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R Software Module

rwasp_centraltendency.wasp

Title produced by software

Central Tendency

Date of computation

Sat, 15 Jan 2011 17:54:35 +0000

Cite this page as follows

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2011/Jan/15/t1295113933c093rf1w33zp3wz.htm/, Retrieved Wed, 14 May 2025 05:45:42 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=117353, Retrieved Wed, 14 May 2025 05:45:42 +0000

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Estimated Impact

227

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)

-       [Central Tendency] [KDGP1W52] [2011-01-15 17:54:35] [9ecedc6075144b73bec317d56fadfdf0] [Current]
- RM      [Mean versus Median] [] [2011-01-15 17:59:46] [e35ce2e7ec49602a729c3c8722e619b0] 

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Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	1 seconds
R Server	'Gwilym Jenkins' @ www.wessa.org

\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' @ www.wessa.org \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=117353&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' @ www.wessa.org[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=117353&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=117353&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 Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	1 seconds
R Server	'Gwilym Jenkins' @ www.wessa.org

Central Tendency - Ungrouped Data
Measure	Value	S.E.	Value/S.E.
Arithmetic Mean	17840.5205479452	639.807908562447	27.8841825947888
Geometric Mean	17054.9137158249
Harmonic Mean	16312.9882831012
Quadratic Mean	18648.2619278985
Winsorized Mean ( 1 / 24 )	17817.4383561644	632.531752707739	28.1684489037769
Winsorized Mean ( 2 / 24 )	17807.4109589041	628.61724017135	28.3279073829571
Winsorized Mean ( 3 / 24 )	17805.0273972603	627.643016736722	28.3680801386642
Winsorized Mean ( 4 / 24 )	17663.4383561644	590.618741093749	29.9066675795861
Winsorized Mean ( 5 / 24 )	17655.6301369863	588.245914478484	30.0140293411797
Winsorized Mean ( 6 / 24 )	17577.6301369863	570.642957457692	30.8032017345794
Winsorized Mean ( 7 / 24 )	17464.3835616438	545.484958584477	32.0162513865892
Winsorized Mean ( 8 / 24 )	17450.7945205479	538.681078559815	32.395410225292
Winsorized Mean ( 9 / 24 )	17378.0547945205	521.911654835349	33.2969280021212
Winsorized Mean ( 10 / 24 )	17343.6712328767	492.866208352651	35.1894103084201
Winsorized Mean ( 11 / 24 )	17245.5753424658	475.70645131489	36.2525572121161
Winsorized Mean ( 12 / 24 )	17219.4383561644	465.987151635601	36.9526032975903
Winsorized Mean ( 13 / 24 )	17198.9589041096	432.623032376282	39.7550699269069
Winsorized Mean ( 14 / 24 )	17292.1643835616	409.703164540051	42.2065677793202
Winsorized Mean ( 15 / 24 )	17362.6438356164	391.276448170142	44.3743647664336
Winsorized Mean ( 16 / 24 )	17525.7123287671	364.677161953315	48.0581570693772
