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Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationMon, 20 Oct 2008 09:45:56 -0600
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2008/Oct/20/t1224517605u28vnpcvg2qfweb.htm/, Retrieved Sun, 19 May 2024 15:56:52 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=17522, Retrieved Sun, 19 May 2024 15:56:52 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsCentral tendency; reeks 3
Estimated Impact147
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
F     [Univariate Data Series] [Industriële produ...] [2008-10-13 18:32:42] [6743688719638b0cb1c0a6e0bf433315]
-   PD  [Univariate Data Series] [Reeks 3 productie...] [2008-10-20 05:50:12] [6743688719638b0cb1c0a6e0bf433315]
- RMPD      [Central Tendency] [Central tendency ...] [2008-10-20 15:45:56] [9b05d7ef5dbcfba4217d280d9092f628] [Current]
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Dataseries X:
77.9
60
99.5
95
105.6
102.5
93.3
97.3
127
111.7
96.4
133
72.2
95.8
124.1
127.6
110.7
104.6
112.7
115.3
139.4
119
97.4
154
81.5
88.8
127.7
105.1
114.9
106.4
104.5
121.6
141.4
99
126.7
134.1
81.3
88.6
132.7
132.9
134.4
103.7
119.7
115
132.9
108.5
113.9
142
97.7
92.2
128.8
134.9
128.2
114.8
117.9
119.1
120.7
129.1
117.6
129.2
99.1




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'George Udny Yule' @ 72.249.76.132

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 2 seconds \tabularnewline
R Server & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=17522&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=17522&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=17522&T=0

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'George Udny Yule' @ 72.249.76.132







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean112.4360655737702.4317953438691946.2358256656892
Geometric Mean110.729479624982
Harmonic Mean108.86402168207
Quadratic Mean114.003011176798
Winsorized Mean ( 1 / 20 )112.4393442622952.3176529472917948.514314618883
Winsorized Mean ( 2 / 20 )112.6065573770492.2625084836389149.7706674654931
Winsorized Mean ( 3 / 20 )112.6754098360662.2008563357449251.1961676035199
Winsorized Mean ( 4 / 20 )112.3934426229512.1419704794214452.4719848862293
Winsorized Mean ( 5 / 20 )112.9344262295082.0055726806326456.3103134182521
Winsorized Mean ( 6 / 20 )112.9245901639341.9963623417755656.565177473494
Winsorized Mean ( 7 / 20 )113.1885245901641.8989141250803959.6069738463672
Winsorized Mean ( 8 / 20 )113.3196721311481.8704720477110860.583461950056
Winsorized Mean ( 9 / 20 )113.5704918032791.8268404811339762.167711399072
Winsorized Mean ( 10 / 20 )113.6688524590161.7990928816022163.1812029392207
Winsorized Mean ( 11 / 20 )113.1459016393441.6748877684780067.554318425862
Winsorized Mean ( 12 / 20 )113.3032786885251.6426104893564468.9775691940917
Winsorized Mean ( 13 / 20 )113.2606557377051.6289446090280569.5300841477259
Winsorized Mean ( 14 / 20 )113.1918032786891.5960492464736970.9199941848754
Winsorized Mean ( 15 / 20 )113.3885245901641.5258091078718874.3137028119542
Winsorized Mean ( 16 / 20 )113.3885245901641.5175928206155774.7160391442622
Winsorized Mean ( 17 / 20 )113.3327868852461.4741594276385176.8795998318828
Winsorized Mean ( 18 / 20 )114.1295081967211.3261830356539286.0586398169733
Winsorized Mean ( 19 / 20 )113.6934426229511.1462694751131999.1856148064342
Winsorized Mean ( 20 / 20 )113.1360655737700.987268774303745114.595000387364
Trimmed Mean ( 1 / 20 )112.6203389830512.2396443678786450.2849204982142
Trimmed Mean ( 2 / 20 )112.8140350877192.1434802916354652.6312443963004
Trimmed Mean ( 3 / 20 )112.9290909090912.0620666837579454.765004351502
Trimmed Mean ( 4 / 20 )113.0264150943401.9911982501216156.7630144750463
Trimmed Mean ( 5 / 20 )113.2156862745101.9253711076946358.8020074789998
Trimmed Mean ( 6 / 20 )113.2857142857141.8896018729074259.9521602460142
Trimmed Mean ( 7 / 20 )113.3638297872341.8456850835603861.4210033970432
Trimmed Mean ( 8 / 20 )113.3977777777781.8162328892431662.4357032896983
Trimmed Mean ( 9 / 20 )113.4116279069771.7838894175558763.5754810757066
Trimmed Mean ( 10 / 20 )113.3853658536591.7510190795007764.753929400921
Trimmed Mean ( 11 / 20 )113.3410256410261.7124562228265666.1862324596808
Trimmed Mean ( 12 / 20 )113.3702702702701.6906911040702767.0555786313276
Trimmed Mean ( 13 / 20 )113.381.6657085201047668.0671309725122
Trimmed Mean ( 14 / 20 )113.3969696969701.6308489426202469.5324789031522
Trimmed Mean ( 15 / 20 )113.4258064516131.5872676715402871.459784940712
Trimmed Mean ( 16 / 20 )113.4310344827591.5421827619124173.5522645461918
Trimmed Mean ( 17 / 20 )113.4370370370371.4739248159913476.9625667512362
Trimmed Mean ( 18 / 20 )113.4521.3825474072643382.0601155547274
Trimmed Mean ( 19 / 20 )113.3521739130431.2969844862289187.396707606445
Trimmed Mean ( 20 / 20 )113.31.2367776872255891.6090265617276
Median114.8
Midrange107
Midmean - Weighted Average at Xnp112.95
Midmean - Weighted Average at X(n+1)p113.425806451613
Midmean - Empirical Distribution Function113.425806451613
