341910135471.9509445956499
Winsorized Mean ( 5 / 18 )17496.0436363636231.21611045898675.6696564163817
Winsorized Mean ( 6 / 18 )17503.4181818182227.54695375290976.9222259104598
Winsorized Mean ( 7 / 18 )17534.1290909091220.20474449811479.6264818493013
Winsorized Mean ( 8 / 18 )17495.5836363636200.71075987530387.1681400998794
Winsorized Mean ( 9 / 18 )17493.2763636364200.00748613874387.4631080133743
Winsorized Mean ( 10 / 18 )17495.5672727273190.87607999124891.6592968250893
Winsorized Mean ( 11 / 18 )17506.9672727273188.69084226116992.7812238417788
Winsorized Mean ( 12 / 18 )17424.4290909091168.791258304306103.230636858547
Winsorized Mean ( 13 / 18 )17430.5745454545163.099089424700106.871072100632
Winsorized Mean ( 14 / 18 )17332.8036363636145.746396019308118.924406433126
Winsorized Mean ( 15 / 18 )17321.3490909091133.548451109535129.700860975934
Winsorized Mean ( 16 / 18 )17242.3381818182117.740086130823146.444076511545
Winsorized Mean ( 17 / 18 )17305.7945454545103.065420739989167.910773770702
Winsorized Mean ( 18 / 18 )17354.4681.3960544134302213.210088929526
Trimmed Mean ( 1 / 18 )17466.9566037736253.76384135799468.8315423911491
Trimmed Mean ( 2 / 18 )17462.3176470588242.53853219167771.998117120864
Trimmed Mean ( 3 / 18 )17454.8326530612232.10757979918775.201476264423
Trimmed Mean ( 4 / 18 )17457.6085106383223.69630605684278.0415591941079
Trimmed Mean ( 5 / 18 )17459.9977777778215.04055146091681.1939778760804
Trimmed Mean ( 6 / 18 )17450.7767441860207.95145620488583.9175500987722
Trimmed Mean ( 7 / 18 )17450.7767441860199.77686105271687.3513411524733
Trimmed Mean ( 8 / 18 )17419.8435897436191.14179772968891.1357107479896
Trimmed Mean ( 9 / 18 )17405.7702702703185.65440603835593.7536072624872
Trimmed Mean ( 10 / 18 )17390.4914285714178.12287598009197.6319932680357
Trimmed Mean ( 11 / 18 )17372.9787878788170.338311249993101.991023982748
Trimmed Mean ( 12 / 18 )17351.3677419355159.663812490737108.674391969327
Trimmed Mean ( 13 / 18 )17339.8206896552151.364884991062114.556428927879
Trimmed Mean ( 14 / 18 )17339.8206896552140.802506209889123.149943537279
Trimmed Mean ( 15 / 18 )17325.6131.687225363738131.566292418602
Trimmed Mean ( 16 / 18 )17324.9652173913122.290132174355141.670999199594
Trimmed Mean ( 17 / 18 )17338.4904761905113.803678052697152.354394628281
Trimmed Mean ( 18 / 18 )17344.0578947368106.782443832612162.424245711446
Median17332.7
Midrange17515.5
Midmean - Weighted Average at Xnp17278.7571428571
Midmean - Weighted Average at X(n+1)p17339.8206896552
Midmean - Empirical Distribution Function17339.8206896552
Midmean - Empirical Distribution Function - Averaging17339.8206896552
Midmean - Empirical Distribution Function - Interpolation17325.6
Midmean - Closest Observation17278.7571428571
Midmean - True Basic - Statistics Graphics Toolkit17339.8206896552
Midmean - MS Excel (old versions)17339.8206896552
Number of observations55



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')