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Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationTue, 08 Mar 2016 18:16:25 +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/2016/Mar/08/t1457461020rnk6fe2evy8k5cw.htm/, Retrieved Mon, 29 Apr 2024 01:48:27 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=293694, Retrieved Mon, 29 Apr 2024 01:48:27 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact72
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [] [2016-03-08 18:16:25] [dce1b7f6243247e331d0750a8103b593] [Current]
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Dataseries X:
10670,5
11129
13474,5
12317,8
11990,1
13478,3
11762,4
11149,1
13597,2
13367,9
13304,2
12407,2
13008,3
13379,5
15696
13529,6
14857
14375,1
12958,4
12612,8
14405,2
13655,8
13783,1
12336,1
13366,7
14042,4
15412
13566,5
13981,5
14042
13131
12771,2
13600,1
14886,9
13813,1
11551
13750,5
13415,4
15040,9
14349,5
13900,2
13956,6
13951
11802,1
14219,1
14914,5
14098,2
12773,6
14225
13513
14754,4
14447,7
13777,8
14328,6
14106,1
12157
15425,1
15448,8
13604,5
12269,3




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Sir Ronald Aylmer Fisher' @ fisher.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 1 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ fisher.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=293694&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]'Sir Ronald Aylmer Fisher' @ fisher.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=293694&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=293694&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'Sir Ronald Aylmer Fisher' @ fisher.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean13527.3066666667144.67351019768393.5023049360098
Geometric Mean13480.1792720147
Harmonic Mean13431.4706206996
Quadratic Mean13572.874445108
Winsorized Mean ( 1 / 20 )13530.8283333333141.29385493076495.7637424498299
Winsorized Mean ( 2 / 20 )13530.7083333333140.92049588274996.0166102778361
Winsorized Mean ( 3 / 20 )13550.1483333333135.369233844712100.097695380897
Winsorized Mean ( 4 / 20 )13539.5016666667126.540553145418106.997332713627
Winsorized Mean ( 5 / 20 )13532.2766666667123.697333582438109.398289152677
Winsorized Mean ( 6 / 20 )13548.3166666667118.85253423296113.992661192322
Winsorized Mean ( 7 / 20 )13564.3113.980910038073119.005015800182
Winsorized Mean ( 8 / 20 )13565.5933333333108.305782429754125.252715312147
Winsorized Mean ( 9 / 20 )13526.863333333398.8748392748104136.807942572094
Winsorized Mean ( 10 / 20 )13522.8397.1385445238057139.211783193704
Winsorized Mean ( 11 / 20 )13530.346666666793.6164034309004144.529656884903
Winsorized Mean ( 12 / 20 )13566.346666666784.7078045039504160.154625020815
Winsorized Mean ( 13 / 20 )13596.138333333377.6179803304259175.167381004421
Winsorized Mean ( 14 / 20 )13572.52573.7679139068954183.989546147804
Winsorized Mean ( 15 / 20 )13617.2565.3363225780469208.417760025193
Winsorized Mean ( 16 / 20 )13600.423333333358.4896792946625232.526891878076
Winsorized Mean ( 17 / 20 )13632.9552.34060476131260.466038980074
Winsorized Mean ( 18 / 20 )13668.1741.6984121755985327.786342137951
Winsorized Mean ( 19 / 20 )13687.83538.824914231882352.552871546588
Winsorized Mean ( 20 / 20 )13668.068333333335.7067489143441382.786692961637
Trimmed Mean ( 1 / 20 )13539.1706896552136.08136513548199.4932015575805
Trimmed Mean ( 2 / 20 )13548.1089285714129.635957821273104.508881303211
Trimmed Mean ( 3 / 20 )13557.7759259259121.827307778598111.286838502292
Trimmed Mean ( 4 / 20 )13560.7096153846114.900037650269118.021803062071
Trimmed Mean ( 5 / 20 )13567.072109.888344855223123.462338229541
Trimmed Mean ( 6 / 20 )13575.7708333333104.530629183861129.873616368028
Trimmed Mean ( 7 / 20 )13581.739130434899.3103700467569136.760532903465
Trimmed Mean ( 8 / 20 )13585.136363636494.1154378155383144.345462114967
Trimmed Mean ( 9 / 20 )13588.626190476289.0643182005756152.570933736608
Trimmed Mean ( 10 / 20 )13598.9285.1184625638338159.764633786725
Trimmed Mean ( 11 / 20 )13610.934210526380.2385818553349169.630792267316
Trimmed Mean ( 12 / 20 )13623.144444444474.6093464552749182.593000631776
Trimmed Mean ( 13 / 20 )13631.497058823569.778733753414195.353173174436
Trimmed Mean ( 14 / 20 )13636.59687565.3480340493918208.676467063923
Trimmed Mean ( 15 / 20 )13645.7560.1024737475482227.041403608727
Trimmed Mean ( 16 / 20 )13649.821428571455.6474993988266245.290832041579
Trimmed Mean ( 17 / 20 )13656.946153846251.4408297070211265.488450159701
Trimmed Mean ( 18 / 20 )13660.47547.5558433180997287.251240791283