Midmean - Empirical Distribution Function - Averaging113.425806451613
Midmean - Empirical Distribution Function - Interpolation113.425806451613
Midmean - Closest Observation112.934375
Midmean - True Basic - Statistics Graphics Toolkit113.425806451613
Midmean - MS Excel (old versions)113.425806451613
Number of observations61

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 112.436065573770 & 2.43179534386919 & 46.2358256656892 \tabularnewline
Geometric Mean & 110.729479624982 &  &  \tabularnewline
Harmonic Mean & 108.86402168207 &  &  \tabularnewline
Quadratic Mean & 114.003011176798 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 112.439344262295 & 2.31765294729179 & 48.514314618883 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 112.606557377049 & 2.26250848363891 & 49.7706674654931 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 112.675409836066 & 2.20085633574492 & 51.1961676035199 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 112.393442622951 & 2.14197047942144 & 52.4719848862293 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 112.934426229508 & 2.00557268063264 & 56.3103134182521 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 112.924590163934 & 1.99636234177556 & 56.565177473494 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 113.188524590164 & 1.89891412508039 & 59.6069738463672 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 113.319672131148 & 1.87047204771108 & 60.583461950056 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 113.570491803279 & 1.82684048113397 & 62.167711399072 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 113.668852459016 & 1.79909288160221 & 63.1812029392207 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 113.145901639344 & 1.67488776847800 & 67.554318425862 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 113.303278688525 & 1.64261048935644 & 68.9775691940917 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 113.260655737705 & 1.62894460902805 & 69.5300841477259 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 113.191803278689 & 1.59604924647369 & 70.9199941848754 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 113.388524590164 & 1.52580910787188 & 74.3137028119542 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 113.388524590164 & 1.51759282061557 & 74.7160391442622 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 113.332786885246 & 1.47415942763851 & 76.8795998318828 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 114.129508196721 & 1.32618303565392 & 86.0586398169733 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 113.693442622951 & 1.14626947511319 & 99.1856148064342 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 113.136065573770 & 0.987268774303745 & 114.595000387364 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 112.620338983051 & 2.23964436787864 & 50.2849204982142 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 112.814035087719 & 2.14348029163546 & 52.6312443963004 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 112.929090909091 & 2.06206668375794 & 54.765004351502 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 113.026415094340 & 1.99119825012161 & 56.7630144750463 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 113.215686274510 & 1.92537110769463 & 58.8020074789998 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 113.285714285714 & 1.88960187290742 & 59.9521602460142 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 113.363829787234 & 1.84568508356038 & 61.4210033970432 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 113.397777777778 & 1.81623288924316 & 62.4357032896983 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 113.411627906977 & 1.78388941755587 & 63.5754810757066 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 113.385365853659 & 1.75101907950077 & 64.753929400921 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 113.341025641026 & 1.71245622282656 & 66.1862324596808 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 113.370270270270 & 1.69069110407027 & 67.0555786313276 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 113.38 & 1.66570852010476 & 68.0671309725122 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 113.396969696970 & 1.63084894262024 & 69.5324789031522 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 113.425806451613 & 1.58726767154028 & 71.459784940712 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 113.431034482759 & 1.54218276191241 & 73.5522645461918 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 113.437037037037 & 1.47392481599134 & 76.9625667512362 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 113.452 & 1.38254740726433 & 82.0601155547274 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 113.352173913043 & 1.29698448622891 & 87.396707606445 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 113.3 & 1.23677768722558 & 91.6090265617276 \tabularnewline
Median & 114.8 &  &  \tabularnewline
