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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 computationFri, 17 Dec 2010 12:29:04 +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/Dec/17/t1292588878oldbbsnwzl067z1.htm/, Retrieved Tue, 07 May 2024 04:34:16 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=111427, Retrieved Tue, 07 May 2024 04:34:16 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact129
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Central Tendency] [Paper CT Werklozen] [2010-12-17 12:21:08] [945bcebba5e7ac34a41d6888338a1ba9]
-    D    [Central Tendency] [Paper CT Failliss...] [2010-12-17 12:29:04] [514029464b0621595fe21c9fa38c7009] [Current]
- RM D      [Variability] [Paper V Werklozen] [2010-12-17 13:31:46] [945bcebba5e7ac34a41d6888338a1ba9]
- RM        [Variability] [Paper V Faillisse...] [2010-12-17 13:35:21] [945bcebba5e7ac34a41d6888338a1ba9]
- RMPD      [Notched Boxplots] [Paper V Notched B...] [2010-12-17 14:04:15] [945bcebba5e7ac34a41d6888338a1ba9]
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Dataseries X:
67
189
342
432
517
623
605
716
677
710
839
886
891
917
820
793
932
906
844
801
957
1159
1264
1097
1240
1411
1535
1862
1894
2239
2465
2423
2692
2856
3450
4162
4260
4225
4092
4160
3896
3628
3754
3749
3907
4449
5272
6197
6446
7157
7559
7674
6929
7156
6805
7095
7222
7593
7910




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=111427&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=111427&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=111427&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 Mean3005.89830508475325.0888101423789.2463911746709
Geometric Mean1923.93506054957
Harmonic Mean978.573046891244
Quadratic Mean3894.22947710314
Winsorized Mean ( 1 / 19 )3003.96610169492323.7550222254339.27851583906314
Winsorized Mean ( 2 / 19 )3006.40677966102322.3183608280059.32744498928899
Winsorized Mean ( 3 / 19 )3009.25423728814321.2525862812849.36725295233351
Winsorized Mean ( 4 / 19 )2992.16949152542315.0281964433969.49810056784252
Winsorized Mean ( 5 / 19 )2994.1186440678312.7622556685239.57314570349267
Winsorized Mean ( 6 / 19 )2995.84745762712312.4985524815669.58675627082735
Winsorized Mean ( 7 / 19 )2995.01694915254310.0104478655729.6610193939375
Winsorized Mean ( 8 / 19 )2976.98305084746304.3484148507529.78149681609915
Winsorized Mean ( 9 / 19 )2958.98305084746300.0227572622359.86252868898594
Winsorized Mean ( 10 / 19 )2911.18644067797285.11250814297310.2106584507268
Winsorized Mean ( 11 / 19 )2866.25423728814275.111440778110.4185206881309
Winsorized Mean ( 12 / 19 )2681.98305084746237.10622650716311.3113143014253
Winsorized Mean ( 13 / 19 )2504.83050847458204.42220058372312.253221525461
Winsorized Mean ( 14 / 19 )2461.16949152542197.04586262324512.4903383342345
Winsorized Mean ( 15 / 19 )2462.94915254237194.14612677322612.6860586583797
Winsorized Mean ( 16 / 19 )2447.22033898305191.2990322393412.7926435922648
Winsorized Mean ( 17 / 19 )2450.96610169492190.6048479069912.8588864795869
Winsorized Mean ( 18 / 19 )2433.57627118644186.94537562558413.0175794027686
Winsorized Mean ( 19 / 19 )2378.83050847458177.28105280799813.4184137040913
Trimmed Mean ( 1 / 19 )2971.42105263158320.9923649215829.25698358388522
Trimmed Mean ( 2 / 19 )2936.50909090909317.2737793968269.25544208693115
Trimmed Mean ( 3 / 19 )2897.60377358491313.2728276479499.24945771818162
Trimmed Mean ( 4 / 19 )2854.54901960784308.4249110176669.25524793113854
Trimmed Mean ( 5 / 19 )2813.12244897959304.4093863821589.24124739520342
Trimmed Mean ( 6 / 19 )2767.68085106383299.6344722068459.23685726371709
Trimmed Mean ( 7 / 19 )2717.82222222222293.1346267207549.27158368366788
Trimmed Mean ( 8 / 19 )2663.48837209302284.9935173867719.34578581476413
Trimmed Mean ( 9 / 19 )2607.09756097561275.5754440653289.46055832303249
Trimmed Mean ( 10 / 19 )2547.94871794872263.8977968158549.65505869579752
