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Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationWed, 12 Dec 2007 02:50:21 -0700
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2007/Dec/12/t11974524433r9xkio7t6o698m.htm/, Retrieved Thu, 02 May 2024 15:46:19 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=3185, Retrieved Thu, 02 May 2024 15:46:19 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact224
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [Paper: Central te...] [2007-12-12 09:50:21] [be66efe1fb01584897056fbc96e4e155] [Current]
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Dataseries X:
0.9383
0.9217
0.9095
0.8920
0.8742
0.8532
0.8607
0.9005
0.9111
0.9059
0.8883
0.8924
0.8833
0.8700
0.8758
0.8858
0.9170
0.9554
0.9922
0.9778
0.9808
0.9811
1.0014
1.0183
1.0622
1.0773
1.0807
1.0848
1.1582
1.1663
1.1372
1.1139
1.1222
1.1692
1.1702
1.2286
1.2613
1.2646
1.2262
1.1985
1.2007
1.2138
1.2266
1.2176
1.2218
1.2490
1.2991
1.3408
1.3119
1.3014
1.3201
1.2938
1.2694
1.2165
1.2037
1.2292
1.2256
1.2015
1.1786
1.1856




Summary of compuational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\begin{tabular}{lllllllll}
\hline
Summary of compuational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 3 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=3185&T=0

[TABLE]
[ROW][C]Summary of compuational 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]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=3185&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=3185&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 compuational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean1.091913333333330.019966574252542654.6870644669696
Geometric Mean1.08086379968339
Harmonic Mean1.06964630275326
Quadratic Mean1.10263135664948
Winsorized Mean ( 1 / 20 )1.091693333333330.019871537273119754.93753796341
Winsorized Mean ( 2 / 20 )1.091730.019759077053058455.2520746322519
Winsorized Mean ( 3 / 20 )1.0914150.019622210093534455.6214103710788
Winsorized Mean ( 4 / 20 )1.091368333333330.019574552471836855.7544462333714
Winsorized Mean ( 5 / 20 )1.091551666666670.019380516672849356.3221138575655
Winsorized Mean ( 6 / 20 )1.089361666666670.01892219948331257.5705624299863
Winsorized Mean ( 7 / 20 )1.089093333333330.018779670891544657.9932065701796
Winsorized Mean ( 8 / 20 )1.089146666666670.018621383198920958.4890314018016
Winsorized Mean ( 9 / 20 )1.087361666666670.018328095824801059.3275852036567
Winsorized Mean ( 10 / 20 )1.085411666666670.017610902679114961.6329376434448
Winsorized Mean ( 11 / 20 )1.086291666666670.017420701091132762.356369068269
Winsorized Mean ( 12 / 20 )1.086611666666670.01723961131400663.0299399954493
Winsorized Mean ( 13 / 20 )1.086871666666670.017167424495093263.3101177743531
Winsorized Mean ( 14 / 20 )1.088108333333330.016910639730983364.3445990597106
Winsorized Mean ( 15 / 20 )1.088333333333330.016579524617275465.6432170678357
Winsorized Mean ( 16 / 20 )1.091640.015682757669988869.607655934709
Winsorized Mean ( 17 / 20 )1.096173333333330.014849097419101273.8208729052626
Winsorized Mean ( 18 / 20 )1.102083333333330.01367919988216480.56635935047
Winsorized Mean ( 19 / 20 )1.0998350.013096419233951483.9798253517089
Winsorized Mean ( 20 / 20 )1.099201666666670.012982749635131784.6663224323602
Trimmed Mean ( 1 / 20 )1.091737931034480.019771382832625955.2180866799536
Trimmed Mean ( 2 / 20 )1.091785714285710.019629792562064555.6188105826263
Trimmed Mean ( 3 / 20 )1.091816666666670.019508041981620655.9675167654095
Trimmed Mean ( 4 / 20 )1.091971153846150.019397892613171056.2932879164778
Trimmed Mean ( 5 / 20 )1.0921520.019254004882101856.7233677714108
Trimmed Mean ( 6 / 20 )1.092302083333330.019111164278634657.1551825628163
Trimmed Mean ( 7 / 20 )1.092941304347830.019034017240964757.4204221059343
Trimmed Mean ( 8 / 20 )1.093690909090910.018938236883613357.7504081194195
Trimmed Mean ( 9 / 20 )1.094502380952380.018817835242308958.1630334658032
Trimmed Mean ( 10 / 20 )1.09569250.018691275006756658.6205328210046
Trimmed Mean ( 11 / 20 )1.097315789473680.018648942371712158.840644557847
Trimmed Mean ( 12 / 20 )1.098986111111110.018580732960399659.1465424670458
Trimmed Mean ( 13 / 20 )1.100805882352940.018468649034754059.6040284420079
Trimmed Mean ( 14 / 20 )1.1028156250.018262833594894860.3857894926164
Trimmed Mean ( 15 / 20 )1.104916666666670.017975940551117761.4664174886785
Trimmed Mean ( 16 / 20 )1.107285714285710.017583502755736662.9729883554892
Trimmed Mean ( 17 / 20 )1.109542307692310.017226185052973664.4102164396974
Trimmed Mean ( 18 / 20 )1.111508333333330.016896390272098265.7837748438388
Trimmed Mean ( 19 / 20 )1.112936363636360.016723043884799366.5510639871002
Trimmed Mean ( 20 / 20 )1.1150050.016497158407626367.5877004056986
Median1.1297
Midrange1.097
Midmean - Weighted Average at Xnp1.09885483870968
Midmean - Weighted Average at X(n+1)p1.10491666666667
Midmean - Empirical Distribution Function1.09885483870968
Midmean - Empirical Distribution Function - Averaging1.10491666666667