Winsorized Mean ( 17 / 24 )	17623.9863013699	329.831694254334	53.4332709935994
Winsorized Mean ( 18 / 24 )	17687.602739726	315.803185715348	56.0083100481098
Winsorized Mean ( 19 / 24 )	17555.3835616438	291.402819753038	60.2443846511914
Winsorized Mean ( 20 / 24 )	17374.8356164384	262.25803519045	66.2509181227598
Winsorized Mean ( 21 / 24 )	17415.9726027397	253.908472025128	68.591537981514
Winsorized Mean ( 22 / 24 )	17287.2876712329	232.827478802731	74.2493444507895
Winsorized Mean ( 23 / 24 )	17328.5616438356	227.161058489404	76.283152398869
Winsorized Mean ( 24 / 24 )	17336.4520547945	204.644984425079	84.7147664209744
Trimmed Mean ( 1 / 24 )	17739.6478873239	615.454514645086	28.8236538447587
Trimmed Mean ( 2 / 24 )	17657.347826087	595.038390526509	29.6743001917291
Trimmed Mean ( 3 / 24 )	17575.5970149254	573.065000524143	30.6694650674011
Trimmed Mean ( 4 / 24 )	17489.7076923077	546.916881131735	31.9787307645656
Trimmed Mean ( 5 / 24 )	17439.380952381	529.793437332842	32.9173215889133
Trimmed Mean ( 6 / 24 )	17387.6229508197	509.744408880238	34.1104731075232
Trimmed Mean ( 7 / 24 )	17348.4406779661	490.627945584452	35.3596667986372
Trimmed Mean ( 8 / 24 )	17327.2280701754	474.215738274293	36.5387031084851
Trimmed Mean ( 9 / 24 )	17306.7272727273	455.692458946939	37.978963515704
Trimmed Mean ( 10 / 24 )	17295.8113207547	436.928834344914	39.5849620377796
Trimmed Mean ( 11 / 24 )	17288.9607843137	420.576976201051	41.1077204950206
Trimmed Mean ( 12 / 24 )	17294.8367346939	404.018432750907	42.8070487203657
Trimmed Mean ( 13 / 24 )	17304.5957446808	385.18120206857	44.9258573672562
Trimmed Mean ( 14 / 24 )	17317.7777777778	369.066899972679	46.9231398943112
Trimmed Mean ( 15 / 24 )	17320.8837209302	353.701009950467	48.9704106961862
Trimmed Mean ( 16 / 24 )	17315.9268292683	337.987543770773	51.2324408056061
Trimmed Mean ( 17 / 24 )	17291.3846153846	323.551670821644	53.4424210249757
Trimmed Mean ( 18 / 24 )	17252.7837837838	312.532480318377	55.2031704551423
Trimmed Mean ( 19 / 24 )	17202.4	300.358282414729	57.2729337166979
Trimmed Mean ( 20 / 24 )	17161.303030303	290.280511814841	59.1197215514406
Trimmed Mean ( 21 / 24 )	17136.1612903226	284.301351162165	60.2746389360216
Trimmed Mean ( 22 / 24 )	17102.6206896552	277.009573796394	61.7401790676947
Trimmed Mean ( 23 / 24 )	17079.9259259259	272.328907714545	62.7180054782474
Trimmed Mean ( 24 / 24 )	17048.36	265.558222617941	64.1982004244978
Median	16438
Midrange	21421.5
Midmean - Weighted Average at Xnp	17138.0555555556
Midmean - Weighted Average at X(n+1)p	17252.7837837838
Midmean - Empirical Distribution Function	17252.7837837838
Midmean - Empirical Distribution Function - Averaging	17252.7837837838
Midmean - Empirical Distribution Function - Interpolation	17252.7837837838
Midmean - Closest Observation	17181.5
Midmean - True Basic - Statistics Graphics Toolkit	17252.7837837838
Midmean - MS Excel (old versions)	17252.7837837838
Number of observations	73

