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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, 25 Dec 2010 12:35:34 +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/25/t12932804329ioj8ff04oxuivp.htm/, Retrieved Sun, 28 Apr 2024 23:54:03 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=115373, Retrieved Sun, 28 Apr 2024 23:54:03 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact123
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [Central Tendency ...] [2010-12-25 12:35:34] [55fca7c82a53ae69fe96aa1750b06058] [Current]
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Dataseries X:
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
7878




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=115373&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=115373&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=115373&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 Mean3442.47169811321344.6415489245589.98855683203409
Geometric Mean2501.20037201541
Harmonic Mean1780.23370659486
Quadratic Mean4245.82816998717
Winsorized Mean ( 1 / 17 )3442.49056603774344.3959812319389.99573384603273
Winsorized Mean ( 2 / 17 )3435.01886792453342.49186581567610.0294903639353
Winsorized Mean ( 3 / 17 )3434.79245283019340.75058271637110.0800780014783
Winsorized Mean ( 4 / 17 )3432.83018867925340.06017005345510.0947728989832
Winsorized Mean ( 5 / 17 )3402.83018867925332.57095637993810.2318922425438
Winsorized Mean ( 6 / 17 )3397.62264150943330.63322962166810.2761075932907
Winsorized Mean ( 7 / 17 )3398.15094339623330.50614129123810.2816574909022
Winsorized Mean ( 8 / 17 )3395.28301886792327.56144282022310.3653317363466
Winsorized Mean ( 9 / 17 )3367.94339622642321.37064429161110.4799347919605
Winsorized Mean ( 10 / 17 )3347.37735849057315.99605487333510.5930985747032
Winsorized Mean ( 11 / 17 )3275.15094339623300.24160976668110.9083845704843
Winsorized Mean ( 12 / 17 )3222.16981132075288.40667563097711.1723135543631
Winsorized Mean ( 13 / 17 )3001.41509433962244.50035161624212.2757087034808
Winsorized Mean ( 14 / 17 )2821201.99409919674613.9657545008396
Winsorized Mean ( 15 / 17 )2785.05660377358190.99546042655514.5817947586484
Winsorized Mean ( 16 / 17 )2798.94339622642185.45098291638915.0926317683003
Winsorized Mean ( 17 / 17 )2786.43396226415181.23787884885615.3744569289950
Trimmed Mean ( 1 / 17 )3409.09803921569342.8188583081279.94431302886953
Trimmed Mean ( 2 / 17 )3372.97959183673340.2980042683339.91184065004702
Trimmed Mean ( 3 / 17 )3338337.8334683818749.88060779172669
Trimmed Mean ( 4 / 17 )3300334.9243620324279.85297092147778
Trimmed Mean ( 5 / 17 )3259.06976744186330.8175138333199.85156356952713
Trimmed Mean ( 6 / 17 )3221.90243902439327.5356391051179.83679958561814
Trimmed Mean ( 7 / 17 )3182.10256410256323.1023093190099.84859121189622
Trimmed Mean ( 8 / 17 )3137.89189189189316.4444900625819.9160895210131
Trimmed Mean ( 9 / 17 )3089.17142857143307.56544288437610.0439483694946
Trimmed Mean ( 10 / 17 )3039.42424242424296.62228567729410.2467831622434
Trimmed Mean ( 11 / 17 )2986.77419354839282.26224254972310.5815576556338
Trimmed Mean ( 12 / 17 )2938.86206896552266.74962765214211.0173052342475
Trimmed Mean ( 13 / 17 )2892.51851851852247.71666317535111.6767216280117
Trimmed Mean ( 14 / 17 )2874.76236.85846885147812.1370369990976
Trimmed Mean ( 15 / 17 )2883.60869565217235.32291109596912.2538374279935
Trimmed Mean ( 16 / 17 )2900.19047619048234.75516748760112.3541070777224
Trimmed Mean ( 17 / 17 )2917.84210526316233.38923219094312.5020425230072
Median2856
Midrange4293.5
Midmean - Weighted Average at Xnp2801
Midmean - Weighted Average at X(n+1)p2892.51851851852
Midmean - Empirical Distribution Function2892.51851851852
Midmean - Empirical Distribution Function - Averaging2892.51851851852
Midmean - Empirical Distribution Function - Interpolation2892.51851851852
Midmean - Closest Observation2822.5
Midmean - True Basic - Statistics Graphics Toolkit2892.51851851852
Midmean - MS Excel (old versions)2892.51851851852
Number of observations53

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 3442.47169811321 & 344.641548924558 & 9.98855683203409 \tabularnewline
Geometric Mean & 2501.20037201541 &  &  \tabularnewline
Harmonic Mean & 1780.23370659486 &  &  \tabularnewline