Trimmed Mean ( 19 / 20 )13659.309090909145.9519714018694297.251862633981
Trimmed Mean ( 20 / 20 )13654.80544.2205450435357308.788708654691
Median13602.3
Midrange13183.25
Midmean - Weighted Average at Xnp13617.6161290323
Midmean - Weighted Average at X(n+1)p13645.75
Midmean - Empirical Distribution Function13617.6161290323
Midmean - Empirical Distribution Function - Averaging13645.75
Midmean - Empirical Distribution Function - Interpolation13645.75
Midmean - Closest Observation13617.6161290323
Midmean - True Basic - Statistics Graphics Toolkit13645.75
Midmean - MS Excel (old versions)13636.596875
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 13527.3066666667 & 144.673510197683 & 93.5023049360098 \tabularnewline
Geometric Mean & 13480.1792720147 &  &  \tabularnewline
Harmonic Mean & 13431.4706206996 &  &  \tabularnewline
Quadratic Mean & 13572.874445108 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 13530.8283333333 & 141.293854930764 & 95.7637424498299 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 13530.7083333333 & 140.920495882749 & 96.0166102778361 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 13550.1483333333 & 135.369233844712 & 100.097695380897 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 13539.5016666667 & 126.540553145418 & 106.997332713627 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 13532.2766666667 & 123.697333582438 & 109.398289152677 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 13548.3166666667 & 118.85253423296 & 113.992661192322 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 13564.3 & 113.980910038073 & 119.005015800182 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 13565.5933333333 & 108.305782429754 & 125.252715312147 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 13526.8633333333 & 98.8748392748104 & 136.807942572094 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 13522.83 & 97.1385445238057 & 139.211783193704 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 13530.3466666667 & 93.6164034309004 & 144.529656884903 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 13566.3466666667 & 84.7078045039504 & 160.154625020815 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 13596.1383333333 & 77.6179803304259 & 175.167381004421 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 13572.525 & 73.7679139068954 & 183.989546147804 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 13617.25 & 65.3363225780469 & 208.417760025193 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 13600.4233333333 & 58.4896792946625 & 232.526891878076 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 13632.95 & 52.34060476131 & 260.466038980074 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 13668.17 & 41.6984121755985 & 327.786342137951 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 13687.835 & 38.824914231882 & 352.552871546588 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 13668.0683333333 & 35.7067489143441 & 382.786692961637 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 13539.1706896552 & 136.081365135481 & 99.4932015575805 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 13548.1089285714 & 129.635957821273 & 104.508881303211 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 13557.7759259259 & 121.827307778598 & 111.286838502292 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 13560.7096153846 & 114.900037650269 & 118.021803062071 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 13567.072 & 109.888344855223 & 123.462338229541 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 13575.7708333333 & 104.530629183861 & 129.873616368028 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 13581.7391304348 & 99.3103700467569 & 136.760532903465 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 13585.1363636364 & 94.1154378155383 & 144.345462114967 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 13588.6261904762 & 89.0643182005756 & 152.570933736608 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 13598.92 & 85.1184625638338 & 159.764633786725 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 13610.9342105263 & 80.2385818553349 & 169.630792267316 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 13623.1444444444 & 74.6093464552749 & 182.593000631776 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 13631.4970588235 & 69.778733753414 & 195.353173174436 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 13636.596875 & 65.3480340493918 & 208.676467063923 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 13645.75 & 60.1024737475482 & 227.041403608727 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 13649.8214285714 & 55.6474993988266 & 245.290832041579 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 13656.9461538462 & 51.4408297070211 & 265.488450159701 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 13660.475 & 47.5558433180997 & 287.251240791283 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 13659.3090909091 & 45.9519714018694 & 297.251862633981 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 13654.805 & 44.2205450435357 & 308.788708654691 \tabularnewline
