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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 computationMon, 20 Oct 2008 07:47:49 -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/2008/Oct/20/t1224510549dp2290w5zj65p60.htm/, Retrieved Sun, 19 May 2024 13:05:01 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=17278, Retrieved Sun, 19 May 2024 13:05:01 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact144
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
F     [Univariate Data Series] [Werkloosheid vrouwen] [2008-10-13 15:31:40] [7d3039e6253bb5fb3b26df1537d500b4]
- RMPD    [Central Tendency] [Central tendency ...] [2008-10-20 13:47:49] [35348cd8592af0baf5f138bd59921307] [Current]
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Dataseries X:
9.0
9.1
8.7
8.2
7.9
7.9
9.1
9.4
9.5
9.1
9.0
9.3
9.9
9.8
9.4
8.3
8.0
8.5
10.4
11.1
10.9
9.9
9.2
9.2
9.5
9.6
9.5
9.1
8.9
9.0
10.1
10.3
10.2
9.6
9.2
9.3
9.4
9.4
9.2
9.0
9.0
9.0
9.8
10.0
9.9
9.3
9.0
9.0
9.1
9.1
9.1
9.2
8.8
8.3
8.4
8.1
7.8
7.9
7.9
8.0




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\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 & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=17278&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]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=17278&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=17278&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'Gwilym Jenkins' @ 72.249.127.135







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean9.146666666666670.094852447608513596.4304759368772
Geometric Mean9.11768322324644
Harmonic Mean9.08869475359295
Quadratic Mean9.17563803412784
Winsorized Mean ( 1 / 20 )9.1450.093350230512426597.964407262847
Winsorized Mean ( 2 / 20 )9.128333333333330.0886525518691877102.967519161803
Winsorized Mean ( 3 / 20 )9.123333333333330.0874745052984743104.29705549295
Winsorized Mean ( 4 / 20 )9.116666666666670.0860024525555776106.004728885786
Winsorized Mean ( 5 / 20 )9.116666666666670.0823101021686932110.759996968321
Winsorized Mean ( 6 / 20 )9.106666666666670.0803546751780848113.330887673731
Winsorized Mean ( 7 / 20 )9.106666666666670.0755345046557995120.563002407503
Winsorized Mean ( 8 / 20 )9.120.0725951547775411125.628218962369
Winsorized Mean ( 9 / 20 )9.1350.0694540859596984131.525739253133
Winsorized Mean ( 10 / 20 )9.118333333333330.0664470251878054137.227111485598
Winsorized Mean ( 11 / 20 )9.136666666666670.0627057817582507145.706925429799
Winsorized Mean ( 12 / 20 )9.116666666666670.0519216416711083175.585100417570
Winsorized Mean ( 13 / 20 )9.160.0436472764988002209.864182482309
Winsorized Mean ( 14 / 20 )9.160.0356695442104436256.801711453270
Winsorized Mean ( 15 / 20 )9.1850.0316071400072045290.598896259085
Winsorized Mean ( 16 / 20 )9.211666666666670.0278303645360092330.993388704912
Winsorized Mean ( 17 / 20 )9.183333333333330.0230654517821215398.142356806188
Winsorized Mean ( 18 / 20 )9.183333333333330.0230654517821215398.142356806188
Winsorized Mean ( 19 / 20 )9.183333333333330.0230654517821215398.142356806188
Winsorized Mean ( 20 / 20 )9.183333333333330.0230654517821215398.142356806188
Trimmed Mean ( 1 / 20 )9.136206896551720.089046106991656102.600857075176
Trimmed Mean ( 2 / 20 )9.126785714285710.083685057062239109.061115982724
Trimmed Mean ( 3 / 20 )9.125925925925930.0802766523762535113.680947769883
Trimmed Mean ( 4 / 20 )9.126923076923080.0766037868220003119.144541746099
Trimmed Mean ( 5 / 20 )9.130.0725764902621745125.798312470318
Trimmed Mean ( 6 / 20 )9.133333333333330.0688258500560204132.702078156671
Trimmed Mean ( 7 / 20 )9.13913043478260.0646415804374017141.381605662208
Trimmed Mean ( 8 / 20 )9.145454545454540.0607784721692108150.471938814011
Trimmed Mean ( 9 / 20 )9.150.0566434331000211161.536818996174
Trimmed Mean ( 10 / 20 )9.15250.0521324127730384175.562562965308
Trimmed Mean ( 11 / 20 )9.15789473684210.0468998477353739195.264914046508
Trimmed Mean ( 12 / 20 )9.161111111111110.0408787944751616224.10423860903
Trimmed Mean ( 13 / 20 )9.167647058823530.0362504135412626252.897723453232
Trimmed Mean ( 14 / 20 )9.168750.0328232989142302279.336639012387
Trimmed Mean ( 15 / 20 )9.170.0307567392857932298.146039305139
Trimmed Mean ( 16 / 20 )9.167857142857140.0291200631888212314.829575863577
Trimmed Mean ( 17 / 20 )9.161538461538460.0277776462850274329.816945882729
Trimmed Mean ( 18 / 20 )9.158333333333330.0275290799255241332.678511527078
Trimmed Mean ( 19 / 20 )9.154545454545450.0269095589054893340.19678608251
Trimmed Mean ( 20 / 20 )9.150.0256494588021289356.732673020008
Median9.1
Midrange9.45
Midmean - Weighted Average at Xnp9.16875
Midmean - Weighted Average at X(n+1)p9.18064516129032
Midmean - Empirical Distribution Function9.16875
Midmean - Empirical Distribution Function - Averaging9.18064516129032
Midmean - Empirical Distribution Function - Interpolation9.18064516129032
