Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationSat, 15 Jan 2011 17:54:35 +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/2011/Jan/15/t1295113933c093rf1w33zp3wz.htm/, Retrieved Thu, 31 Oct 2024 23:37:08 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=117353, Retrieved Thu, 31 Oct 2024 23:37:08 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact188
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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Dataseries X:
10574
10653
10805
10872
10625
10407
10463
10556
10646
10702
11353
11346
11451
11964
12574
13031
13812
14544
14931
14886
16005
17064
15168
16050
15839
15137
14954
15648
15305
15579
16348
15928
16171
15937
15713
15594
15683
16438
17032
17696
17745
19394
20148
20108
18584
18441
18391
19178
18073
18483
19644
19195
19650
20830
23595
22937
21814
21928
21777
21383
21467
22052
22680
24320
24977
25204
27390
26434
27525
30695
32436
30160
30236




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







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean17840.5205479452639.80790856244727.8841825947888
Geometric Mean17054.9137158249
Harmonic Mean16312.9882831012
Quadratic Mean18648.2619278985
Winsorized Mean ( 1 / 24 )17817.4383561644632.53175270773928.1684489037769
Winsorized Mean ( 2 / 24 )17807.4109589041628.6172401713528.3279073829571
Winsorized Mean ( 3 / 24 )17805.0273972603627.64301673672228.3680801386642
Winsorized Mean ( 4 / 24 )17663.4383561644590.61874109374929.9066675795861
Winsorized Mean ( 5 / 24 )17655.6301369863588.24591447848430.0140293411797
Winsorized Mean ( 6 / 24 )17577.6301369863570.64295745769230.8032017345794
Winsorized Mean ( 7 / 24 )17464.3835616438545.48495858447732.0162513865892
Winsorized Mean ( 8 / 24 )17450.7945205479538.68107855981532.395410225292
Winsorized Mean ( 9 / 24 )17378.0547945205521.91165483534933.2969280021212
Winsorized Mean ( 10 / 24 )17343.6712328767492.86620835265135.1894103084201
Winsorized Mean ( 11 / 24 )17245.5753424658475.7064513148936.2525572121161
Winsorized Mean ( 12 / 24 )17219.4383561644465.98715163560136.9526032975903
Winsorized Mean ( 13 / 24 )17198.9589041096432.62303237628239.7550699269069
Winsorized Mean ( 14 / 24 )17292.1643835616409.70316454005142.2065677793202
Winsorized Mean ( 15 / 24 )17362.6438356164391.27644817014244.3743647664336
Winsorized Mean ( 16 / 24 )17525.7123287671364.67716195331548.0581570693772
Winsorized Mean ( 17 / 24 )17623.9863013699329.83169425433453.4332709935994
Winsorized Mean ( 18 / 24 )17687.602739726315.80318571534856.0083100481098
Winsorized Mean ( 19 / 24 )17555.3835616438291.40281975303860.2443846511914
Winsorized Mean ( 20 / 24 )17374.8356164384262.2580351904566.2509181227598
Winsorized Mean ( 21 / 24 )17415.9726027397253.90847202512868.591537981514
Winsorized Mean ( 22 / 24 )17287.2876712329232.82747880273174.2493444507895
Winsorized Mean ( 23 / 24 )17328.5616438356227.16105848940476.283152398869
Winsorized Mean ( 24 / 24 )17336.4520547945204.64498442507984.7147664209744
Trimmed Mean ( 1 / 24 )17739.6478873239615.45451464508628.8236538447587
Trimmed Mean ( 2 / 24 )17657.347826087595.03839052650929.6743001917291
Trimmed Mean ( 3 / 24 )17575.5970149254573.06500052414330.6694650674011