Midmean - Empirical Distribution Function - Interpolation1.10491666666667
Midmean - Closest Observation1.09885483870968
Midmean - True Basic - Statistics Graphics Toolkit1.10491666666667
Midmean - MS Excel (old versions)1.102815625
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 1.09191333333333 & 0.0199665742525426 & 54.6870644669696 \tabularnewline
Geometric Mean & 1.08086379968339 &  &  \tabularnewline
Harmonic Mean & 1.06964630275326 &  &  \tabularnewline
Quadratic Mean & 1.10263135664948 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 1.09169333333333 & 0.0198715372731197 & 54.93753796341 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 1.09173 & 0.0197590770530584 & 55.2520746322519 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 1.091415 & 0.0196222100935344 & 55.6214103710788 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 1.09136833333333 & 0.0195745524718368 & 55.7544462333714 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 1.09155166666667 & 0.0193805166728493 & 56.3221138575655 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 1.08936166666667 & 0.018922199483312 & 57.5705624299863 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 1.08909333333333 & 0.0187796708915446 & 57.9932065701796 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 1.08914666666667 & 0.0186213831989209 & 58.4890314018016 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 1.08736166666667 & 0.0183280958248010 & 59.3275852036567 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 1.08541166666667 & 0.0176109026791149 & 61.6329376434448 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 1.08629166666667 & 0.0174207010911327 & 62.356369068269 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 1.08661166666667 & 0.017239611314006 & 63.0299399954493 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 1.08687166666667 & 0.0171674244950932 & 63.3101177743531 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 1.08810833333333 & 0.0169106397309833 & 64.3445990597106 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 1.08833333333333 & 0.0165795246172754 & 65.6432170678357 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 1.09164 & 0.0156827576699888 & 69.607655934709 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 1.09617333333333 & 0.0148490974191012 & 73.8208729052626 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 1.10208333333333 & 0.013679199882164 & 80.56635935047 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 1.099835 & 0.0130964192339514 & 83.9798253517089 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 1.09920166666667 & 0.0129827496351317 & 84.6663224323602 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 1.09173793103448 & 0.0197713828326259 & 55.2180866799536 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 1.09178571428571 & 0.0196297925620645 & 55.6188105826263 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 1.09181666666667 & 0.0195080419816206 & 55.9675167654095 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 1.09197115384615 & 0.0193978926131710 & 56.2932879164778 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 1.092152 & 0.0192540048821018 & 56.7233677714108 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 1.09230208333333 & 0.0191111642786346 & 57.1551825628163 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 1.09294130434783 & 0.0190340172409647 & 57.4204221059343 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 1.09369090909091 & 0.0189382368836133 & 57.7504081194195 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 1.09450238095238 & 0.0188178352423089 & 58.1630334658032 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 1.0956925 & 0.0186912750067566 & 58.6205328210046 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 1.09731578947368 & 0.0186489423717121 & 58.840644557847 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 1.09898611111111 & 0.0185807329603996 & 59.1465424670458 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 1.10080588235294 & 0.0184686490347540 & 59.6040284420079 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 1.102815625 & 0.0182628335948948 & 60.3857894926164 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 1.10491666666667 & 0.0179759405511177 & 61.4664174886785 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 1.10728571428571 & 0.0175835027557366 & 62.9729883554892 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 1.10954230769231 & 0.0172261850529736 & 64.4102164396974 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 1.11150833333333 & 0.0168963902720982 & 65.7837748438388 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 1.11293636363636 & 0.0167230438847993 & 66.5510639871002 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 1.115005 & 0.0164971584076263 & 67.5877004056986 \tabularnewline
Median & 1.1297 &  &  \tabularnewline
