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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 computationSat, 17 Dec 2011 04:45:34 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2011/Dec/17/t1324115744ut5l0nkvp0o16ev.htm/, Retrieved Fri, 29 Mar 2024 13:16:16 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=156162, Retrieved Fri, 29 Mar 2024 13:16:16 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact137
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Bivariate Kernel Density Estimation] [] [2011-12-17 08:18:41] [f1de53e71fac758e9834be8effee591f]
- RMPD    [Central Tendency] [] [2011-12-17 09:45:34] [13d85cac30d4a10947636c080219d4f4] [Current]
- RMP       [Notched Boxplots] [] [2011-12-17 10:27:26] [f1de53e71fac758e9834be8effee591f]
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Dataseries X:
9.829
9.125
9.782
9.441
9.162
9.915
10.444
10.209
9.985
9.842
9.429
10.132
9.849
9.172
10.313
9.819
9.955
10.048
10.082
10.541
10.208
10.233
9.439
9.963
10.158
9.225
10.474
9.757
10.490
10.281
10.444
10.640
10.695
10.786
9.832
9.747
10.411
9.511
10.402
9.701
10.540
10.112
10.915
11.183
10.384
10.834
9.886
10.216
10.943
9.867
10.203
10.837
10.573
10.647
11.502
10.656
10.866
10.835
9.945
10.331




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=156162&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=156162&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=156162&T=0

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean10.17910.0669728619463745151.988427912047
Geometric Mean10.1660645065263
Harmonic Mean10.1529891768704
Quadratic Mean10.1920907227124
Winsorized Mean ( 1 / 20 )10.17440.065220140904946156.00088958453
Winsorized Mean ( 2 / 20 )10.16673333333330.0632480135981001160.743915183428
Winsorized Mean ( 3 / 20 )10.16798333333330.0622666241349859163.29748841515
Winsorized Mean ( 4 / 20 )10.17831666666670.0583747173218898174.361729420314
Winsorized Mean ( 5 / 20 )10.17673333333330.0577182072668076176.317557582661
Winsorized Mean ( 6 / 20 )10.17673333333330.0576361609002066176.568549576952
Winsorized Mean ( 7 / 20 )10.18478333333330.0558948927437912182.213129561191
Winsorized Mean ( 8 / 20 )10.20371666666670.0498546763338611204.66919889993
Winsorized Mean ( 9 / 20 )10.19696666666670.0460883453205683221.248269942032
Winsorized Mean ( 10 / 20 )10.19213333333330.0446448285429666228.293705362186
Winsorized Mean ( 11 / 20 )10.19506666666670.0436080051912585233.788879403049
Winsorized Mean ( 12 / 20 )10.20106666666670.0421994113720874241.734809443672
Winsorized Mean ( 13 / 20 )10.18871666666670.0393827523382074258.710122115615
Winsorized Mean ( 14 / 20 )10.181950.0380592938010254267.528610836328
Winsorized Mean ( 15 / 20 )10.18420.0376318007724654270.627495653932
Winsorized Mean ( 16 / 20 )10.17273333333330.03525589157534288.539953998745
Winsorized Mean ( 17 / 20 )10.17330.0337792125091766301.170431289252
Winsorized Mean ( 18 / 20 )10.170.0315648556624984322.193774897656
Winsorized Mean ( 19 / 20 )10.17918333333330.030183033843785337.248514712491
Winsorized Mean ( 20 / 20 )10.17818333333330.027091271674501375.699725565608
Trimmed Mean ( 1 / 20 )10.17446551724140.0627455911183377162.154269900054
Trimmed Mean ( 2 / 20 )10.17453571428570.0596894667788327170.457808778648
Trimmed Mean ( 3 / 20 )10.17887037037040.0572393496561065177.82994446172
Trimmed Mean ( 4 / 20 )10.18305769230770.0546627767818873186.288701229717
Trimmed Mean ( 5 / 20 )10.184480.0530271877898306192.061476847791
Trimmed Mean ( 6 / 20 )10.18641666666670.0511716000694165199.063868490498
Trimmed Mean ( 7 / 20 )10.18852173913040.0488065266397651208.753263970834
Trimmed Mean ( 8 / 20 )10.189250.0462962142685829220.088189951949
Trimmed Mean ( 9 / 20 )10.18666666666670.0448278377437384227.239750551866
Trimmed Mean ( 10 / 20 )10.184950.0439156526910628231.920724750442
Trimmed Mean ( 11 / 20 )10.18381578947370.0430315781905476236.659128428403
Trimmed Mean ( 12 / 20 )10.18211111111110.0420450774307196242.171301215674
Trimmed Mean ( 13 / 20 )10.17932352941180.0409951677641973248.305448777838
Trimmed Mean ( 14 / 20 )10.177968750.040259628290769252.808313988673
Trimmed Mean ( 15 / 20 )10.17740.0394848319487748257.754674331742
Trimmed Mean ( 16 / 20 )10.17642857142860.0383588054973519265.295762980187
Trimmed Mean ( 17 / 20 )10.17696153846150.0373514073782515272.465276486135
Trimmed Mean ( 18 / 20 )10.17750.0361788532196622281.310740785693
Trimmed Mean ( 19 / 20 )10.17863636363640.0350168509499724290.678233122056
Trimmed Mean ( 20 / 20 )10.178550.0335046324369757303.7953041015
Median10.2055
Midrange10.3135
Midmean - Weighted Average at Xnp10.1662580645161
Midmean - Weighted Average at X(n+1)p10.1774
Midmean - Empirical Distribution Function10.1662580645161
Midmean - Empirical Distribution Function - Averaging10.1774
Midmean - Empirical Distribution Function - Interpolation10.1774
Midmean - Closest Observation10.1662580645161
