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Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationTue, 06 Nov 2007 13:10:29 -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/Nov/06/oquqiw00da30ppc1194379673.htm/, Retrieved Fri, 03 May 2024 15:13:04 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=561, Retrieved Fri, 03 May 2024 15:13:04 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact249
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [Central Tendency ...] [2007-11-06 20:10:29] [d9ccf6bb4f7743d5d52b9a9a992ccbd5] [Current]
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Dataseries X:
105.1
113.3
99.1
100.3
93.5
98.8
106.2
98.3
102.1
117.1
101.5
80.5
105.9
109.5
97.2
114.5
93.5
100.9
121.1
116.5
109.3
118.1
108.3
105.4
116.2
111.2
105.8
122.7
99.5
107.9
124.6
115
110.3
132.7
99.7
96.5
118.7
112.9
130.5
137.9
115
116.8
140.9
120.7
134.2
147.3
112.4
107.1
128.4
137.7
135
151
137.4
132.4
161.3
139.8
146
154.6
142.1
120.5




Summary of compuational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Herman Ole Andreas Wold' @ 193.190.124.10:1001

\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 & 'Herman Ole Andreas Wold' @ 193.190.124.10:1001 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=561&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]'Herman Ole Andreas Wold' @ 193.190.124.10:1001[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=561&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=561&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'Herman Ole Andreas Wold' @ 193.190.124.10:1001







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean117.3116666666672.2459003349438652.2336921373669
Geometric Mean116.080345234446
Harmonic Mean114.885155408247
Quadratic Mean118.573298708717
Winsorized Mean ( 1 / 20 )117.4166666666672.1604223361262454.3489412709932
Winsorized Mean ( 2 / 20 )117.2966666666672.1267929845771855.1518965490598
Winsorized Mean ( 3 / 20 )117.2616666666672.0518519837182557.1491840528242
Winsorized Mean ( 4 / 20 )117.2216666666672.0227311229762857.952174332585
Winsorized Mean ( 5 / 20 )116.9883333333331.9324716933436360.5381873050446
Winsorized Mean ( 6 / 20 )116.9183333333331.8982633926094961.5922604779356
Winsorized Mean ( 7 / 20 )116.8251.8654767570445562.6247416693009
Winsorized Mean ( 8 / 20 )116.6251.8051317697649464.6074718496517
Winsorized Mean ( 9 / 20 )116.6251.794339223387764.99607124444
Winsorized Mean ( 10 / 20 )116.6751.7685555806385965.9719158828307
Winsorized Mean ( 11 / 20 )116.3451.6657677095402369.8446724196093
Winsorized Mean ( 12 / 20 )116.3051.6168296120340871.9339868186112
Winsorized Mean ( 13 / 20 )116.111.5364529184525975.5701646340965
Winsorized Mean ( 14 / 20 )116.741.4205994596855182.1765763770204
Winsorized Mean ( 15 / 20 )116.341.3226198107702087.9617854296705
Winsorized Mean ( 16 / 20 )115.8866666666671.2075339455912595.9696968269694
Winsorized Mean ( 17 / 20 )114.8383333333331.02103606311656112.472357717520
Winsorized Mean ( 18 / 20 )114.3583333333330.917354005277198124.661071598829
Winsorized Mean ( 19 / 20 )114.1366666666670.797938610649559143.039408224342
Winsorized Mean ( 20 / 20 )114.270.738812224333665154.667175550675
Trimmed Mean ( 1 / 20 )117.1879310344832.0989613390629355.8313909139463
Trimmed Mean ( 2 / 20 )116.9428571428572.0226715924878957.8160377478862
Trimmed Mean ( 3 / 20 )116.7462962962961.9505911465105459.8517513550426
Trimmed Mean ( 4 / 20 )116.5480769230771.8970356536916261.4369459510553
Trimmed Mean ( 5 / 20 )116.3461.8405926507846563.2111618778884
Trimmed Mean ( 6 / 20 )116.1854166666671.8000566125438664.5454236589104
Trimmed Mean ( 7 / 20 )116.0260869565221.7577528330383166.0081922644202
Trimmed Mean ( 8 / 20 )115.8704545454551.7116241670016267.6962015256149
Trimmed Mean ( 9 / 20 )115.7357142857141.6676286007854569.4013728423723
Trimmed Mean ( 10 / 20 )115.58751.6109409079709871.7515455893323
Trimmed Mean ( 11 / 20 )115.4157894736841.5407666817229974.9080252336573
Trimmed Mean ( 12 / 20 )115.2751.4754142544459278.1305993571889
Trimmed Mean ( 13 / 20 )115.1235294117651.3984142969356382.3243366890893
Trimmed Mean ( 14 / 20 )114.981251.3148304004147687.4494915570323
Trimmed Mean ( 15 / 20 )114.731.2280266386717293.426312090507
Trimmed Mean ( 16 / 20 )114.51.13551377551817100.83541254068
Trimmed Mean ( 17 / 20 )114.31.04133050986189109.763421812311
Trimmed Mean ( 18 / 20 )114.2208333333330.978055953444195116.783536699621
Trimmed Mean ( 19 / 20 )114.20.920897360215539124.009476988045
Trimmed Mean ( 20 / 20 )114.210.87926105338517129.893163765516
Median114.75
Midrange120.9
Midmean - Weighted Average at Xnp114.419354838710
Midmean - Weighted Average at X(n+1)p114.73
Midmean - Empirical Distribution Function114.419354838710
Midmean - Empirical Distribution Function - Averaging114.73