Median & 13602.3 &  &  \tabularnewline
Midrange & 13183.25 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 13617.6161290323 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 13645.75 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 13617.6161290323 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 13645.75 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 13645.75 &  &  \tabularnewline
Midmean - Closest Observation & 13617.6161290323 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 13645.75 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 13636.596875 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=293694&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]13527.3066666667[/C][C]144.673510197683[/C][C]93.5023049360098[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]13480.1792720147[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]13431.4706206996[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]13572.874445108[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]13530.8283333333[/C][C]141.293854930764[/C][C]95.7637424498299[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]13530.7083333333[/C][C]140.920495882749[/C][C]96.0166102778361[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]13550.1483333333[/C][C]135.369233844712[/C][C]100.097695380897[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]13539.5016666667[/C][C]126.540553145418[/C][C]106.997332713627[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]13532.2766666667[/C][C]123.697333582438[/C][C]109.398289152677[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]13548.3166666667[/C][C]118.85253423296[/C][C]113.992661192322[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]13564.3[/C][C]113.980910038073[/C][C]119.005015800182[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]13565.5933333333[/C][C]108.305782429754[/C][C]125.252715312147[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]13526.8633333333[/C][C]98.8748392748104[/C][C]136.807942572094[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]13522.83[/C][C]97.1385445238057[/C][C]139.211783193704[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]13530.3466666667[/C][C]93.6164034309004[/C][C]144.529656884903[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]13566.3466666667[/C][C]84.7078045039504[/C][C]160.154625020815[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]13596.1383333333[/C][C]77.6179803304259[/C][C]175.167381004421[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]13572.525[/C][C]73.7679139068954[/C][C]183.989546147804[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]13617.25[/C][C]65.3363225780469[/C][C]208.417760025193[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]13600.4233333333[/C][C]58.4896792946625[/C][C]232.526891878076[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]13632.95[/C][C]52.34060476131[/C][C]260.466038980074[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]13668.17[/C][C]41.6984121755985[/C][C]327.786342137951[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]13687.835[/C][C]38.824914231882[/C][C]352.552871546588[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]13668.0683333333[/C][C]35.7067489143441[/C][C]382.786692961637[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]13539.1706896552[/C][C]136.081365135481[/C][C]99.4932015575805[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]13548.1089285714[/C][C]129.635957821273[/C][C]104.508881303211[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]13557.7759259259[/C][C]121.827307778598[/C][C]111.286838502292[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]13560.7096153846[/C][C]114.900037650269[/C][C]118.021803062071[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]13567.072[/C][C]109.888344855223[/C][C]123.462338229541[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]13575.7708333333[/C][C]104.530629183861[/C][C]129.873616368028[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]13581.7391304348[