Midmean - True Basic - Statistics Graphics Toolkit10.1774
Midmean - MS Excel (old versions)10.17796875
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 10.1791 & 0.0669728619463745 & 151.988427912047 \tabularnewline
Geometric Mean & 10.1660645065263 &  &  \tabularnewline
Harmonic Mean & 10.1529891768704 &  &  \tabularnewline
Quadratic Mean & 10.1920907227124 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 10.1744 & 0.065220140904946 & 156.00088958453 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 10.1667333333333 & 0.0632480135981001 & 160.743915183428 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 10.1679833333333 & 0.0622666241349859 & 163.29748841515 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 10.1783166666667 & 0.0583747173218898 & 174.361729420314 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 10.1767333333333 & 0.0577182072668076 & 176.317557582661 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 10.1767333333333 & 0.0576361609002066 & 176.568549576952 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 10.1847833333333 & 0.0558948927437912 & 182.213129561191 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 10.2037166666667 & 0.0498546763338611 & 204.66919889993 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 10.1969666666667 & 0.0460883453205683 & 221.248269942032 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 10.1921333333333 & 0.0446448285429666 & 228.293705362186 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 10.1950666666667 & 0.0436080051912585 & 233.788879403049 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 10.2010666666667 & 0.0421994113720874 & 241.734809443672 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 10.1887166666667 & 0.0393827523382074 & 258.710122115615 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 10.18195 & 0.0380592938010254 & 267.528610836328 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 10.1842 & 0.0376318007724654 & 270.627495653932 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 10.1727333333333 & 0.03525589157534 & 288.539953998745 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 10.1733 & 0.0337792125091766 & 301.170431289252 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 10.17 & 0.0315648556624984 & 322.193774897656 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 10.1791833333333 & 0.030183033843785 & 337.248514712491 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 10.1781833333333 & 0.027091271674501 & 375.699725565608 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 10.1744655172414 & 0.0627455911183377 & 162.154269900054 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 10.1745357142857 & 0.0596894667788327 & 170.457808778648 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 10.1788703703704 & 0.0572393496561065 & 177.82994446172 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 10.1830576923077 & 0.0546627767818873 & 186.288701229717 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 10.18448 & 0.0530271877898306 & 192.061476847791 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 10.1864166666667 & 0.0511716000694165 & 199.063868490498 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 10.1885217391304 & 0.0488065266397651 & 208.753263970834 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 10.18925 & 0.0462962142685829 & 220.088189951949 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 10.1866666666667 & 0.0448278377437384 & 227.239750551866 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 10.18495 & 0.0439156526910628 & 231.920724750442 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 10.1838157894737 & 0.0430315781905476 & 236.659128428403 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 10.1821111111111 & 0.0420450774307196 & 242.171301215674 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 10.1793235294118 & 0.0409951677641973 & 248.305448777838 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 10.17796875 & 0.040259628290769 & 252.808313988673 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 10.1774 & 0.0394848319487748 & 257.754674331742 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 10.1764285714286 & 0.0383588054973519 & 265.295762980187 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 10.1769615384615 & 0.0373514073782515 & 272.465276486135 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 10.1775 & 0.0361788532196622 & 281.310740785693 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 10.1786363636364 & 0.0350168509499724 & 290.678233122056 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 10.17855 & 0.0335046324369757 & 303.7953041015 \tabularnewline
Median & 10.2055 &  &  \tabularnewline