Midrange & 107 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 112.95 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 113.425806451613 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 113.425806451613 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 113.425806451613 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 113.425806451613 &  &  \tabularnewline
Midmean - Closest Observation & 112.934375 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 113.425806451613 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 113.425806451613 &  &  \tabularnewline
Number of observations & 61 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=17522&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]112.436065573770[/C][C]2.43179534386919[/C][C]46.2358256656892[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]110.729479624982[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]108.86402168207[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]114.003011176798[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]112.439344262295[/C][C]2.31765294729179[/C][C]48.514314618883[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]112.606557377049[/C][C]2.26250848363891[/C][C]49.7706674654931[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]112.675409836066[/C][C]2.20085633574492[/C][C]51.1961676035199[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]112.393442622951[/C][C]2.14197047942144[/C][C]52.4719848862293[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]112.934426229508[/C][C]2.00557268063264[/C][C]56.3103134182521[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]112.924590163934[/C][C]1.99636234177556[/C][C]56.565177473494[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]113.188524590164[/C][C]1.89891412508039[/C][C]59.6069738463672[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]113.319672131148[/C][C]1.87047204771108[/C][C]60.583461950056[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]113.570491803279[/C][C]1.82684048113397[/C][C]62.167711399072[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]113.668852459016[/C][C]1.79909288160221[/C][C]63.1812029392207[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]113.145901639344[/C][C]1.67488776847800[/C][C]67.554318425862[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]113.303278688525[/C][C]1.64261048935644[/C][C]68.9775691940917[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]113.260655737705[/C][C]1.62894460902805[/C][C]69.5300841477259[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]113.191803278689[/C][C]1.59604924647369[/C][C]70.9199941848754[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]113.388524590164[/C][C]1.52580910787188[/C][C]74.3137028119542[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]113.388524590164[/C][C]1.51759282061557[/C][C]74.7160391442622[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]113.332786885246[/C][C]1.47415942763851[/C][C]76.8795998318828[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]114.129508196721[/C][C]1.32618303565392[/C][C]86.0586398169733[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]113.693442622951[/C][C]1.14626947511319[/C][C]99.1856148064342[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]113.136065573770[/C][C]0.987268774303745[/C][C]114.595000387364[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]112.620338983051[/C][C]2.23964436787864[/C][C]50.2849204982142[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]112.814035087719[/C][C]2.14348029163546[/C][C]52.6312443963004[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]112.929090909091[/C][C]2.06206668375794[/C][C]54.765004351502[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]113.026415094340[/C][C]1.99119825012161[/C][C]56.7630144750463[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]113.215686274510[/C][C]1.92537110769463[/C][C]58.8020074789998[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]113.285714285714[/C][C]1.88960187290742[/C][C]59.9521602460142[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]113.363829787234[/C][C]1.84568508356038[/C][C]61.4210033970432[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]113.397777777778[/C][C]1.81623288924316[/C][C]62.4357032896983[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]113.411627906977[/C][C]1.78388941755587[/C][C]63.5754810757066[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]113.385365853659[/C][C]1.75101907950077[/C][C]64.753929400921[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]113.341025641026[/C][C]1.71245622282656[/C][C]66.1862324596808[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]113.370270270270[/C][C]1.69069110407027[/C][C]67.0555786313276[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]113.38[/C][C]1.66570852010476[/C][C]68.0671309725122[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]113.396969696970[/C][C]1.63084894262024[/C][C]69.5324789031522[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]113.425806451613[/C][C]1.58726767154028[/C][C]71.459784940712[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]113.431034482759[/C][C]1.54218276191241[/C][C]73.5522645461918[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]113.437037037037[/C][C]1.47392481599134[/C][C]76.9625667512362[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]113.452[/C][C]1.38254740726433[/C][C]82.0601155547274[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]113.352173913043[/C][C]1.29698448622891[/C][C]87.396707606445[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]113.3[/C][C]1.23677768722558[/C][C]91.6090265617276[/C][/ROW]