Quadratic Mean & 4245.82816998717 &  &  \tabularnewline
Winsorized Mean ( 1 / 17 ) & 3442.49056603774 & 344.395981231938 & 9.99573384603273 \tabularnewline
Winsorized Mean ( 2 / 17 ) & 3435.01886792453 & 342.491865815676 & 10.0294903639353 \tabularnewline
Winsorized Mean ( 3 / 17 ) & 3434.79245283019 & 340.750582716371 & 10.0800780014783 \tabularnewline
Winsorized Mean ( 4 / 17 ) & 3432.83018867925 & 340.060170053455 & 10.0947728989832 \tabularnewline
Winsorized Mean ( 5 / 17 ) & 3402.83018867925 & 332.570956379938 & 10.2318922425438 \tabularnewline
Winsorized Mean ( 6 / 17 ) & 3397.62264150943 & 330.633229621668 & 10.2761075932907 \tabularnewline
Winsorized Mean ( 7 / 17 ) & 3398.15094339623 & 330.506141291238 & 10.2816574909022 \tabularnewline
Winsorized Mean ( 8 / 17 ) & 3395.28301886792 & 327.561442820223 & 10.3653317363466 \tabularnewline
Winsorized Mean ( 9 / 17 ) & 3367.94339622642 & 321.370644291611 & 10.4799347919605 \tabularnewline
Winsorized Mean ( 10 / 17 ) & 3347.37735849057 & 315.996054873335 & 10.5930985747032 \tabularnewline
Winsorized Mean ( 11 / 17 ) & 3275.15094339623 & 300.241609766681 & 10.9083845704843 \tabularnewline
Winsorized Mean ( 12 / 17 ) & 3222.16981132075 & 288.406675630977 & 11.1723135543631 \tabularnewline
Winsorized Mean ( 13 / 17 ) & 3001.41509433962 & 244.500351616242 & 12.2757087034808 \tabularnewline
Winsorized Mean ( 14 / 17 ) & 2821 & 201.994099196746 & 13.9657545008396 \tabularnewline
Winsorized Mean ( 15 / 17 ) & 2785.05660377358 & 190.995460426555 & 14.5817947586484 \tabularnewline
Winsorized Mean ( 16 / 17 ) & 2798.94339622642 & 185.450982916389 & 15.0926317683003 \tabularnewline
Winsorized Mean ( 17 / 17 ) & 2786.43396226415 & 181.237878848856 & 15.3744569289950 \tabularnewline
Trimmed Mean ( 1 / 17 ) & 3409.09803921569 & 342.818858308127 & 9.94431302886953 \tabularnewline
Trimmed Mean ( 2 / 17 ) & 3372.97959183673 & 340.298004268333 & 9.91184065004702 \tabularnewline
Trimmed Mean ( 3 / 17 ) & 3338 & 337.833468381874 & 9.88060779172669 \tabularnewline
Trimmed Mean ( 4 / 17 ) & 3300 & 334.924362032427 & 9.85297092147778 \tabularnewline
Trimmed Mean ( 5 / 17 ) & 3259.06976744186 & 330.817513833319 & 9.85156356952713 \tabularnewline
Trimmed Mean ( 6 / 17 ) & 3221.90243902439 & 327.535639105117 & 9.83679958561814 \tabularnewline
Trimmed Mean ( 7 / 17 ) & 3182.10256410256 & 323.102309319009 & 9.84859121189622 \tabularnewline
Trimmed Mean ( 8 / 17 ) & 3137.89189189189 & 316.444490062581 & 9.9160895210131 \tabularnewline
Trimmed Mean ( 9 / 17 ) & 3089.17142857143 & 307.565442884376 & 10.0439483694946 \tabularnewline
Trimmed Mean ( 10 / 17 ) & 3039.42424242424 & 296.622285677294 & 10.2467831622434 \tabularnewline
Trimmed Mean ( 11 / 17 ) & 2986.77419354839 & 282.262242549723 & 10.5815576556338 \tabularnewline
Trimmed Mean ( 12 / 17 ) & 2938.86206896552 & 266.749627652142 & 11.0173052342475 \tabularnewline
Trimmed Mean ( 13 / 17 ) & 2892.51851851852 & 247.716663175351 & 11.6767216280117 \tabularnewline
Trimmed Mean ( 14 / 17 ) & 2874.76 & 236.858468851478 & 12.1370369990976 \tabularnewline
Trimmed Mean ( 15 / 17 ) & 2883.60869565217 & 235.322911095969 & 12.2538374279935 \tabularnewline
Trimmed Mean ( 16 / 17 ) & 2900.19047619048 & 234.755167487601 & 12.3541070777224 \tabularnewline
Trimmed Mean ( 17 / 17 ) & 2917.84210526316 & 233.389232190943 & 12.5020425230072 \tabularnewline
Median & 2856 &  &  \tabularnewline
Midrange & 4293.5 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 2801 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 2892.51851851852 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 2892.51851851852 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 2892.51851851852 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 2892.51851851852 &  &  \tabularnewline
Midmean - Closest Observation & 2822.5 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 2892.51851851852 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 2892.51851851852 &  &  \tabularnewline