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 17840.5205479452 & 639.807908562447 & 27.8841825947888 \tabularnewline
Geometric Mean & 17054.9137158249 &  &  \tabularnewline
Harmonic Mean & 16312.9882831012 &  &  \tabularnewline
Quadratic Mean & 18648.2619278985 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 17817.4383561644 & 632.531752707739 & 28.1684489037769 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 17807.4109589041 & 628.61724017135 & 28.3279073829571 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 17805.0273972603 & 627.643016736722 & 28.3680801386642 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 17663.4383561644 & 590.618741093749 & 29.9066675795861 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 17655.6301369863 & 588.245914478484 & 30.0140293411797 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 17577.6301369863 & 570.642957457692 & 30.8032017345794 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 17464.3835616438 & 545.484958584477 & 32.0162513865892 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 17450.7945205479 & 538.681078559815 & 32.395410225292 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 17378.0547945205 & 521.911654835349 & 33.2969280021212 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 17343.6712328767 & 492.866208352651 & 35.1894103084201 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 17245.5753424658 & 475.70645131489 & 36.2525572121161 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 17219.4383561644 & 465.987151635601 & 36.9526032975903 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 17198.9589041096 & 432.623032376282 & 39.7550699269069 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 17292.1643835616 & 409.703164540051 & 42.2065677793202 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 17362.6438356164 & 391.276448170142 & 44.3743647664336 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 17525.7123287671 & 364.677161953315 & 48.0581570693772 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 17623.9863013699 & 329.831694254334 & 53.4332709935994 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 17687.602739726 & 315.803185715348 & 56.0083100481098 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 17555.3835616438 & 291.402819753038 & 60.2443846511914 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 17374.8356164384 & 262.25803519045 & 66.2509181227598 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 17415.9726027397 & 253.908472025128 & 68.591537981514 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 17287.2876712329 & 232.827478802731 & 74.2493444507895 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 17328.5616438356 & 227.161058489404 & 76.283152398869 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 17336.4520547945 & 204.644984425079 & 84.7147664209744 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 17739.6478873239 & 615.454514645086 & 28.8236538447587 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 17657.347826087 & 595.038390526509 & 29.6743001917291 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 17575.5970149254 & 573.065000524143 & 30.6694650674011 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 17489.7076923077 & 546.916881131735 & 31.9787307645656 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 17439.380952381 & 529.793437332842 & 32.9173215889133 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 17387.6229508197 & 509.744408880238 & 34.1104731075232 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 17348.4406779661 & 490.627945584452 & 35.3596667986372 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 17327.2280701754 & 474.215738274293 & 36.5387031084851 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 17306.7272727273 & 455.692458946939 & 37.978963515704 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 17295.8113207547 & 436.928834344914 & 39.5849620377796 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 17288.9607843137 & 420.576976201051 & 41.1077204950206 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 17294.8367346939 & 404.018432750907 & 42.8070487203657 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 17304.5957446808 & 385.18120206857 & 44.9258573672562 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 17317.7777777778 & 369.066899972679 & 46.9231398943112 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 17320.8837209302 & 353.701009950467 & 48.9704106961862 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 17315.9268292683 & 337.987543770773 & 51.2324408056061 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 17291.3846153846 & 323.551670821644 & 53.4424210249757 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 17252.7837837838 & 312.532480318377 & 55.2031704551423 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 17202.4 & 300.358282414729 & 57.2729337166979 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 17161.303030303 & 290.280511814841 & 59.1197215514406 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 17136.1612903226 & 284.301351162165 & 60.2746389360216 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 17102.6206896552 & 277.009573796394 & 61.7401790676947 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 17079.9259259259 & 272.328907714545 & 62.7180054782474 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 17048.36 & 265.558222617941 & 64.1982004244978 \tabularnewline
Median & 16438 &  &  \tabularnewline
Midrange & 21421.5 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 17138.0555555556 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 17252.7837837838 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 17252.7837837838 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 17252.7837837838 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 17252.7837837838 &  &  \tabularnewline