Midrange & 10.3135 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 10.1662580645161 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 10.1774 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 10.1662580645161 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 10.1774 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 10.1774 &  &  \tabularnewline
Midmean - Closest Observation & 10.1662580645161 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 10.1774 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 10.17796875 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=156162&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]10.1791[/C][C]0.0669728619463745[/C][C]151.988427912047[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]10.1660645065263[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]10.1529891768704[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]10.1920907227124[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]10.1744[/C][C]0.065220140904946[/C][C]156.00088958453[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]10.1667333333333[/C][C]0.0632480135981001[/C][C]160.743915183428[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]10.1679833333333[/C][C]0.0622666241349859[/C][C]163.29748841515[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]10.1783166666667[/C][C]0.0583747173218898[/C][C]174.361729420314[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]10.1767333333333[/C][C]0.0577182072668076[/C][C]176.317557582661[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]10.1767333333333[/C][C]0.0576361609002066[/C][C]176.568549576952[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]10.1847833333333[/C][C]0.0558948927437912[/C][C]182.213129561191[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]10.2037166666667[/C][C]0.0498546763338611[/C][C]204.66919889993[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]10.1969666666667[/C][C]0.0460883453205683[/C][C]221.248269942032[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]10.1921333333333[/C][C]0.0446448285429666[/C][C]228.293705362186[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]10.1950666666667[/C][C]0.0436080051912585[/C][C]233.788879403049[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]10.2010666666667[/C][C]0.0421994113720874[/C][C]241.734809443672[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]10.1887166666667[/C][C]0.0393827523382074[/C][C]258.710122115615[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]10.18195[/C][C]0.0380592938010254[/C][C]267.528610836328[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]10.1842[/C][C]0.0376318007724654[/C][C]270.627495653932[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]10.1727333333333[/C][C]0.03525589157534[/C][C]288.539953998745[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]10.1733[/C][C]0.0337792125091766[/C][C]301.170431289252[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]10.17[/C][C]0.0315648556624984[/C][C]322.193774897656[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]10.1791833333333[/C][C]0.030183033843785[/C][C]337.248514712491[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]10.1781833333333[/C][C]0.027091271674501[/C][C]375.699725565608[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]10.1744655172414[/C][C]0.0627455911183377[/C][C]162.154269900054[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]10.1745357142857[/C][C]0.0596894667788327[/C][C]170.457808778648[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]10.1788703703704[/C][C]0.0572393496561065[/C][C]177.82994446172[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]10.1830576923077[/C][C]0.0546627767818873[/C][C]186.288701229717[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]10.18448[/C][C]0.0530271877898306[/C][C]192.061476847791[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]10.1864166666667[/C][C]0.0511716000694165[/C][C]199.063868490498[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]10.1885217391304[/C][C]0.0488065266397651[/C][C]208.753263970834[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]10.18925[/C][C]0.0462962142685829[/C][C]220.088189951949[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]10.1866666666667[/C][C]0.0448278377437384[/C][C]227.239750551866[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]10.18495[/C][C]0.0439156526910628[/C][C]231.920724750442[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]10.1838157894737[/C][C]0.0430315781905476[/C][C]236.659128428403[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]10.1821111111111[/C][C]0.0420450774307196[/C][C]242.171301215674[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]10.1793235294118[/C][C]0.0409951677641973[/C][C]248.305448777838[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]10.17796875[/C][C]0.040259628290769[/C][C]252.808313988673[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]10.1774[/C][C]0.0394848319487748[/C][C]257.754674331742[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]10.1764285714286[/C][C]0.0383588054973519[/C][C]265.295762980187[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]10.1769615384615[/C][C]0.0373514073782515[/C][C]272.465276486135[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]10.1775[/C][C]0.0361788532196622[/C][C]281.310740785693[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]10.1786363636364[/C][C]0.0350168509499724[/C][C]290.678233122056[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]10.17855[/C][C]0.0335046324369757[/C][C]303.7953041015[/C][/ROW]