Midmean - Closest Observation9.16875
Midmean - True Basic - Statistics Graphics Toolkit9.18064516129032
Midmean - MS Excel (old versions)9.16875
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 9.14666666666667 & 0.0948524476085135 & 96.4304759368772 \tabularnewline
Geometric Mean & 9.11768322324644 &  &  \tabularnewline
Harmonic Mean & 9.08869475359295 &  &  \tabularnewline
Quadratic Mean & 9.17563803412784 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 9.145 & 0.0933502305124265 & 97.964407262847 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 9.12833333333333 & 0.0886525518691877 & 102.967519161803 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 9.12333333333333 & 0.0874745052984743 & 104.29705549295 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 9.11666666666667 & 0.0860024525555776 & 106.004728885786 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 9.11666666666667 & 0.0823101021686932 & 110.759996968321 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 9.10666666666667 & 0.0803546751780848 & 113.330887673731 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 9.10666666666667 & 0.0755345046557995 & 120.563002407503 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 9.12 & 0.0725951547775411 & 125.628218962369 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 9.135 & 0.0694540859596984 & 131.525739253133 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 9.11833333333333 & 0.0664470251878054 & 137.227111485598 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 9.13666666666667 & 0.0627057817582507 & 145.706925429799 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 9.11666666666667 & 0.0519216416711083 & 175.585100417570 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 9.16 & 0.0436472764988002 & 209.864182482309 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 9.16 & 0.0356695442104436 & 256.801711453270 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 9.185 & 0.0316071400072045 & 290.598896259085 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 9.21166666666667 & 0.0278303645360092 & 330.993388704912 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 9.18333333333333 & 0.0230654517821215 & 398.142356806188 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 9.18333333333333 & 0.0230654517821215 & 398.142356806188 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 9.18333333333333 & 0.0230654517821215 & 398.142356806188 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 9.18333333333333 & 0.0230654517821215 & 398.142356806188 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 9.13620689655172 & 0.089046106991656 & 102.600857075176 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 9.12678571428571 & 0.083685057062239 & 109.061115982724 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 9.12592592592593 & 0.0802766523762535 & 113.680947769883 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 9.12692307692308 & 0.0766037868220003 & 119.144541746099 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 9.13 & 0.0725764902621745 & 125.798312470318 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 9.13333333333333 & 0.0688258500560204 & 132.702078156671 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 9.1391304347826 & 0.0646415804374017 & 141.381605662208 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 9.14545454545454 & 0.0607784721692108 & 150.471938814011 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 9.15 & 0.0566434331000211 & 161.536818996174 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 9.1525 & 0.0521324127730384 & 175.562562965308 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 9.1578947368421 & 0.0468998477353739 & 195.264914046508 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 9.16111111111111 & 0.0408787944751616 & 224.10423860903 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 9.16764705882353 & 0.0362504135412626 & 252.897723453232 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 9.16875 & 0.0328232989142302 & 279.336639012387 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 9.17 & 0.0307567392857932 & 298.146039305139 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 9.16785714285714 & 0.0291200631888212 & 314.829575863577 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 9.16153846153846 & 0.0277776462850274 & 329.816945882729 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 9.15833333333333 & 0.0275290799255241 & 332.678511527078 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 9.15454545454545 & 0.0269095589054893 & 340.19678608251 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 9.15 & 0.0256494588021289 & 356.732673020008 \tabularnewline
Median & 9.1 &  &  \tabularnewline