Midmean - Empirical Distribution Function - Interpolation114.73
Midmean - Closest Observation114.419354838710
Midmean - True Basic - Statistics Graphics Toolkit114.73
Midmean - MS Excel (old versions)114.98125
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 117.311666666667 & 2.24590033494386 & 52.2336921373669 \tabularnewline
Geometric Mean & 116.080345234446 &  &  \tabularnewline
Harmonic Mean & 114.885155408247 &  &  \tabularnewline
Quadratic Mean & 118.573298708717 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 117.416666666667 & 2.16042233612624 & 54.3489412709932 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 117.296666666667 & 2.12679298457718 & 55.1518965490598 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 117.261666666667 & 2.05185198371825 & 57.1491840528242 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 117.221666666667 & 2.02273112297628 & 57.952174332585 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 116.988333333333 & 1.93247169334363 & 60.5381873050446 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 116.918333333333 & 1.89826339260949 & 61.5922604779356 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 116.825 & 1.86547675704455 & 62.6247416693009 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 116.625 & 1.80513176976494 & 64.6074718496517 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 116.625 & 1.7943392233877 & 64.99607124444 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 116.675 & 1.76855558063859 & 65.9719158828307 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 116.345 & 1.66576770954023 & 69.8446724196093 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 116.305 & 1.61682961203408 & 71.9339868186112 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 116.11 & 1.53645291845259 & 75.5701646340965 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 116.74 & 1.42059945968551 & 82.1765763770204 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 116.34 & 1.32261981077020 & 87.9617854296705 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 115.886666666667 & 1.20753394559125 & 95.9696968269694 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 114.838333333333 & 1.02103606311656 & 112.472357717520 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 114.358333333333 & 0.917354005277198 & 124.661071598829 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 114.136666666667 & 0.797938610649559 & 143.039408224342 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 114.27 & 0.738812224333665 & 154.667175550675 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 117.187931034483 & 2.09896133906293 & 55.8313909139463 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 116.942857142857 & 2.02267159248789 & 57.8160377478862 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 116.746296296296 & 1.95059114651054 & 59.8517513550426 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 116.548076923077 & 1.89703565369162 & 61.4369459510553 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 116.346 & 1.84059265078465 & 63.2111618778884 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 116.185416666667 & 1.80005661254386 & 64.5454236589104 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 116.026086956522 & 1.75775283303831 & 66.0081922644202 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 115.870454545455 & 1.71162416700162 & 67.6962015256149 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 115.735714285714 & 1.66762860078545 & 69.4013728423723 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 115.5875 & 1.61094090797098 & 71.7515455893323 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 115.415789473684 & 1.54076668172299 & 74.9080252336573 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 115.275 & 1.47541425444592 & 78.1305993571889 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 115.123529411765 & 1.39841429693563 & 82.3243366890893 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 114.98125 & 1.31483040041476 & 87.4494915570323 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 114.73 & 1.22802663867172 & 93.426312090507 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 114.5 & 1.13551377551817 & 100.83541254068 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 114.3 & 1.04133050986189 & 109.763421812311 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 114.220833333333 & 0.978055953444195 & 116.783536699621 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 114.2 & 0.920897360215539 & 124.009476988045 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 114.21 & 0.87926105338517 & 129.893163765516 \tabularnewline
Median & 114.75 &  &  \tabularnewline