Midmean - Closest Observation & 17181.5 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 17252.7837837838 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 17252.7837837838 &  &  \tabularnewline
Number of observations & 73 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=117353&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]17840.5205479452[/C][C]639.807908562447[/C][C]27.8841825947888[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]17054.9137158249[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]16312.9882831012[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]18648.2619278985[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]17817.4383561644[/C][C]632.531752707739[/C][C]28.1684489037769[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]17807.4109589041[/C][C]628.61724017135[/C][C]28.3279073829571[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]17805.0273972603[/C][C]627.643016736722[/C][C]28.3680801386642[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]17663.4383561644[/C][C]590.618741093749[/C][C]29.9066675795861[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]17655.6301369863[/C][C]588.245914478484[/C][C]30.0140293411797[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]17577.6301369863[/C][C]570.642957457692[/C][C]30.8032017345794[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]17464.3835616438[/C][C]545.484958584477[/C][C]32.0162513865892[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]17450.7945205479[/C][C]538.681078559815[/C][C]32.395410225292[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]17378.0547945205[/C][C]521.911654835349[/C][C]33.2969280021212[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]17343.6712328767[/C][C]492.866208352651[/C][C]35.1894103084201[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]17245.5753424658[/C][C]475.70645131489[/C][C]36.2525572121161[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]17219.4383561644[/C][C]465.987151635601[/C][C]36.9526032975903[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]17198.9589041096[/C][C]432.623032376282[/C][C]39.7550699269069[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]17292.1643835616[/C][C]409.703164540051[/C][C]42.2065677793202[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]17362.6438356164[/C][C]391.276448170142[/C][C]44.3743647664336[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]17525.7123287671[/C][C]364.677161953315[/C][C]48.0581570693772[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]17623.9863013699[/C][C]329.831694254334[/C][C]53.4332709935994[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]17687.602739726[/C][C]315.803185715348[/C][C]56.0083100481098[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]17555.3835616438[/C][C]291.402819753038[/C][C]60.2443846511914[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]17374.8356164384[/C][C]262.25803519045[/C][C]66.2509181227598[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]17415.9726027397[/C][C]253.908472025128[/C][C]68.591537981514[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]17287.2876712329[/C][C]232.827478802731[/C][C]74.2493444507895[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]17328.5616438356[/C][C]227.161058489404[/C][C]76.283152398869[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]17336.4520547945[/C][C]204.644984425079[/C][C]84.7147664209744[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]17739.6478873239[/C][C]615.454514645086[/C][C]28.8236538447587[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]17657.347826087[/C][C]595.038390526509[/C][C]29.6743001917291[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]17575.5970149254[/C][C]573.065000524143[/C][C]30.6694650674011[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]17489.7076923077[/C][C]546.916881131735[/C][C]31.9787307645656[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]17439.380952381[/C][C]529.793437332842[/C][C]32.9173215889133[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]17387.6229508197[/C][C]509.744408880238[/C][C]34.1104731075232[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]17348.4406779661[/C][C]490.627945584452[/C][C]35.3596667986372[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]17327.2280701754[/C][C]474.215738274293[/C][C]36.5387031084851[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]17306.7272727273[/C][C]455.692458946939[/C][C]37.978963515704[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]17295.8113207547[/C][C]436.928834344914[/C][C]39.5849620377796[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]17288.9607843137[/C][C]420.576976201051[/C][C]41.1077204950206[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]17294.8367346939[/C][C]404.018432750907[/C][C]42.8070487203657[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]17304.5957446808[/C][C]385.18120206857[/C][C]44.9258573672562[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]17317.7777777778[/C][C]369.066899972679[/C][C]46.9231398943112[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]17320.8837209302[/C][C]353.701009950467[/C][C]48.9704106961862[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]17315.9268292683[/C][C]337.987543770773[/C][C]51.2324408056061[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]17291.3846153846[/C][C]323.551670821644[/C][C]53.4424210249757[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]17252.7837837838[/C][C]312.532480318377[/C][C]55.2031704551423[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]17202.4[/C][C]300.358282414729[/C][C]57.2729337166979[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]17161.303030303[/C][C]290.280511814841[/C][C]59.1197215514406[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]17136.1612903226[/C][C]284.301351162165[/C][C]60.2746389360216[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]17102.6206896552[/C][C]277.009573796394[/C][C]61.7401790676947[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]17079.9259259259[/C][C]272.328907714545[/C][C]62.7180054782474[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]17048.36[/C][C]265.558222617941[/C][C]64.1982004244978[/C][/ROW]