Number of observations & 53 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=115373&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]3442.47169811321[/C][C]344.641548924558[/C][C]9.98855683203409[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]2501.20037201541[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]1780.23370659486[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]4245.82816998717[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 17 )[/C][C]3442.49056603774[/C][C]344.395981231938[/C][C]9.99573384603273[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 17 )[/C][C]3435.01886792453[/C][C]342.491865815676[/C][C]10.0294903639353[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 17 )[/C][C]3434.79245283019[/C][C]340.750582716371[/C][C]10.0800780014783[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 17 )[/C][C]3432.83018867925[/C][C]340.060170053455[/C][C]10.0947728989832[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 17 )[/C][C]3402.83018867925[/C][C]332.570956379938[/C][C]10.2318922425438[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 17 )[/C][C]3397.62264150943[/C][C]330.633229621668[/C][C]10.2761075932907[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 17 )[/C][C]3398.15094339623[/C][C]330.506141291238[/C][C]10.2816574909022[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 17 )[/C][C]3395.28301886792[/C][C]327.561442820223[/C][C]10.3653317363466[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 17 )[/C][C]3367.94339622642[/C][C]321.370644291611[/C][C]10.4799347919605[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 17 )[/C][C]3347.37735849057[/C][C]315.996054873335[/C][C]10.5930985747032[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 17 )[/C][C]3275.15094339623[/C][C]300.241609766681[/C][C]10.9083845704843[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 17 )[/C][C]3222.16981132075[/C][C]288.406675630977[/C][C]11.1723135543631[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 17 )[/C][C]3001.41509433962[/C][C]244.500351616242[/C][C]12.2757087034808[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 17 )[/C][C]2821[/C][C]201.994099196746[/C][C]13.9657545008396[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 17 )[/C][C]2785.05660377358[/C][C]190.995460426555[/C][C]14.5817947586484[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 17 )[/C][C]2798.94339622642[/C][C]185.450982916389[/C][C]15.0926317683003[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 17 )[/C][C]2786.43396226415[/C][C]181.237878848856[/C][C]15.3744569289950[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 17 )[/C][C]3409.09803921569[/C][C]342.818858308127[/C][C]9.94431302886953[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 17 )[/C][C]3372.97959183673[/C][C]340.298004268333[/C][C]9.91184065004702[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 17 )[/C][C]3338[/C][C]337.833468381874[/C][C]9.88060779172669[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 17 )[/C][C]3300[/C][C]334.924362032427[/C][C]9.85297092147778[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 17 )[/C][C]3259.06976744186[/C][C]330.817513833319[/C][C]9.85156356952713[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 17 )[/C][C]3221.90243902439[/C][C]327.535639105117[/C][C]9.83679958561814[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 17 )[/C][C]3182.10256410256[/C][C]323.102309319009[/C][C]9.84859121189622[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 17 )[/C][C]3137.89189189189[/C][C]316.444490062581[/C][C]9.9160895210131[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 17 )[/C][C]3089.17142857143[/C][C]307.565442884376[/C][C]10.0439483694946[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 17 )[/C][C]3039.42424242424[/C][C]296.622285677294[/C][C]10.2467831622434[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 17 )[/C][C]2986.77419354839[/C][C]282.262242549723[/C][C]10.5815576556338[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 17 )[/C][C]2938.86206896552[/C][C]266.749627652142[/C][C]11.0173052342475[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 17 )[/C][C]2892.51851851852[/C][C]247.716663175351[/C][C]11.6767216280117[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 17 )[/C][C]2874.76[/C][C]236.858468851478[/C][C]12.1370369990976[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 17 )[/C][C]2883.60869565217[/C][C]235.322911095969[/C][C]12.2538374279935[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 17 )[/C][C]2900.19047619048[/C][C]234.755167487601[/C][C]12.3541070777224[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 17 )[/C][C]2917.84210526316[/C][C]233.389232190943[/C][C]12.5020425230072[/C][/ROW]