Midrange & 120.9 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 114.419354838710 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 114.73 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 114.419354838710 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 114.73 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 114.73 &  &  \tabularnewline
Midmean - Closest Observation & 114.419354838710 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 114.73 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 114.98125 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=561&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]117.311666666667[/C][C]2.24590033494386[/C][C]52.2336921373669[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]116.080345234446[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]114.885155408247[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]118.573298708717[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]117.416666666667[/C][C]2.16042233612624[/C][C]54.3489412709932[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]117.296666666667[/C][C]2.12679298457718[/C][C]55.1518965490598[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]117.261666666667[/C][C]2.05185198371825[/C][C]57.1491840528242[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]117.221666666667[/C][C]2.02273112297628[/C][C]57.952174332585[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]116.988333333333[/C][C]1.93247169334363[/C][C]60.5381873050446[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]116.918333333333[/C][C]1.89826339260949[/C][C]61.5922604779356[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]116.825[/C][C]1.86547675704455[/C][C]62.6247416693009[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]116.625[/C][C]1.80513176976494[/C][C]64.6074718496517[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]116.625[/C][C]1.7943392233877[/C][C]64.99607124444[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]116.675[/C][C]1.76855558063859[/C][C]65.9719158828307[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]116.345[/C][C]1.66576770954023[/C][C]69.8446724196093[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]116.305[/C][C]1.61682961203408[/C][C]71.9339868186112[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]116.11[/C][C]1.53645291845259[/C][C]75.5701646340965[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]116.74[/C][C]1.42059945968551[/C][C]82.1765763770204[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]116.34[/C][C]1.32261981077020[/C][C]87.9617854296705[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]115.886666666667[/C][C]1.20753394559125[/C][C]95.9696968269694[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]114.838333333333[/C][C]1.02103606311656[/C][C]112.472357717520[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]114.358333333333[/C][C]0.917354005277198[/C][C]124.661071598829[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]114.136666666667[/C][C]0.797938610649559[/C][C]143.039408224342[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]114.27[/C][C]0.738812224333665[/C][C]154.667175550675[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]117.187931034483[/C][C]2.09896133906293[/C][C]55.8313909139463[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]116.942857142857[/C][C]2.02267159248789[/C][C]57.8160377478862[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]116.746296296296[/C][C]1.95059114651054[/C][C]59.8517513550426[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]116.548076923077[/C][C]1.89703565369162[/C][C]61.4369459510553[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]116.346[/C][C]1.84059265078465[/C][C]63.2111618778884[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]116.185416666667[/C][C]1.80005661254386[/C][C]64.5454236589104[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]116.026086956522[/C][C]1.75775283303831[/C][C]66.0081922644202[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]115.870454545455[/C][C]1.71162416700162[/C][C]67.6962015256149[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]115.735714285714[/C][C]1.66762860078545[/C][C]69.4013728423723[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]115.5875[/C][C]1.61094090797098[/C][C]71.7515455893323[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]115.415789473684[/C][C]1.54076668172299[/C][C]74.9080252336573[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]115.275[/C][C]1.47541425444592[/C][C]78.1305993571889[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]115.123529411765[/C][C]1.39841429693563[/C][C]82.3243366890893[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]114.98125[/C][C]1.31483040041476[/C][C]87.4494915570323[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]114.73[/C][C]1.22802663867172[/C][C]93.426312090507[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]114.5[/C][C]1.13551377551817[/C][C]100.83541254068[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]114.3[/C][C]1.04133050986189[/C][C]109.763421812311[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]114.220833333333[/C][C]0.978055953444195[/C][C]116.783536699621[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]114.2[/C][C]0.920897360215539[/C][C]124.009476988045[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]114.21[/C][C]0.87926105338517[/C][C]129.893163765516[/C][/ROW]