Trimmed Mean ( 11 / 19 )2490.02702702703252.3325612186849.86803690732979
Trimmed Mean ( 12 / 19 )2432.37142857143239.22129653416310.1678716059632
Trimmed Mean ( 13 / 19 )2395.18181818182233.12569138148110.2742078918381
Trimmed Mean ( 14 / 19 )2379.12903225806233.58633016204310.1852237269519
Trimmed Mean ( 15 / 19 )2367.20689655172235.00543636574510.0729878132163
Trimmed Mean ( 16 / 19 )2353.25925925926236.2882287470619.95927419549262
Trimmed Mean ( 17 / 19 )2339.4237.274826590049.85945299642758
Trimmed Mean ( 18 / 19 )2322.5652173913236.9264143037039.80289692146411
Trimmed Mean ( 19 / 19 )2305.2380952381235.4885995093319.78917068614504
Median2239
Midrange3988.5
Midmean - Weighted Average at Xnp2316.43333333333
Midmean - Weighted Average at X(n+1)p2379.12903225806
Midmean - Empirical Distribution Function2379.12903225806
Midmean - Empirical Distribution Function - Averaging2379.12903225806
Midmean - Empirical Distribution Function - Interpolation2367.20689655172
Midmean - Closest Observation2316.43333333333
Midmean - True Basic - Statistics Graphics Toolkit2379.12903225806
Midmean - MS Excel (old versions)2379.12903225806
Number of observations59

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 3005.89830508475 & 325.088810142378 & 9.2463911746709 \tabularnewline
Geometric Mean & 1923.93506054957 &  &  \tabularnewline
Harmonic Mean & 978.573046891244 &  &  \tabularnewline
Quadratic Mean & 3894.22947710314 &  &  \tabularnewline
Winsorized Mean ( 1 / 19 ) & 3003.96610169492 & 323.755022225433 & 9.27851583906314 \tabularnewline
Winsorized Mean ( 2 / 19 ) & 3006.40677966102 & 322.318360828005 & 9.32744498928899 \tabularnewline
Winsorized Mean ( 3 / 19 ) & 3009.25423728814 & 321.252586281284 & 9.36725295233351 \tabularnewline
Winsorized Mean ( 4 / 19 ) & 2992.16949152542 & 315.028196443396 & 9.49810056784252 \tabularnewline
Winsorized Mean ( 5 / 19 ) & 2994.1186440678 & 312.762255668523 & 9.57314570349267 \tabularnewline
Winsorized Mean ( 6 / 19 ) & 2995.84745762712 & 312.498552481566 & 9.58675627082735 \tabularnewline
Winsorized Mean ( 7 / 19 ) & 2995.01694915254 & 310.010447865572 & 9.6610193939375 \tabularnewline
Winsorized Mean ( 8 / 19 ) & 2976.98305084746 & 304.348414850752 & 9.78149681609915 \tabularnewline
Winsorized Mean ( 9 / 19 ) & 2958.98305084746 & 300.022757262235 & 9.86252868898594 \tabularnewline
Winsorized Mean ( 10 / 19 ) & 2911.18644067797 & 285.112508142973 & 10.2106584507268 \tabularnewline
Winsorized Mean ( 11 / 19 ) & 2866.25423728814 & 275.1114407781 & 10.4185206881309 \tabularnewline
Winsorized Mean ( 12 / 19 ) & 2681.98305084746 & 237.106226507163 & 11.3113143014253 \tabularnewline
Winsorized Mean ( 13 / 19 ) & 2504.83050847458 & 204.422200583723 & 12.253221525461 \tabularnewline
Winsorized Mean ( 14 / 19 ) & 2461.16949152542 & 197.045862623245 & 12.4903383342345 \tabularnewline
Winsorized Mean ( 15 / 19 ) & 2462.94915254237 & 194.146126773226 & 12.6860586583797 \tabularnewline
Winsorized Mean ( 16 / 19 ) & 2447.22033898305 & 191.29903223934 & 12.7926435922648 \tabularnewline
Winsorized Mean ( 17 / 19 ) & 2450.96610169492 & 190.60484790699 & 12.8588864795869 \tabularnewline
Winsorized Mean ( 18 / 19 ) & 2433.57627118644 & 186.945375625584 & 13.0175794027686 \tabularnewline
Winsorized Mean ( 19 / 19 ) & 2378.83050847458 & 177.281052807998 & 13.4184137040913 \tabularnewline
Trimmed Mean ( 1 / 19 ) & 2971.42105263158 & 320.992364921582 & 9.25698358388522 \tabularnewline
Trimmed Mean ( 2 / 19 ) & 2936.50909090909 & 317.273779396826 & 9.25544208693115 \tabularnewline
Trimmed Mean ( 3 / 19 ) & 2897.60377358491 & 313.272827647949 & 9.24945771818162 \tabularnewline
Trimmed Mean ( 4 / 19 ) & 2854.54901960784 & 308.424911017666 & 9.25524793113854 \tabularnewline
Trimmed Mean ( 5 / 19 ) & 2813.12244897959 & 304.409386382158 & 9.24124739520342 \tabularnewline