Midrange & 9.45 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 9.16875 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 9.18064516129032 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 9.16875 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 9.18064516129032 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 9.18064516129032 &  &  \tabularnewline
Midmean - Closest Observation & 9.16875 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 9.18064516129032 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 9.16875 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=17278&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]9.14666666666667[/C][C]0.0948524476085135[/C][C]96.4304759368772[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]9.11768322324644[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]9.08869475359295[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]9.17563803412784[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]9.145[/C][C]0.0933502305124265[/C][C]97.964407262847[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]9.12833333333333[/C][C]0.0886525518691877[/C][C]102.967519161803[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]9.12333333333333[/C][C]0.0874745052984743[/C][C]104.29705549295[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]9.11666666666667[/C][C]0.0860024525555776[/C][C]106.004728885786[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]9.11666666666667[/C][C]0.0823101021686932[/C][C]110.759996968321[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]9.10666666666667[/C][C]0.0803546751780848[/C][C]113.330887673731[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]9.10666666666667[/C][C]0.0755345046557995[/C][C]120.563002407503[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]9.12[/C][C]0.0725951547775411[/C][C]125.628218962369[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]9.135[/C][C]0.0694540859596984[/C][C]131.525739253133[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]9.11833333333333[/C][C]0.0664470251878054[/C][C]137.227111485598[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]9.13666666666667[/C][C]0.0627057817582507[/C][C]145.706925429799[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]9.11666666666667[/C][C]0.0519216416711083[/C][C]175.585100417570[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]9.16[/C][C]0.0436472764988002[/C][C]209.864182482309[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]9.16[/C][C]0.0356695442104436[/C][C]256.801711453270[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]9.185[/C][C]0.0316071400072045[/C][C]290.598896259085[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]9.21166666666667[/C][C]0.0278303645360092[/C][C]330.993388704912[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]9.18333333333333[/C][C]0.0230654517821215[/C][C]398.142356806188[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]9.18333333333333[/C][C]0.0230654517821215[/C][C]398.142356806188[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]9.18333333333333[/C][C]0.0230654517821215[/C][C]398.142356806188[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]9.18333333333333[/C][C]0.0230654517821215[/C][C]398.142356806188[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]9.13620689655172[/C][C]0.089046106991656[/C][C]102.600857075176[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]9.12678571428571[/C][C]0.083685057062239[/C][C]109.061115982724[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]9.12592592592593[/C][C]0.0802766523762535[/C][C]113.680947769883[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]9.12692307692308[/C][C]0.0766037868220003[/C][C]119.144541746099[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]9.13[/C][C]0.0725764902621745[/C][C]125.798312470318[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]9.13333333333333[/C][C]0.0688258500560204[/C][C]132.702078156671[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]9.1391304347826[/C][C]0.0646415804374017[/C][C]141.381605662208[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]9.14545454545454[/C][C]0.0607784721692108[/C][C]150.471938814011[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]9.15[/C][C]0.0566434331000211[/C][C]161.536818996174[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]9.1525[/C][C]0.0521324127730384[/C][C]175.562562965308[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]9.1578947368421[/C][C]0.0468998477353739[/C][C]195.264914046508[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]9.16111111111111[/C][C]0.0408787944751616[/C][C]224.10423860903[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]9.16764705882353[/C][C]0.0362504135412626[/C][C]252.897723453232[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]9.16875[/C][C]0.0328232989142302[/C][C]279.336639012387[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]9.17[/C][C]0.0307567392857932[/C][C]298.146039305139[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]9.16785714285714[/C][C]0.0291200631888212[/C][C]314.829575863577[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]9.16153846153846[/C][C]0.0277776462850274[/C][C]329.816945882729[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]9.15833333333333[/C][C]0.0275290799255241[/C][C]332.678511527078[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]9.15454545454545[/C][C]0.0269095589054893[/C][C]340.19678608251[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]9.15[/C][C]0.0256494588021289[/C][C]356.732673020008[/C][/ROW]