[ROW][C]Median[/C][C]114.75[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]120.9[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]114.419354838710[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]114.73[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]114.419354838710[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]114.73[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]114.73[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]114.419354838710[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]114.73[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]114.98125[/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=561&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=561&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 Mean117.3116666666672.2459003349438652.2336921373669
Geometric Mean116.080345234446
Harmonic Mean114.885155408247
Quadratic Mean118.573298708717
Winsorized Mean ( 1 / 20 )117.4166666666672.1604223361262454.3489412709932
Winsorized Mean ( 2 / 20 )117.2966666666672.1267929845771855.1518965490598
Winsorized Mean ( 3 / 20 )117.2616666666672.0518519837182557.1491840528242
Winsorized Mean ( 4 / 20 )117.2216666666672.0227311229762857.952174332585
Winsorized Mean ( 5 / 20 )116.9883333333331.9324716933436360.5381873050446
Winsorized Mean ( 6 / 20 )116.9183333333331.8982633926094961.5922604779356
Winsorized Mean ( 7 / 20 )116.8251.8654767570445562.6247416693009
Winsorized Mean ( 8 / 20 )116.6251.8051317697649464.6074718496517
Winsorized Mean ( 9 / 20 )116.6251.794339223387764.99607124444
Winsorized Mean ( 10 / 20 )116.6751.7685555806385965.9719158828307
Winsorized Mean ( 11 / 20 )116.3451.6657677095402369.8446724196093
Winsorized Mean ( 12 / 20 )116.3051.6168296120340871.9339868186112
Winsorized Mean ( 13 / 20 )116.111.5364529184525975.5701646340965
Winsorized Mean ( 14 / 20 )116.741.4205994596855182.1765763770204
Winsorized Mean ( 15 / 20 )116.341.3226198107702087.9617854296705
Winsorized Mean ( 16 / 20 )115.8866666666671.2075339455912595.9696968269694
Winsorized Mean ( 17 / 20 )114.8383333333331.02103606311656112.472357717520
Winsorized Mean ( 18 / 20 )114.3583333333330.917354005277198124.661071598829
Winsorized Mean ( 19 / 20 )114.1366666666670.797938610649559143.039408224342
Winsorized Mean ( 20 / 20 )114.270.738812224333665154.667175550675
Trimmed Mean ( 1 / 20 )117.1879310344832.0989613390629355.8313909139463
Trimmed Mean ( 2 / 20 )116.9428571428572.0226715924878957.8160377478862
Trimmed Mean ( 3 / 20 )116.7462962962961.9505911465105459.8517513550426
Trimmed Mean ( 4 / 20 )116.5480769230771.8970356536916261.4369459510553
Trimmed Mean ( 5 / 20 )116.3461.8405926507846563.2111618778884
Trimmed Mean ( 6 / 20 )116.1854166666671.8000566125438664.5454236589104
Trimmed Mean ( 7 / 20 )116.0260869565221.7577528330383166.0081922644202
Trimmed Mean ( 8 / 20 )115.8704545454551.7116241670016267.6962015256149
Trimmed Mean ( 9 / 20 )115.7357142857141.6676286007854569.4013728423723
Trimmed Mean ( 10 / 20 )115.58751.6109409079709871.7515455893323
Trimmed Mean ( 11 / 20 )115.4157894736841.5407666817229974.9080252336573
Trimmed Mean ( 12 / 20 )115.2751.4754142544459278.1305993571889
Trimmed Mean ( 13 / 20 )115.1235294117651.3984142969356382.3243366890893
Trimmed Mean ( 14 / 20 )114.981251.3148304004147687.4494915570323
Trimmed Mean ( 15 / 20 )114.731.2280266386717293.426312090507
Trimmed Mean ( 16 / 20 )114.51.13551377551817100.83541254068
Trimmed Mean ( 17 / 20 )114.31.04133050986189109.763421812311
Trimmed Mean ( 18 / 20 )114.2208333333330.978055953444195116.783536699621
Trimmed Mean ( 19 / 20 )114.20.920897360215539124.009476988045
Trimmed Mean ( 20 / 20 )114.210.87926105338517129.893163765516
Median114.75
Midrange120.9
Midmean - Weighted Average at Xnp114.419354838710
Midmean - Weighted Average at X(n+1)p114.73
Midmean - Empirical Distribution Function114.419354838710
Midmean - Empirical Distribution Function - Averaging114.73
Midmean - Empirical Distribution Function - Interpolation114.73
Midmean - Closest Observation114.419354838710
Midmean - True Basic - Statistics Graphics Toolkit114.73
Midmean - MS Excel (old versions)114.98125
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')