/C][C]99.3103700467569[/C][C]136.760532903465[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]13585.1363636364[/C][C]94.1154378155383[/C][C]144.345462114967[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]13588.6261904762[/C][C]89.0643182005756[/C][C]152.570933736608[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]13598.92[/C][C]85.1184625638338[/C][C]159.764633786725[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]13610.9342105263[/C][C]80.2385818553349[/C][C]169.630792267316[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]13623.1444444444[/C][C]74.6093464552749[/C][C]182.593000631776[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]13631.4970588235[/C][C]69.778733753414[/C][C]195.353173174436[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]13636.596875[/C][C]65.3480340493918[/C][C]208.676467063923[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]13645.75[/C][C]60.1024737475482[/C][C]227.041403608727[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]13649.8214285714[/C][C]55.6474993988266[/C][C]245.290832041579[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]13656.9461538462[/C][C]51.4408297070211[/C][C]265.488450159701[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]13660.475[/C][C]47.5558433180997[/C][C]287.251240791283[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]13659.3090909091[/C][C]45.9519714018694[/C][C]297.251862633981[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]13654.805[/C][C]44.2205450435357[/C][C]308.788708654691[/C][/ROW]
[ROW][C]Median[/C][C]13602.3[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]13183.25[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]13617.6161290323[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]13645.75[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]13617.6161290323[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]13645.75[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]13645.75[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]13617.6161290323[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]13645.75[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]13636.596875[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]60[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=293694&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=293694&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 Mean13527.3066666667144.67351019768393.5023049360098
Geometric Mean13480.1792720147
Harmonic Mean13431.4706206996
Quadratic Mean13572.874445108
Winsorized Mean ( 1 / 20 )13530.8283333333141.29385493076495.7637424498299
Winsorized Mean ( 2 / 20 )13530.7083333333140.92049588274996.0166102778361
Winsorized Mean ( 3 / 20 )13550.1483333333135.369233844712100.097695380897
Winsorized Mean ( 4 / 20 )13539.5016666667126.540553145418106.997332713627
Winsorized Mean ( 5 / 20 )13532.2766666667123.697333582438109.398289152677
Winsorized Mean ( 6 / 20 )13548.3166666667118.85253423296113.992661192322
Winsorized Mean ( 7 / 20 )13564.3113.980910038073119.005015800182
Winsorized Mean ( 8 / 20 )13565.5933333333108.305782429754125.252715312147
Winsorized Mean ( 9 / 20 )13526.863333333398.8748392748104136.807942572094
Winsorized Mean ( 10 / 20 )13522.8397.1385445238057139.211783193704
Winsorized Mean ( 11 / 20 )13530.346666666793.6164034309004144.529656884903
Winsorized Mean ( 12 / 20 )13566.346666666784.7078045039504160.154625020815
Winsorized Mean ( 13 / 20 )13596.138333333377.6179803304259175.167381004421
Winsorized Mean ( 14 / 20 )13572.52573.7679139068954183.989546147804
Winsorized Mean ( 15 / 20 )13617.2565.3363225780469208.417760025193
Winsorized Mean ( 16 / 20 )13600.423333333358.4896792946625232.526891878076
Winsorized Mean ( 17 / 20 )13632.9552.34060476131260.466038980074
Winsorized Mean ( 18 / 20 )13668.1741.6984121755985327.786342137951
Winsorized Mean ( 19 / 20 )13687.83538.824914231882352.552871546588
Winsorized Mean ( 20 / 20 )13668.068333333335.7067489143441382.786692961637
Trimmed Mean ( 1 / 20 )13539.1706896552136.08136513548199.4932015575805
Trimmed Mean ( 2 / 20 )13548.1089285714129.635957821273104.508881303211
Trimmed Mean ( 3 / 20 )13557.7759259259121.827307778598111.286838502292
Trimmed Mean ( 4 / 20 )13560.7096153846114.900037650269118.021803062071
Trimmed Mean ( 5 / 20 )13567.072109.888344855223123.462338229541
Trimmed Mean ( 6 / 20 )13575.7708333333104.530629183861129.873616368028
Trimmed Mean ( 7 / 20 )13581.739130434899.3103700467569136.760532903465
Trimmed Mean ( 8 / 20 )13585.136363636494.1154378155383144.345462114967