Trimmed Mean ( 6 / 19 ) & 2767.68085106383 & 299.634472206845 & 9.23685726371709 \tabularnewline
Trimmed Mean ( 7 / 19 ) & 2717.82222222222 & 293.134626720754 & 9.27158368366788 \tabularnewline
Trimmed Mean ( 8 / 19 ) & 2663.48837209302 & 284.993517386771 & 9.34578581476413 \tabularnewline
Trimmed Mean ( 9 / 19 ) & 2607.09756097561 & 275.575444065328 & 9.46055832303249 \tabularnewline
Trimmed Mean ( 10 / 19 ) & 2547.94871794872 & 263.897796815854 & 9.65505869579752 \tabularnewline
Trimmed Mean ( 11 / 19 ) & 2490.02702702703 & 252.332561218684 & 9.86803690732979 \tabularnewline
Trimmed Mean ( 12 / 19 ) & 2432.37142857143 & 239.221296534163 & 10.1678716059632 \tabularnewline
Trimmed Mean ( 13 / 19 ) & 2395.18181818182 & 233.125691381481 & 10.2742078918381 \tabularnewline
Trimmed Mean ( 14 / 19 ) & 2379.12903225806 & 233.586330162043 & 10.1852237269519 \tabularnewline
Trimmed Mean ( 15 / 19 ) & 2367.20689655172 & 235.005436365745 & 10.0729878132163 \tabularnewline
Trimmed Mean ( 16 / 19 ) & 2353.25925925926 & 236.288228747061 & 9.95927419549262 \tabularnewline
Trimmed Mean ( 17 / 19 ) & 2339.4 & 237.27482659004 & 9.85945299642758 \tabularnewline
Trimmed Mean ( 18 / 19 ) & 2322.5652173913 & 236.926414303703 & 9.80289692146411 \tabularnewline
Trimmed Mean ( 19 / 19 ) & 2305.2380952381 & 235.488599509331 & 9.78917068614504 \tabularnewline
Median & 2239 &  &  \tabularnewline
Midrange & 3988.5 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 2316.43333333333 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 2379.12903225806 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 2379.12903225806 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 2379.12903225806 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 2367.20689655172 &  &  \tabularnewline
Midmean - Closest Observation & 2316.43333333333 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 2379.12903225806 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 2379.12903225806 &  &  \tabularnewline
Number of observations & 59 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=111427&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]3005.89830508475[/C][C]325.088810142378[/C][C]9.2463911746709[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]1923.93506054957[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]978.573046891244[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]3894.22947710314[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 19 )[/C][C]3003.96610169492[/C][C]323.755022225433[/C][C]9.27851583906314[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 19 )[/C][C]3006.40677966102[/C][C]322.318360828005[/C][C]9.32744498928899[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 19 )[/C][C]3009.25423728814[/C][C]321.252586281284[/C][C]9.36725295233351[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 19 )[/C][C]2992.16949152542[/C][C]315.028196443396[/C][C]9.49810056784252[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 19 )[/C][C]2994.1186440678[/C][C]312.762255668523[/C][C]9.57314570349267[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 19 )[/C][C]2995.84745762712[/C][C]312.498552481566[/C][C]9.58675627082735[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 19 )[/C][C]2995.01694915254[/C][C]310.010447865572[/C][C]9.6610193939375[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 19 )[/C][C]2976.98305084746[/C][C]304.348414850752[/C][C]9.78149681609915[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 19 )[/C][C]2958.98305084746[/C][C]300.022757262235[/C][C]9.86252868898594[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 19 )[/C][C]2911.18644067797[/C][C]285.112508142973[/C][C]10.2106584507268[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 19 )[/C][C]2866.25423728814[/C][C]275.1114407781[/C][C]10.4185206881309[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 19 )[/C][C]2681.98305084746[/C][C]237.106226507163[/C][C]11.3113143014253[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 19 )[/C][C]2504.83050847458[/C][C]204.422200583723[/C][C]12.253221525461[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 19 )[/C][C]2461.16949152542[/C][C]197.045862623245[/C][C]12.4903383342345[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 19 )[/C][C]2462.94915254237[/C][C]194.146126773226[/C][C]12.6860586583797[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 19 )[/C][C]2447.22033898305[/C][C]191.29903223934[/C][C]12.7926435922648[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 19 )[/C][C]2450.96610169492[/C][C]190.60484790699[/C][C]12.8588864795869[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 19 )[/C][C]2433.57627118644[/C][C]186.945375625584[/C][C]13.0175794027686[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 19 )[/C][C]2378.83050847458[/C][C]177.281052807998[/C][C]13.4184137040913[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 19 )[/C][C]2971.42105263158[/C][C]320.992364921582[/C][C]9.25698358388522[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 19 )[/C][C]2936.50909090909[/C][C]317.273779396826[/C][C]9.25544208693115[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 19 )[/C][C]2897.60377358491[/C][C]313.272827647949[/C][C]9.24945771818162[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 19 )[/C][C]2854.54901960784[/C][C]308.424911017666[/C][C]9.25524793113854[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 19 )[/C][C]2813.12244897959[/C][C]304.409386382158[/C][C]9.24124739520342[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 19 )[/C][C]2767.68085106383[/C][C]299.634472206845[/C][C]9.23685726371709[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 19 )[/C][C]2717.82222222222[/C][C]293.134626720754[/C][C]9.27158368366788[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 19 )[/C][C]2663.48837209302[/C][C]284.993517386771[/C][C]9.34578581476413[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 19 )[/C][C]2607.09756097561[/C][C]275.575444065328[/C][C]9.46055832303249[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 19 )[/C][C]2547.94871794872[/C][C]263.897796815854[/C][C]9.65505869579752[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 19 )[/C][C]2490.02702702703[/C][C]252.332561218684[/C][C]9.86803690732979[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 19 )[/C][C]2432.37142857143[/C][C]239.221296534163[/C][C]10.1678716059632[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 19 )[/C][C]2395.18181818182[/C][C]233.125691381481[/C][C]10.2742078918381[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 19 )[/C][C]2379.12903225806[/C][C]233.586330162043[/C][C]10.1852237269519[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 19 )[/C][C]2367.20689655172[/C][C]235.005436365745[/C][C]10.0729878132163[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 19 )[/C][C]2353.25925925926[/C][C]236.288228747061[/C][C]9.95927419549262[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 19 )[/C][C]2339.4[/C][C]237.27482659004[/C][C]9.85945299642758[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 19 )[/C][C]2322.5652173913[/C][C]236.926414303703[/C][C]9.80289692146411[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 19 )[/C][C]2305.2380952381[/C][C]235.488599509331[/C][C]9.78917068614504[/C][/ROW]
[ROW][C]Median[/C][C]2239[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]3988.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]2316.43333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]2379.12903225806[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]2379.12903225806[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]2379.12903225806[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]2367.20689655172[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]2316.43333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]2379.12903225806[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]2379.12903225806[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]59[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=111427&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=111427&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 Mean3005.89830508475325.0888101423789.2463911746709