[ROW][C]Median[/C][C]114.8[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]107[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]112.95[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]113.425806451613[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]113.425806451613[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]113.425806451613[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]113.425806451613[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]112.934375[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]113.425806451613[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]113.425806451613[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]61[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=17522&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=17522&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 Mean112.4360655737702.4317953438691946.2358256656892
Geometric Mean110.729479624982
Harmonic Mean108.86402168207
Quadratic Mean114.003011176798
Winsorized Mean ( 1 / 20 )112.4393442622952.3176529472917948.514314618883
Winsorized Mean ( 2 / 20 )112.6065573770492.2625084836389149.7706674654931
Winsorized Mean ( 3 / 20 )112.6754098360662.2008563357449251.1961676035199
Winsorized Mean ( 4 / 20 )112.3934426229512.1419704794214452.4719848862293
Winsorized Mean ( 5 / 20 )112.9344262295082.0055726806326456.3103134182521
Winsorized Mean ( 6 / 20 )112.9245901639341.9963623417755656.565177473494
Winsorized Mean ( 7 / 20 )113.1885245901641.8989141250803959.6069738463672
Winsorized Mean ( 8 / 20 )113.3196721311481.8704720477110860.583461950056
Winsorized Mean ( 9 / 20 )113.5704918032791.8268404811339762.167711399072
Winsorized Mean ( 10 / 20 )113.6688524590161.7990928816022163.1812029392207
Winsorized Mean ( 11 / 20 )113.1459016393441.6748877684780067.554318425862
Winsorized Mean ( 12 / 20 )113.3032786885251.6426104893564468.9775691940917
Winsorized Mean ( 13 / 20 )113.2606557377051.6289446090280569.5300841477259
Winsorized Mean ( 14 / 20 )113.1918032786891.5960492464736970.9199941848754
Winsorized Mean ( 15 / 20 )113.3885245901641.5258091078718874.3137028119542
Winsorized Mean ( 16 / 20 )113.3885245901641.5175928206155774.7160391442622
Winsorized Mean ( 17 / 20 )113.3327868852461.4741594276385176.8795998318828
Winsorized Mean ( 18 / 20 )114.1295081967211.3261830356539286.0586398169733
Winsorized Mean ( 19 / 20 )113.6934426229511.1462694751131999.1856148064342
Winsorized Mean ( 20 / 20 )113.1360655737700.987268774303745114.595000387364
Trimmed Mean ( 1 / 20 )112.6203389830512.2396443678786450.2849204982142
Trimmed Mean ( 2 / 20 )112.8140350877192.1434802916354652.6312443963004
Trimmed Mean ( 3 / 20 )112.9290909090912.0620666837579454.765004351502
Trimmed Mean ( 4 / 20 )113.0264150943401.9911982501216156.7630144750463
Trimmed Mean ( 5 / 20 )113.2156862745101.9253711076946358.8020074789998
Trimmed Mean ( 6 / 20 )113.2857142857141.8896018729074259.9521602460142
Trimmed Mean ( 7 / 20 )113.3638297872341.8456850835603861.4210033970432
Trimmed Mean ( 8 / 20 )113.3977777777781.8162328892431662.4357032896983
Trimmed Mean ( 9 / 20 )113.4116279069771.7838894175558763.5754810757066
Trimmed Mean ( 10 / 20 )113.3853658536591.7510190795007764.753929400921
Trimmed Mean ( 11 / 20 )113.3410256410261.7124562228265666.1862324596808
Trimmed Mean ( 12 / 20 )113.3702702702701.6906911040702767.0555786313276
Trimmed Mean ( 13 / 20 )113.381.6657085201047668.0671309725122
Trimmed Mean ( 14 / 20 )113.3969696969701.6308489426202469.5324789031522
Trimmed Mean ( 15 / 20 )113.4258064516131.5872676715402871.459784940712
Trimmed Mean ( 16 / 20 )113.4310344827591.5421827619124173.5522645461918
Trimmed Mean ( 17 / 20 )113.4370370370371.4739248159913476.9625667512362
Trimmed Mean ( 18 / 20 )113.4521.3825474072643382.0601155547274
Trimmed Mean ( 19 / 20 )113.3521739130431.2969844862289187.396707606445
Trimmed Mean ( 20 / 20 )113.31.2367776872255891.6090265617276
Median114.8
Midrange107
Midmean - Weighted Average at Xnp112.95
Midmean - Weighted Average at X(n+1)p113.425806451613
Midmean - Empirical Distribution Function113.425806451613
Midmean - Empirical Distribution Function - Averaging113.425806451613
Midmean - Empirical Distribution Function - Interpolation113.425806451613
Midmean - Closest Observation112.934375
Midmean - True Basic - Statistics Graphics Toolkit113.425806451613
Midmean - MS Excel (old versions)113.425806451613
Number of observations61



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')