[ROW][C]Median[/C][C]10.2055[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]10.3135[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]10.1662580645161[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]10.1774[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]10.1662580645161[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]10.1774[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]10.1774[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]10.1662580645161[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]10.1774[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]10.17796875[/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=156162&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=156162&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 Mean10.17910.0669728619463745151.988427912047
Geometric Mean10.1660645065263
Harmonic Mean10.1529891768704
Quadratic Mean10.1920907227124
Winsorized Mean ( 1 / 20 )10.17440.065220140904946156.00088958453
Winsorized Mean ( 2 / 20 )10.16673333333330.0632480135981001160.743915183428
Winsorized Mean ( 3 / 20 )10.16798333333330.0622666241349859163.29748841515
Winsorized Mean ( 4 / 20 )10.17831666666670.0583747173218898174.361729420314
Winsorized Mean ( 5 / 20 )10.17673333333330.0577182072668076176.317557582661
Winsorized Mean ( 6 / 20 )10.17673333333330.0576361609002066176.568549576952
Winsorized Mean ( 7 / 20 )10.18478333333330.0558948927437912182.213129561191
Winsorized Mean ( 8 / 20 )10.20371666666670.0498546763338611204.66919889993
Winsorized Mean ( 9 / 20 )10.19696666666670.0460883453205683221.248269942032
Winsorized Mean ( 10 / 20 )10.19213333333330.0446448285429666228.293705362186
Winsorized Mean ( 11 / 20 )10.19506666666670.0436080051912585233.788879403049
Winsorized Mean ( 12 / 20 )10.20106666666670.0421994113720874241.734809443672
Winsorized Mean ( 13 / 20 )10.18871666666670.0393827523382074258.710122115615
Winsorized Mean ( 14 / 20 )10.181950.0380592938010254267.528610836328
Winsorized Mean ( 15 / 20 )10.18420.0376318007724654270.627495653932
Winsorized Mean ( 16 / 20 )10.17273333333330.03525589157534288.539953998745
Winsorized Mean ( 17 / 20 )10.17330.0337792125091766301.170431289252
Winsorized Mean ( 18 / 20 )10.170.0315648556624984322.193774897656
Winsorized Mean ( 19 / 20 )10.17918333333330.030183033843785337.248514712491
Winsorized Mean ( 20 / 20 )10.17818333333330.027091271674501375.699725565608
Trimmed Mean ( 1 / 20 )10.17446551724140.0627455911183377162.154269900054
Trimmed Mean ( 2 / 20 )10.17453571428570.0596894667788327170.457808778648
Trimmed Mean ( 3 / 20 )10.17887037037040.0572393496561065177.82994446172
Trimmed Mean ( 4 / 20 )10.18305769230770.0546627767818873186.288701229717
Trimmed Mean ( 5 / 20 )10.184480.0530271877898306192.061476847791
Trimmed Mean ( 6 / 20 )10.18641666666670.0511716000694165199.063868490498
Trimmed Mean ( 7 / 20 )10.18852173913040.0488065266397651208.753263970834
Trimmed Mean ( 8 / 20 )10.189250.0462962142685829220.088189951949
Trimmed Mean ( 9 / 20 )10.18666666666670.0448278377437384227.239750551866
Trimmed Mean ( 10 / 20 )10.184950.0439156526910628231.920724750442
Trimmed Mean ( 11 / 20 )10.18381578947370.0430315781905476236.659128428403
Trimmed Mean ( 12 / 20 )10.18211111111110.0420450774307196242.171301215674
Trimmed Mean ( 13 / 20 )10.17932352941180.0409951677641973248.305448777838
Trimmed Mean ( 14 / 20 )10.177968750.040259628290769252.808313988673
Trimmed Mean ( 15 / 20 )10.17740.0394848319487748257.754674331742
Trimmed Mean ( 16 / 20 )10.17642857142860.0383588054973519265.295762980187
Trimmed Mean ( 17 / 20 )10.17696153846150.0373514073782515272.465276486135
Trimmed Mean ( 18 / 20 )10.17750.0361788532196622281.310740785693
Trimmed Mean ( 19 / 20 )10.17863636363640.0350168509499724290.678233122056
Trimmed Mean ( 20 / 20 )10.178550.0335046324369757303.7953041015
Median10.2055
Midrange10.3135
Midmean - Weighted Average at Xnp10.1662580645161
Midmean - Weighted Average at X(n+1)p10.1774
Midmean - Empirical Distribution Function10.1662580645161
Midmean - Empirical Distribution Function - Averaging10.1774
Midmean - Empirical Distribution Function - Interpolation10.1774
Midmean - Closest Observation10.1662580645161
Midmean - True Basic - Statistics Graphics Toolkit10.1774
Midmean - MS Excel (old versions)10.17796875
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')