Geometric Mean1923.93506054957
Harmonic Mean978.573046891244
Quadratic Mean3894.22947710314
Winsorized Mean ( 1 / 19 )3003.96610169492323.7550222254339.27851583906314
Winsorized Mean ( 2 / 19 )3006.40677966102322.3183608280059.32744498928899
Winsorized Mean ( 3 / 19 )3009.25423728814321.2525862812849.36725295233351
Winsorized Mean ( 4 / 19 )2992.16949152542315.0281964433969.49810056784252
Winsorized Mean ( 5 / 19 )2994.1186440678312.7622556685239.57314570349267
Winsorized Mean ( 6 / 19 )2995.84745762712312.4985524815669.58675627082735
Winsorized Mean ( 7 / 19 )2995.01694915254310.0104478655729.6610193939375
Winsorized Mean ( 8 / 19 )2976.98305084746304.3484148507529.78149681609915
Winsorized Mean ( 9 / 19 )2958.98305084746300.0227572622359.86252868898594
Winsorized Mean ( 10 / 19 )2911.18644067797285.11250814297310.2106584507268
Winsorized Mean ( 11 / 19 )2866.25423728814275.111440778110.4185206881309
Winsorized Mean ( 12 / 19 )2681.98305084746237.10622650716311.3113143014253
Winsorized Mean ( 13 / 19 )2504.83050847458204.42220058372312.253221525461
Winsorized Mean ( 14 / 19 )2461.16949152542197.04586262324512.4903383342345
Winsorized Mean ( 15 / 19 )2462.94915254237194.14612677322612.6860586583797
Winsorized Mean ( 16 / 19 )2447.22033898305191.2990322393412.7926435922648
Winsorized Mean ( 17 / 19 )2450.96610169492190.6048479069912.8588864795869
Winsorized Mean ( 18 / 19 )2433.57627118644186.94537562558413.0175794027686
Winsorized Mean ( 19 / 19 )2378.83050847458177.28105280799813.4184137040913
Trimmed Mean ( 1 / 19 )2971.42105263158320.9923649215829.25698358388522
Trimmed Mean ( 2 / 19 )2936.50909090909317.2737793968269.25544208693115
Trimmed Mean ( 3 / 19 )2897.60377358491313.2728276479499.24945771818162
Trimmed Mean ( 4 / 19 )2854.54901960784308.4249110176669.25524793113854
Trimmed Mean ( 5 / 19 )2813.12244897959304.4093863821589.24124739520342
Trimmed Mean ( 6 / 19 )2767.68085106383299.6344722068459.23685726371709
Trimmed Mean ( 7 / 19 )2717.82222222222293.1346267207549.27158368366788
Trimmed Mean ( 8 / 19 )2663.48837209302284.9935173867719.34578581476413
Trimmed Mean ( 9 / 19 )2607.09756097561275.5754440653289.46055832303249
Trimmed Mean ( 10 / 19 )2547.94871794872263.8977968158549.65505869579752
Trimmed Mean ( 11 / 19 )2490.02702702703252.3325612186849.86803690732979
Trimmed Mean ( 12 / 19 )2432.37142857143239.22129653416310.1678716059632
Trimmed Mean ( 13 / 19 )2395.18181818182233.12569138148110.2742078918381
Trimmed Mean ( 14 / 19 )2379.12903225806233.58633016204310.1852237269519
Trimmed Mean ( 15 / 19 )2367.20689655172235.00543636574510.0729878132163
Trimmed Mean ( 16 / 19 )2353.25925925926236.2882287470619.95927419549262
Trimmed Mean ( 17 / 19 )2339.4237.274826590049.85945299642758
Trimmed Mean ( 18 / 19 )2322.5652173913236.9264143037039.80289692146411
Trimmed Mean ( 19 / 19 )2305.2380952381235.4885995093319.78917068614504
Median2239
Midrange3988.5
Midmean - Weighted Average at Xnp2316.43333333333
Midmean - Weighted Average at X(n+1)p2379.12903225806
Midmean - Empirical Distribution Function2379.12903225806
Midmean - Empirical Distribution Function - Averaging2379.12903225806
Midmean - Empirical Distribution Function - Interpolation2367.20689655172
Midmean - Closest Observation2316.43333333333
Midmean - True Basic - Statistics Graphics Toolkit2379.12903225806
Midmean - MS Excel (old versions)2379.12903225806
Number of observations59



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')