Midrange & 1.097 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 1.09885483870968 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 1.10491666666667 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 1.09885483870968 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 1.10491666666667 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 1.10491666666667 &  &  \tabularnewline
Midmean - Closest Observation & 1.09885483870968 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 1.10491666666667 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 1.102815625 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=3185&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]1.09191333333333[/C][C]0.0199665742525426[/C][C]54.6870644669696[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]1.08086379968339[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]1.06964630275326[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]1.10263135664948[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]1.09169333333333[/C][C]0.0198715372731197[/C][C]54.93753796341[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]1.09173[/C][C]0.0197590770530584[/C][C]55.2520746322519[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]1.091415[/C][C]0.0196222100935344[/C][C]55.6214103710788[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]1.09136833333333[/C][C]0.0195745524718368[/C][C]55.7544462333714[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]1.09155166666667[/C][C]0.0193805166728493[/C][C]56.3221138575655[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]1.08936166666667[/C][C]0.018922199483312[/C][C]57.5705624299863[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]1.08909333333333[/C][C]0.0187796708915446[/C][C]57.9932065701796[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]1.08914666666667[/C][C]0.0186213831989209[/C][C]58.4890314018016[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]1.08736166666667[/C][C]0.0183280958248010[/C][C]59.3275852036567[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]1.08541166666667[/C][C]0.0176109026791149[/C][C]61.6329376434448[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]1.08629166666667[/C][C]0.0174207010911327[/C][C]62.356369068269[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]1.08661166666667[/C][C]0.017239611314006[/C][C]63.0299399954493[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]1.08687166666667[/C][C]0.0171674244950932[/C][C]63.3101177743531[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]1.08810833333333[/C][C]0.0169106397309833[/C][C]64.3445990597106[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]1.08833333333333[/C][C]0.0165795246172754[/C][C]65.6432170678357[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]1.09164[/C][C]0.0156827576699888[/C][C]69.607655934709[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]1.09617333333333[/C][C]0.0148490974191012[/C][C]73.8208729052626[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]1.10208333333333[/C][C]0.013679199882164[/C][C]80.56635935047[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]1.099835[/C][C]0.0130964192339514[/C][C]83.9798253517089[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]1.09920166666667[/C][C]0.0129827496351317[/C][C]84.6663224323602[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]1.09173793103448[/C][C]0.0197713828326259[/C][C]55.2180866799536[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]1.09178571428571[/C][C]0.0196297925620645[/C][C]55.6188105826263[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]1.09181666666667[/C][C]0.0195080419816206[/C][C]55.9675167654095[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]1.09197115384615[/C][C]0.0193978926131710[/C][C]56.2932879164778[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]1.092152[/C][C]0.0192540048821018[/C][C]56.7233677714108[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]1.09230208333333[/C][C]0.0191111642786346[/C][C]57.1551825628163[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]1.09294130434783[/C][C]0.0190340172409647[/C][C]57.4204221059343[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]1.09369090909091[/C][C]0.0189382368836133[/C][C]57.7504081194195[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]1.09450238095238[/C][C]0.0188178352423089[/C][C]58.1630334658032[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]1.0956925[/C][C]0.0186912750067566[/C][C]58.6205328210046[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]1.09731578947368[/C][C]0.0186489423717121[/C][C]58.840644557847[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]1.09898611111111[/C][C]0.0185807329603996[/C][C]59.1465424670458[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]1.10080588235294[/C][C]0.0184686490347540[/C][C]59.6040284420079[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]1.102815625[/C][C]0.0182628335948948[/C][C]60.3857894926164[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]1.10491666666667[/C][C]0.0179759405511177[/C][C]61.4664174886785[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]1.10728571428571[/C][C]0.0175835027557366[/C][C]62.9729883554892[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]1.10954230769231[/C][C]0.0172261850529736[/C][C]64.4102164396974[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]1.11150833333333[/C][C]0.0168963902720982[/C][C]65.7837748438388[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]1.11293636363636[/C][C]0.0167230438847993[/C][C]66.5510639871002[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]1.115005[/C][C]0.0164971584076263[/C][C]67.5877004056986[/C][/ROW]