[ROW][C]Median[/C][C]16438[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]21421.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]17138.0555555556[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]17252.7837837838[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]17252.7837837838[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]17252.7837837838[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]17252.7837837838[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]17181.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]17252.7837837838[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]17252.7837837838[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]73[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=117353&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=117353&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
Measure	Value	S.E.	Value/S.E.
Arithmetic Mean	17840.5205479452	639.807908562447	27.8841825947888
Geometric Mean	17054.9137158249
Harmonic Mean	16312.9882831012
Quadratic Mean	18648.2619278985
Winsorized Mean ( 1 / 24 )	17817.4383561644	632.531752707739	28.1684489037769
Winsorized Mean ( 2 / 24 )	17807.4109589041	628.61724017135	28.3279073829571
Winsorized Mean ( 3 / 24 )	17805.0273972603	627.643016736722	28.3680801386642
Winsorized Mean ( 4 / 24 )	17663.4383561644	590.618741093749	29.9066675795861
Winsorized Mean ( 5 / 24 )	17655.6301369863	588.245914478484	30.0140293411797
Winsorized Mean ( 6 / 24 )	17577.6301369863	570.642957457692	30.8032017345794
Winsorized Mean ( 7 / 24 )	17464.3835616438	545.484958584477	32.0162513865892
Winsorized Mean ( 8 / 24 )	17450.7945205479	538.681078559815	32.395410225292
Winsorized Mean ( 9 / 24 )	17378.0547945205	521.911654835349	33.2969280021212
Winsorized Mean ( 10 / 24 )	17343.6712328767	492.866208352651	35.1894103084201
Winsorized Mean ( 11 / 24 )	17245.5753424658	475.70645131489	36.2525572121161
Winsorized Mean ( 12 / 24 )	17219.4383561644	465.987151635601	36.9526032975903
Winsorized Mean ( 13 / 24 )	17198.9589041096	432.623032376282	39.7550699269069
Winsorized Mean ( 14 / 24 )	17292.1643835616	409.703164540051	42.2065677793202
Winsorized Mean ( 15 / 24 )	17362.6438356164	391.276448170142	44.3743647664336
Winsorized Mean ( 16 / 24 )	17525.7123287671	364.677161953315	48.0581570693772
Winsorized Mean ( 17 / 24 )	17623.9863013699	329.831694254334	53.4332709935994
Winsorized Mean ( 18 / 24 )	17687.602739726	315.803185715348	56.0083100481098
Winsorized Mean ( 19 / 24 )	17555.3835616438	291.402819753038	60.2443846511914
Winsorized Mean ( 20 / 24 )	17374.8356164384	262.25803519045	66.2509181227598
Winsorized Mean ( 21 / 24 )	17415.9726027397	253.908472025128	68.591537981514
Winsorized Mean ( 22 / 24 )	17287.2876712329	232.827478802731	74.2493444507895
Winsorized Mean ( 23 / 24 )	17328.5616438356	227.161058489404	76.283152398869
Winsorized Mean ( 24 / 24 )	17336.4520547945	204.644984425079	84.7147664209744
Trimmed Mean ( 1 / 24 )	17739.6478873239	615.454514645086	28.8236538447587
Trimmed Mean ( 2 / 24 )	17657.347826087	595.038390526509	29.6743001917291
Trimmed Mean ( 3 / 24 )	17575.5970149254	573.065000524143	30.6694650674011
Trimmed Mean ( 4 / 24 )	17489.7076923077	546.916881131735	31.9787307645656
Trimmed Mean ( 5 / 24 )	17439.380952381	529.793437332842	32.9173215889133
Trimmed Mean ( 6 / 24 )	17387.6229508197	509.744408880238	34.1104731075232
Trimmed Mean ( 7 / 24 )	17348.4406779661	490.627945584452	35.3596667986372
Trimmed Mean ( 8 / 24 )	17327.2280701754	474.215738274293	36.5387031084851
Trimmed Mean ( 9 / 24 )	17306.7272727273	455.692458946939	37.978963515704
Trimmed Mean ( 10 / 24 )	17295.8113207547	436.928834344914	39.5849620377796
Trimmed Mean ( 11 / 24 )	17288.9607843137	420.576976201051	41.1077204950206
Trimmed Mean ( 12 / 24 )	17294.8367346939	404.018432750907	42.8070487203657
Trimmed Mean ( 13 / 24 )	17304.5957446808	385.18120206857	44.9258573672562
Trimmed Mean ( 14 / 24 )	17317.7777777778	369.066899972679	46.9231398943112
Trimmed Mean ( 15 / 24 )	17320.8837209302	353.701009950467	48.9704106961862
Trimmed Mean ( 16 / 24 )	17315.9268292683	337.987543770773	51.2324408056061
Trimmed Mean ( 17 / 24 )	17291.3846153846	323.551670821644	53.4424210249757
Trimmed Mean ( 18 / 24 )	17252.7837837838	312.532480318377	55.2031704551423
Trimmed Mean ( 19 / 24 )	17202.4	300.358282414729	57.2729337166979
Trimmed Mean ( 20 / 24 )	17161.303030303	290.280511814841	59.1197215514406
Trimmed Mean ( 21 / 24 )	17136.1612903226	284.301351162165	60.2746389360216
Trimmed Mean ( 22 / 24 )	17102.6206896552	277.009573796394	61.7401790676947
Trimmed Mean ( 23 / 24 )	17079.9259259259	272.328907714545	62.7180054782474
Trimmed Mean ( 24 / 24 )	17048.36	265.558222617941	64.1982004244978
Median	16438
Midrange	21421.5
Midmean - Weighted Average at Xnp	17138.0555555556
Midmean - Weighted Average at X(n+1)p	17252.7837837838
Midmean - Empirical Distribution Function	17252.7837837838
Midmean - Empirical Distribution Function - Averaging	17252.7837837838
Midmean - Empirical Distribution Function - Interpolation	17252.7837837838
Midmean - Closest Observation	17181.5
Midmean - True Basic - Statistics Graphics Toolkit	17252.7837837838
Midmean - MS Excel (old versions)	17252.7837837838
Number of observations	73

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

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')

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code