Trimmed Mean ( 9 / 20 )13588.626190476289.0643182005756152.570933736608
Trimmed Mean ( 10 / 20 )13598.9285.1184625638338159.764633786725
Trimmed Mean ( 11 / 20 )13610.934210526380.2385818553349169.630792267316
Trimmed Mean ( 12 / 20 )13623.144444444474.6093464552749182.593000631776
Trimmed Mean ( 13 / 20 )13631.497058823569.778733753414195.353173174436
Trimmed Mean ( 14 / 20 )13636.59687565.3480340493918208.676467063923
Trimmed Mean ( 15 / 20 )13645.7560.1024737475482227.041403608727
Trimmed Mean ( 16 / 20 )13649.821428571455.6474993988266245.290832041579
Trimmed Mean ( 17 / 20 )13656.946153846251.4408297070211265.488450159701
Trimmed Mean ( 18 / 20 )13660.47547.5558433180997287.251240791283
Trimmed Mean ( 19 / 20 )13659.309090909145.9519714018694297.251862633981
Trimmed Mean ( 20 / 20 )13654.80544.2205450435357308.788708654691
Median13602.3
Midrange13183.25
Midmean - Weighted Average at Xnp13617.6161290323
Midmean - Weighted Average at X(n+1)p13645.75
Midmean - Empirical Distribution Function13617.6161290323
Midmean - Empirical Distribution Function - Averaging13645.75
Midmean - Empirical Distribution Function - Interpolation13645.75
Midmean - Closest Observation13617.6161290323
Midmean - True Basic - Statistics Graphics Toolkit13645.75
Midmean - MS Excel (old versions)13636.596875
Number of observations60



Parameters (Session):
Parameters (R input):
R code (references can be found in the software module):
geomean <- function(x) {
return(exp(mean(log(x))))
}
harmean <- function(x) {
return(1/mean(1/x))
}
quamean <- function(x) {
return(sqrt(mean(x*x)))
}
winmean <- function(x) {
x <-sort(x[!is.na(x)])
n<-length(x)
denom <- 3
nodenom <- n/denom
if (nodenom>40) denom <- n/40
sqrtn = sqrt(n)
roundnodenom = floor(nodenom)
win <- array(NA,dim=c(roundnodenom,2))
for (j in 1:roundnodenom) {
win[j,1] <- (j*x[j+1]+sum(x[(j+1):(n-j)])+j*x[n-j])/n
win[j,2] <- sd(c(rep(x[j+1],j),x[(j+1):(n-j)],rep(x[n-j],j)))/sqrtn
}
return(win)
}
trimean <- function(x) {
x <-sort(x[!is.na(x)])
n<-length(x)
denom <- 3
nodenom <- n/denom
if (nodenom>40) denom <- n/40
sqrtn = sqrt(n)
roundnodenom = floor(nodenom)
tri <- array(NA,dim=c(roundnodenom,2))
for (j in 1:roundnodenom) {
tri[j,1] <- mean(x,trim=j/n)
tri[j,2] <- sd(x[(j+1):(n-j)]) / sqrt(n-j*2)
}
return(tri)
}
midrange <- function(x) {
return((max(x)+min(x))/2)
}
q1 <- function(data,n,p,i,f) {
np <- n*p;
i <<- floor(np)
f <<- np - i
qvalue <- (1-f)*data[i] + f*data[i+1]
}
q2 <- function(data,n,p,i,f) {
np <- (n+1)*p
i <<- floor(np)
f <<- np - i
qvalue <- (1-f)*data[i] + f*data[i+1]
}
q3 <- function(data,n,p,i,f) {
np <- n*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i]
} else {
qvalue <- data[i+1]
}
}
q4 <- function(data,n,p,i,f) {
np <- n*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- (data[i]+data[i+1])/2
} else {
qvalue <- data[i+1]
}
}
q5 <- function(data,n,p,i,f) {
np <- (n-1)*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i+1]
} else {
qvalue <- data[i+1] + f*(data[i+2]-data[i+1])
}
}
q6 <- function(data,n,p,i,f) {
np <- n*p+0.5
i <<- floor(np)
f <<- np - i
qvalue <- data[i]
}
q7 <- function(data,n,p,i,f) {
np <- (n+1)*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i]
} else {
qvalue <- f*data[i] + (1-f)*data[i+1]
}
}
q8 <- function(data,n,p,i,f) {
np <- (n+1)*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i]
} else {
if (f == 0.5) {
qvalue <- (data[i]+data[i+1])/2
} else {
if (f < 0.5) {
qvalue <- data[i]
} else {
qvalue <- data[i+1]
}
}
}
}
midmean <- function(x,def) {
x <-sort(x[!is.na(x)])
n<-length(x)
if (def==1) {
qvalue1 <- q1(x,n,0.25,i,f)
qvalue3 <- q1(x,n,0.75,i,f)
}
if (def==2) {
qvalue1 <- q2(x,n,0.25,i,f)
qvalue3 <- q2(x,n,0.75,i,f)
}
if (def==3) {
qvalue1 <- q3(x,n,0.25,i,f)
qvalue3 <- q3(x,n,0.75,i,f)
}
if (def==4) {
qvalue1 <- q4(x,n,0.25,i,f)
qvalue3 <- q4(x,n,0.75,i,f)
}
if (def==5) {
qvalue1 <- q5(x,n,0.25,i,f)
qvalue3 <- q5(x,n,0.75,i,f)
}
if (def==6) {
qvalue1 <- q6(x,n,0.25,i,f)
qvalue3 <- q6(x,n,0.75,i,f)
}
if (def==7) {
qvalue1 <- q7(x,n,0.25,i,f)
qvalue3 <- q7(x,n,0.75,i,f)
}
if (def==8) {
qvalue1 <- q8(x,n,0.25,i,f)
qvalue3 <- q8(x,n,0.75,i,f)
}
midm <- 0
myn <- 0
roundno4 <- round(n/4)
round3no4 <- round(3*n/4)
for (i in 1:n) {
if ((x[i]>=qvalue1) & (x[i]<=qvalue3)){
midm = midm + x[i]
myn = myn + 1
}
}
midm = midm / myn
return(midm)
}
(arm <- mean(x))
sqrtn <- sqrt(length(x))
(armse <- sd(x) / sqrtn)
(armose <- arm / armse)
(geo <- geomean(x))
(har <- harmean(x))
(qua <- quamean(x))
(win <- winmean(x))
(tri <- trimean(x))
(midr <- midrange(x))
midm <- array(NA,dim=8)
for (j in 1:8) midm[j] <- midmean(x,j)
midm