[ROW][C]Median[/C][C]1.1297[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]1.097[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]1.09885483870968[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]1.10491666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]1.09885483870968[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]1.10491666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]1.10491666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]1.09885483870968[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]1.10491666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]1.102815625[/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=3185&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=3185&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 Mean1.091913333333330.019966574252542654.6870644669696
Geometric Mean1.08086379968339
Harmonic Mean1.06964630275326
Quadratic Mean1.10263135664948
Winsorized Mean ( 1 / 20 )1.091693333333330.019871537273119754.93753796341
Winsorized Mean ( 2 / 20 )1.091730.019759077053058455.2520746322519
Winsorized Mean ( 3 / 20 )1.0914150.019622210093534455.6214103710788
Winsorized Mean ( 4 / 20 )1.091368333333330.019574552471836855.7544462333714
Winsorized Mean ( 5 / 20 )1.091551666666670.019380516672849356.3221138575655
Winsorized Mean ( 6 / 20 )1.089361666666670.01892219948331257.5705624299863
Winsorized Mean ( 7 / 20 )1.089093333333330.018779670891544657.9932065701796
Winsorized Mean ( 8 / 20 )1.089146666666670.018621383198920958.4890314018016
Winsorized Mean ( 9 / 20 )1.087361666666670.018328095824801059.3275852036567
Winsorized Mean ( 10 / 20 )1.085411666666670.017610902679114961.6329376434448
Winsorized Mean ( 11 / 20 )1.086291666666670.017420701091132762.356369068269
Winsorized Mean ( 12 / 20 )1.086611666666670.01723961131400663.0299399954493
Winsorized Mean ( 13 / 20 )1.086871666666670.017167424495093263.3101177743531
Winsorized Mean ( 14 / 20 )1.088108333333330.016910639730983364.3445990597106
Winsorized Mean ( 15 / 20 )1.088333333333330.016579524617275465.6432170678357
Winsorized Mean ( 16 / 20 )1.091640.015682757669988869.607655934709
Winsorized Mean ( 17 / 20 )1.096173333333330.014849097419101273.8208729052626
Winsorized Mean ( 18 / 20 )1.102083333333330.01367919988216480.56635935047
Winsorized Mean ( 19 / 20 )1.0998350.013096419233951483.9798253517089
Winsorized Mean ( 20 / 20 )1.099201666666670.012982749635131784.6663224323602
Trimmed Mean ( 1 / 20 )1.091737931034480.019771382832625955.2180866799536
Trimmed Mean ( 2 / 20 )1.091785714285710.019629792562064555.6188105826263
Trimmed Mean ( 3 / 20 )1.091816666666670.019508041981620655.9675167654095
Trimmed Mean ( 4 / 20 )1.091971153846150.019397892613171056.2932879164778
Trimmed Mean ( 5 / 20 )1.0921520.019254004882101856.7233677714108
Trimmed Mean ( 6 / 20 )1.092302083333330.019111164278634657.1551825628163
Trimmed Mean ( 7 / 20 )1.092941304347830.019034017240964757.4204221059343
Trimmed Mean ( 8 / 20 )1.093690909090910.018938236883613357.7504081194195
Trimmed Mean ( 9 / 20 )1.094502380952380.018817835242308958.1630334658032
Trimmed Mean ( 10 / 20 )1.09569250.018691275006756658.6205328210046
Trimmed Mean ( 11 / 20 )1.097315789473680.018648942371712158.840644557847
Trimmed Mean ( 12 / 20 )1.098986111111110.018580732960399659.1465424670458
Trimmed Mean ( 13 / 20 )1.100805882352940.018468649034754059.6040284420079
Trimmed Mean ( 14 / 20 )1.1028156250.018262833594894860.3857894926164
Trimmed Mean ( 15 / 20 )1.104916666666670.017975940551117761.4664174886785
Trimmed Mean ( 16 / 20 )1.107285714285710.017583502755736662.9729883554892
Trimmed Mean ( 17 / 20 )1.109542307692310.017226185052973664.4102164396974
Trimmed Mean ( 18 / 20 )1.111508333333330.016896390272098265.7837748438388
Trimmed Mean ( 19 / 20 )1.112936363636360.016723043884799366.5510639871002
Trimmed Mean ( 20 / 20 )1.1150050.016497158407626367.5877004056986
Median1.1297
Midrange1.097
Midmean - Weighted Average at Xnp1.09885483870968
Midmean - Weighted Average at X(n+1)p1.10491666666667
Midmean - Empirical Distribution Function1.09885483870968
Midmean - Empirical Distribution Function - Averaging1.10491666666667
Midmean - Empirical Distribution Function - Interpolation1.10491666666667
Midmean - Closest Observation1.09885483870968
Midmean - True Basic - Statistics Graphics Toolkit1.10491666666667
Midmean - MS Excel (old versions)1.102815625
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')