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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 10:39:49 +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/t1290681497i1b6g619qw6t9ne.htm/, Retrieved Fri, 29 Mar 2024 08:02:26 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=100733, Retrieved Fri, 29 Mar 2024 08:02:26 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact116
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]
F    D  [Central Tendency] [Measures of Centr...] [2010-10-04 17:31:06] [62f7c80c4d96454bbd2b2b026ea9aad9]
-    D    [Central Tendency] [Central tendency:...] [2010-11-25 10:36:37] [62f7c80c4d96454bbd2b2b026ea9aad9]
-    D        [Central Tendency] [Central tendency:...] [2010-11-25 10:39:49] [8eb352cba3cf694c3df89d0a436a2f1b] [Current]
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Dataseries X:
16896.2
16698,00
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
13881,00
15465.9
14238.2
13557.7
16127.6
16793.9
16014,00
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'RServer@AstonUniversity' @ vre.aston.ac.uk

\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 & 'RServer@AstonUniversity' @ vre.aston.ac.uk \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=100733&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]'RServer@AstonUniversity' @ vre.aston.ac.uk[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=100733&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=100733&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'RServer@AstonUniversity' @ vre.aston.ac.uk







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 )17430.5745454545163.0990894247106.871072100632
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 )17466.9566037736253.76384135799468.831542391149
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 )17450.776744186207.95145620488583.9175500987722
Trimmed Mean ( 7 / 18 )17450.776744186199.77686105271687.3513411524733
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 & 163.0990894247 & 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 & 68.831542391149 \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 ) & 17450.776744186 & 207.951456204885 & 83.9175500987722 \tabularnewline
Trimmed Mean ( 7 / 18 ) & 17450.776744186 & 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=100733&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]163.0990894247[/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]68.831542391149[/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]17450.776744186[/C][C]207.951456204885[/C][C]83.9175500987722[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 18 )[/C][C]17450.776744186[/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=100733&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=100733&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 )17430.5745454545163.0990894247106.871072100632
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 )17466.9566037736253.76384135799468.831542391149
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 )17450.776744186207.95145620488583.9175500987722
Trimmed Mean ( 7 / 18 )17450.776744186199.77686105271687.3513411524733
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')