Trimmed Mean ( 4 / 24 )17489.7076923077546.91688113173531.9787307645656
Trimmed Mean ( 5 / 24 )17439.380952381529.79343733284232.9173215889133
Trimmed Mean ( 6 / 24 )17387.6229508197509.74440888023834.1104731075232
Trimmed Mean ( 7 / 24 )17348.4406779661490.62794558445235.3596667986372
Trimmed Mean ( 8 / 24 )17327.2280701754474.21573827429336.5387031084851
Trimmed Mean ( 9 / 24 )17306.7272727273455.69245894693937.978963515704
Trimmed Mean ( 10 / 24 )17295.8113207547436.92883434491439.5849620377796
Trimmed Mean ( 11 / 24 )17288.9607843137420.57697620105141.1077204950206
Trimmed Mean ( 12 / 24 )17294.8367346939404.01843275090742.8070487203657
Trimmed Mean ( 13 / 24 )17304.5957446808385.1812020685744.9258573672562
Trimmed Mean ( 14 / 24 )17317.7777777778369.06689997267946.9231398943112
Trimmed Mean ( 15 / 24 )17320.8837209302353.70100995046748.9704106961862
Trimmed Mean ( 16 / 24 )17315.9268292683337.98754377077351.2324408056061
Trimmed Mean ( 17 / 24 )17291.3846153846323.55167082164453.4424210249757
Trimmed Mean ( 18 / 24 )17252.7837837838312.53248031837755.2031704551423
Trimmed Mean ( 19 / 24 )17202.4300.35828241472957.2729337166979
Trimmed Mean ( 20 / 24 )17161.303030303290.28051181484159.1197215514406
Trimmed Mean ( 21 / 24 )17136.1612903226284.30135116216560.2746389360216
Trimmed Mean ( 22 / 24 )17102.6206896552277.00957379639461.7401790676947
Trimmed Mean ( 23 / 24 )17079.9259259259272.32890771454562.7180054782474
Trimmed Mean ( 24 / 24 )17048.36265.55822261794164.1982004244978
Median16438
Midrange21421.5
Midmean - Weighted Average at Xnp17138.0555555556
Midmean - Weighted Average at X(n+1)p17252.7837837838
Midmean - Empirical Distribution Function17252.7837837838
Midmean - Empirical Distribution Function - Averaging17252.7837837838
Midmean - Empirical Distribution Function - Interpolation17252.7837837838
Midmean - Closest Observation17181.5
Midmean - True Basic - Statistics Graphics Toolkit17252.7837837838
Midmean - MS Excel (old versions)17252.7837837838
Number of observations73

\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
MeasureValueS.E.Value/S.E.
Arithmetic Mean17840.5205479452639.80790856244727.8841825947888
Geometric Mean17054.9137158249
Harmonic Mean16312.9882831012
Quadratic Mean18648.2619278985
Winsorized Mean ( 1 / 24 )17817.4383561644632.53175270773928.1684489037769
Winsorized Mean ( 2 / 24 )17807.4109589041628.6172401713528.3279073829571
Winsorized Mean ( 3 / 24 )17805.0273972603627.64301673672228.3680801386642
Winsorized Mean ( 4 / 24 )17663.4383561644590.61874109374929.9066675795861
Winsorized Mean ( 5 / 24 )17655.6301369863588.24591447848430.0140293411797
Winsorized Mean ( 6 / 24 )17577.6301369863570.64295745769230.8032017345794
Winsorized Mean ( 7 / 24 )17464.3835616438545.48495858447732.0162513865892
Winsorized Mean ( 8 / 24 )17450.7945205479538.68107855981532.395410225292
Winsorized Mean ( 9 / 24 )17378.0547945205521.91165483534933.2969280021212
Winsorized Mean ( 10 / 24 )17343.6712328767492.86620835265135.1894103084201
Winsorized Mean ( 11 / 24 )17245.5753424658475.7064513148936.2525572121161
Winsorized Mean ( 12 / 24 )17219.4383561644465.98715163560136.9526032975903