[ROW][C]Median[/C][C]9.1[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]9.45[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]9.16875[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]9.18064516129032[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]9.16875[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]9.18064516129032[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]9.18064516129032[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]9.16875[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]9.18064516129032[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]9.16875[/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=17278&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=17278&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 Mean9.146666666666670.094852447608513596.4304759368772
Geometric Mean9.11768322324644
Harmonic Mean9.08869475359295
Quadratic Mean9.17563803412784
Winsorized Mean ( 1 / 20 )9.1450.093350230512426597.964407262847
Winsorized Mean ( 2 / 20 )9.128333333333330.0886525518691877102.967519161803
Winsorized Mean ( 3 / 20 )9.123333333333330.0874745052984743104.29705549295
Winsorized Mean ( 4 / 20 )9.116666666666670.0860024525555776106.004728885786
Winsorized Mean ( 5 / 20 )9.116666666666670.0823101021686932110.759996968321
Winsorized Mean ( 6 / 20 )9.106666666666670.0803546751780848113.330887673731
Winsorized Mean ( 7 / 20 )9.106666666666670.0755345046557995120.563002407503
Winsorized Mean ( 8 / 20 )9.120.0725951547775411125.628218962369
Winsorized Mean ( 9 / 20 )9.1350.0694540859596984131.525739253133
Winsorized Mean ( 10 / 20 )9.118333333333330.0664470251878054137.227111485598
Winsorized Mean ( 11 / 20 )9.136666666666670.0627057817582507145.706925429799
Winsorized Mean ( 12 / 20 )9.116666666666670.0519216416711083175.585100417570
Winsorized Mean ( 13 / 20 )9.160.0436472764988002209.864182482309
Winsorized Mean ( 14 / 20 )9.160.0356695442104436256.801711453270
Winsorized Mean ( 15 / 20 )9.1850.0316071400072045290.598896259085
Winsorized Mean ( 16 / 20 )9.211666666666670.0278303645360092330.993388704912
Winsorized Mean ( 17 / 20 )9.183333333333330.0230654517821215398.142356806188
Winsorized Mean ( 18 / 20 )9.183333333333330.0230654517821215398.142356806188
Winsorized Mean ( 19 / 20 )9.183333333333330.0230654517821215398.142356806188
Winsorized Mean ( 20 / 20 )9.183333333333330.0230654517821215398.142356806188
Trimmed Mean ( 1 / 20 )9.136206896551720.089046106991656102.600857075176
Trimmed Mean ( 2 / 20 )9.126785714285710.083685057062239109.061115982724
Trimmed Mean ( 3 / 20 )9.125925925925930.0802766523762535113.680947769883
Trimmed Mean ( 4 / 20 )9.126923076923080.0766037868220003119.144541746099
Trimmed Mean ( 5 / 20 )9.130.0725764902621745125.798312470318
Trimmed Mean ( 6 / 20 )9.133333333333330.0688258500560204132.702078156671
Trimmed Mean ( 7 / 20 )9.13913043478260.0646415804374017141.381605662208
Trimmed Mean ( 8 / 20 )9.145454545454540.0607784721692108150.471938814011
Trimmed Mean ( 9 / 20 )9.150.0566434331000211161.536818996174
Trimmed Mean ( 10 / 20 )9.15250.0521324127730384175.562562965308
Trimmed Mean ( 11 / 20 )9.15789473684210.0468998477353739195.264914046508
Trimmed Mean ( 12 / 20 )9.161111111111110.0408787944751616224.10423860903
Trimmed Mean ( 13 / 20 )9.167647058823530.0362504135412626252.897723453232
Trimmed Mean ( 14 / 20 )9.168750.0328232989142302279.336639012387
Trimmed Mean ( 15 / 20 )9.170.0307567392857932298.146039305139
Trimmed Mean ( 16 / 20 )9.167857142857140.0291200631888212314.829575863577
Trimmed Mean ( 17 / 20 )9.161538461538460.0277776462850274329.816945882729
Trimmed Mean ( 18 / 20 )9.158333333333330.0275290799255241332.678511527078
Trimmed Mean ( 19 / 20 )9.154545454545450.0269095589054893340.19678608251
Trimmed Mean ( 20 / 20 )9.150.0256494588021289356.732673020008
Median9.1
Midrange9.45
Midmean - Weighted Average at Xnp9.16875
Midmean - Weighted Average at X(n+1)p9.18064516129032
Midmean - Empirical Distribution Function9.16875
Midmean - Empirical Distribution Function - Averaging9.18064516129032
Midmean - Empirical Distribution Function - Interpolation9.18064516129032
Midmean - Closest Observation9.16875
Midmean - True Basic - Statistics Graphics Toolkit9.18064516129032
Midmean - MS Excel (old versions)9.16875
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')