bitmap(file='test1.png')
lb <- win[,1] - 2*win[,2]
ub <- win[,1] + 2*win[,2]
if ((ylimmin == '') | (ylimmax == '')) plot(win[,1],type='b',main=main, xlab='j', pch=19, ylab='Winsorized Mean(j/n)', ylim=c(min(lb),max(ub))) else plot(win[,1],type='l',main=main, xlab='j', pch=19, ylab='Winsorized Mean(j/n)', ylim=c(ylimmin,ylimmax))
lines(ub,lty=3)
lines(lb,lty=3)
grid()
dev.off()
bitmap(file='test2.png')
lb <- tri[,1] - 2*tri[,2]
ub <- tri[,1] + 2*tri[,2]
if ((ylimmin == '') | (ylimmax == '')) plot(tri[,1],type='b',main=main, xlab='j', pch=19, ylab='Trimmed Mean(j/n)', ylim=c(min(lb),max(ub))) else plot(tri[,1],type='l',main=main, xlab='j', pch=19, ylab='Trimmed Mean(j/n)', ylim=c(ylimmin,ylimmax))
lines(ub,lty=3)
lines(lb,lty=3)
grid()
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Central Tendency - Ungrouped Data',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Measure',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.element(a,'S.E.',header=TRUE)
a<-table.element(a,'Value/S.E.',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('arithmetic_mean.htm', 'Arithmetic Mean', 'click to view the definition of the Arithmetic Mean'),header=TRUE)
a<-table.element(a,arm)
a<-table.element(a,hyperlink('arithmetic_mean_standard_error.htm', armse, 'click to view the definition of the Standard Error of the Arithmetic Mean'))
a<-table.element(a,armose)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('geometric_mean.htm', 'Geometric Mean', 'click to view the definition of the Geometric Mean'),header=TRUE)
a<-table.element(a,geo)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('harmonic_mean.htm', 'Harmonic Mean', 'click to view the definition of the Harmonic Mean'),header=TRUE)
a<-table.element(a,har)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('quadratic_mean.htm', 'Quadratic Mean', 'click to view the definition of the Quadratic Mean'),header=TRUE)
a<-table.element(a,qua)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
for (j in 1:length(win[,1])) {
a<-table.row.start(a)
mylabel <- paste('Winsorized Mean (',j)
mylabel <- paste(mylabel,'/')
mylabel <- paste(mylabel,length(win[,1]))
mylabel <- paste(mylabel,')')
a<-table.element(a,hyperlink('winsorized_mean.htm', mylabel, 'click to view the definition of the Winsorized Mean'),header=TRUE)
a<-table.element(a,win[j,1])
a<-table.element(a,win[j,2])
a<-table.element(a,win[j,1]/win[j,2])
a<-table.row.end(a)
}
for (j in 1:length(tri[,1])) {
a<-table.row.start(a)
mylabel <- paste('Trimmed Mean (',j)
mylabel <- paste(mylabel,'/')
mylabel <- paste(mylabel,length(tri[,1]))
mylabel <- paste(mylabel,')')
a<-table.element(a,hyperlink('arithmetic_mean.htm', mylabel, 'click to view the definition of the Trimmed Mean'),header=TRUE)
a<-table.element(a,tri[j,1])
a<-table.element(a,tri[j,2])
a<-table.element(a,tri[j,1]/tri[j,2])
a<-table.row.end(a)
}
a<-table.row.start(a)
a<-table.element(a,hyperlink('median_1.htm', 'Median', 'click to view the definition of the Median'),header=TRUE)
a<-table.element(a,median(x))
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('midrange.htm', 'Midrange', 'click to view the definition of the Midrange'),header=TRUE)
a<-table.element(a,midr)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_1.htm','Weighted Average at Xnp',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[1])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_2.htm','Weighted Average at X(n+1)p',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[2])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_3.htm','Empirical Distribution Function',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[3])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_4.htm','Empirical Distribution Function - Averaging',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[4])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_5.htm','Empirical Distribution Function - Interpolation',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[5])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_6.htm','Closest Observation',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[6])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_7.htm','True Basic - Statistics Graphics Toolkit',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[7])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_8.htm','MS Excel (old versions)',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[8])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Number of observations',header=TRUE)
a<-table.element(a,length(x))
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')