Winsorized Mean ( 13 / 24 )17198.9589041096432.62303237628239.7550699269069
Winsorized Mean ( 14 / 24 )17292.1643835616409.70316454005142.2065677793202
Winsorized Mean ( 15 / 24 )17362.6438356164391.27644817014244.3743647664336
Winsorized Mean ( 16 / 24 )17525.7123287671364.67716195331548.0581570693772
Winsorized Mean ( 17 / 24 )17623.9863013699329.83169425433453.4332709935994
Winsorized Mean ( 18 / 24 )17687.602739726315.80318571534856.0083100481098
Winsorized Mean ( 19 / 24 )17555.3835616438291.40281975303860.2443846511914
Winsorized Mean ( 20 / 24 )17374.8356164384262.2580351904566.2509181227598
Winsorized Mean ( 21 / 24 )17415.9726027397253.90847202512868.591537981514
Winsorized Mean ( 22 / 24 )17287.2876712329232.82747880273174.2493444507895
Winsorized Mean ( 23 / 24 )17328.5616438356227.16105848940476.283152398869
Winsorized Mean ( 24 / 24 )17336.4520547945204.64498442507984.7147664209744
Trimmed Mean ( 1 / 24 )17739.6478873239615.45451464508628.8236538447587
Trimmed Mean ( 2 / 24 )17657.347826087595.03839052650929.6743001917291
Trimmed Mean ( 3 / 24 )17575.5970149254573.06500052414330.6694650674011
Trimmed Mean ( 4 / 24 )17489.7076923077546.91688113173531.9787307645656
Trimmed Mean ( 5 / 24 )17439.380952381529.79343733284232.9173215889133
Trimmed Mean ( 6 / 24 )17387.6229508197509.74440888023834.1104731075232
Trimmed Mean ( 7 / 24 )17348.4406779661490.62794558445235.3596667986372
Trimmed Mean ( 8 / 24 )17327.2280701754474.21573827429336.5387031084851
Trimmed Mean ( 9 / 24 )17306.7272727273455.69245894693937.978963515704
Trimmed Mean ( 10 / 24 )17295.8113207547436.92883434491439.5849620377796
Trimmed Mean ( 11 / 24 )17288.9607843137420.57697620105141.1077204950206
Trimmed Mean ( 12 / 24 )17294.8367346939404.01843275090742.8070487203657
Trimmed Mean ( 13 / 24 )17304.5957446808385.1812020685744.9258573672562
Trimmed Mean ( 14 / 24 )17317.7777777778369.06689997267946.9231398943112
Trimmed Mean ( 15 / 24 )17320.8837209302353.70100995046748.9704106961862
Trimmed Mean ( 16 / 24 )17315.9268292683337.98754377077351.2324408056061
Trimmed Mean ( 17 / 24 )17291.3846153846323.55167082164453.4424210249757
Trimmed Mean ( 18 / 24 )17252.7837837838312.53248031837755.2031704551423
Trimmed Mean ( 19 / 24 )17202.4300.35828241472957.2729337166979
Trimmed Mean ( 20 / 24 )17161.303030303290.28051181484159.1197215514406
Trimmed Mean ( 21 / 24 )17136.1612903226284.30135116216560.2746389360216
Trimmed Mean ( 22 / 24 )17102.6206896552277.00957379639461.7401790676947
Trimmed Mean ( 23 / 24 )17079.9259259259272.32890771454562.7180054782474
Trimmed Mean ( 24 / 24 )17048.36265.55822261794164.1982004244978
Median16438
Midrange21421.5
Midmean - Weighted Average at Xnp17138.0555555556
Midmean - Weighted Average at X(n+1)p17252.7837837838
Midmean - Empirical Distribution Function17252.7837837838
Midmean - Empirical Distribution Function - Averaging17252.7837837838
Midmean - Empirical Distribution Function - Interpolation17252.7837837838
Midmean - Closest Observation17181.5
Midmean - True Basic - Statistics Graphics Toolkit17252.7837837838
Midmean - MS Excel (old versions)17252.7837837838
Number of observations73



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')