[ROW][C]Median[/C][C]2856[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]4293.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]2801[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]2892.51851851852[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]2892.51851851852[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]2892.51851851852[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]2892.51851851852[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]2822.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]2892.51851851852[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]2892.51851851852[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]53[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=115373&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=115373&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 Mean3442.47169811321344.6415489245589.98855683203409
Geometric Mean2501.20037201541
Harmonic Mean1780.23370659486
Quadratic Mean4245.82816998717
Winsorized Mean ( 1 / 17 )3442.49056603774344.3959812319389.99573384603273
Winsorized Mean ( 2 / 17 )3435.01886792453342.49186581567610.0294903639353
Winsorized Mean ( 3 / 17 )3434.79245283019340.75058271637110.0800780014783
Winsorized Mean ( 4 / 17 )3432.83018867925340.06017005345510.0947728989832
Winsorized Mean ( 5 / 17 )3402.83018867925332.57095637993810.2318922425438
Winsorized Mean ( 6 / 17 )3397.62264150943330.63322962166810.2761075932907
Winsorized Mean ( 7 / 17 )3398.15094339623330.50614129123810.2816574909022
Winsorized Mean ( 8 / 17 )3395.28301886792327.56144282022310.3653317363466
Winsorized Mean ( 9 / 17 )3367.94339622642321.37064429161110.4799347919605
Winsorized Mean ( 10 / 17 )3347.37735849057315.99605487333510.5930985747032
Winsorized Mean ( 11 / 17 )3275.15094339623300.24160976668110.9083845704843
Winsorized Mean ( 12 / 17 )3222.16981132075288.40667563097711.1723135543631
Winsorized Mean ( 13 / 17 )3001.41509433962244.50035161624212.2757087034808
Winsorized Mean ( 14 / 17 )2821201.99409919674613.9657545008396
Winsorized Mean ( 15 / 17 )2785.05660377358190.99546042655514.5817947586484
Winsorized Mean ( 16 / 17 )2798.94339622642185.45098291638915.0926317683003
Winsorized Mean ( 17 / 17 )2786.43396226415181.23787884885615.3744569289950
Trimmed Mean ( 1 / 17 )3409.09803921569342.8188583081279.94431302886953
Trimmed Mean ( 2 / 17 )3372.97959183673340.2980042683339.91184065004702
Trimmed Mean ( 3 / 17 )3338337.8334683818749.88060779172669
Trimmed Mean ( 4 / 17 )3300334.9243620324279.85297092147778
Trimmed Mean ( 5 / 17 )3259.06976744186330.8175138333199.85156356952713
Trimmed Mean ( 6 / 17 )3221.90243902439327.5356391051179.83679958561814
Trimmed Mean ( 7 / 17 )3182.10256410256323.1023093190099.84859121189622
Trimmed Mean ( 8 / 17 )3137.89189189189316.4444900625819.9160895210131
Trimmed Mean ( 9 / 17 )3089.17142857143307.56544288437610.0439483694946
Trimmed Mean ( 10 / 17 )3039.42424242424296.62228567729410.2467831622434
Trimmed Mean ( 11 / 17 )2986.77419354839282.26224254972310.5815576556338
Trimmed Mean ( 12 / 17 )2938.86206896552266.74962765214211.0173052342475
Trimmed Mean ( 13 / 17 )2892.51851851852247.71666317535111.6767216280117
Trimmed Mean ( 14 / 17 )2874.76236.85846885147812.1370369990976
Trimmed Mean ( 15 / 17 )2883.60869565217235.32291109596912.2538374279935
Trimmed Mean ( 16 / 17 )2900.19047619048234.75516748760112.3541070777224
Trimmed Mean ( 17 / 17 )2917.84210526316233.38923219094312.5020425230072
Median2856
Midrange4293.5
Midmean - Weighted Average at Xnp2801
Midmean - Weighted Average at X(n+1)p2892.51851851852
Midmean - Empirical Distribution Function2892.51851851852
Midmean - Empirical Distribution Function - Averaging2892.51851851852
Midmean - Empirical Distribution Function - Interpolation2892.51851851852
Midmean - Closest Observation2822.5
Midmean - True Basic - Statistics Graphics Toolkit2892.51851851852
Midmean - MS Excel (old versions)2892.51851851852
Number of observations53



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')