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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 computationTue, 02 Dec 2008 11:12:10 -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/2008/Dec/02/t1228241578x4m20idw9neemr8.htm/, Retrieved Mon, 27 May 2024 23:11:27 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=28188, Retrieved Mon, 27 May 2024 23:11:27 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact150
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [central tendency-...] [2008-12-02 18:12:10] [541f63fa3157af9df10fc4d202b2a90b] [Current]
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Dataseries X:
103,3
101,2
107,7
110,4
101,9
115,9
89,9
88,6
117,2
123,9
100
103,6
94,1
98,7
119,5
112,7
104,4
124,7
89,1
97
121,6
118,8
114
111,5
97,2
102,5
113,4
109,8
104,9
126,1
80
96,8
117,2
112,3
117,3
111,1
102,2
104,3
122,9
107,6
121,3
131,5
89
104,4
128,9
135,9
133,3
121,3
120,5
120,4
137,9
126,1
133,2
151,1
105
119
140,4
156,6
137,1
122,7




Summary of computational 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 computational 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=28188&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]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=28188&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=28188&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 time3 seconds
R Server'Herman Ole Andreas Wold' @ 193.190.124.10:1001







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean113.8483333333332.0210215737360656.3320722612937
Geometric Mean112.800144606646
Harmonic Mean111.758674672239
Quadratic Mean114.901828386961
Winsorized Mean ( 1 / 20 )113.91.9536160879786658.3021406820255
Winsorized Mean ( 2 / 20 )113.5566666666671.8488358937338361.420630706889
Winsorized Mean ( 3 / 20 )113.4366666666671.8180621810493662.3942722361633
Winsorized Mean ( 4 / 20 )113.4366666666671.7940374670404863.2298203079319
Winsorized Mean ( 5 / 20 )113.6866666666671.6985278881482466.9324698522374
Winsorized Mean ( 6 / 20 )113.6966666666671.5917796717952271.4273895321448
Winsorized Mean ( 7 / 20 )113.7083333333331.5851630076520971.7328961024366
Winsorized Mean ( 8 / 20 )113.5083333333331.5342148503897173.9846399638884
Winsorized Mean ( 9 / 20 )113.3433333333331.4191613793771479.8664161669047
Winsorized Mean ( 10 / 20 )113.0933333333331.2985517066485787.0918984236796
Winsorized Mean ( 11 / 20 )113.3133333333331.2618421352879189.7999283464086
Winsorized Mean ( 12 / 20 )113.1733333333331.1922107524858094.9272878955029
Winsorized Mean ( 13 / 20 )113.0651.1538117251853397.9925905865095
Winsorized Mean ( 14 / 20 )112.9016666666671.10619082667025102.063463142713
Winsorized Mean ( 15 / 20 )113.0516666666671.06709514257844105.943380450124
Winsorized Mean ( 16 / 20 )112.8383333333331.01064976488856111.649294595913
Winsorized Mean ( 17 / 20 )112.9516666666670.967793493832404116.710504241339
Winsorized Mean ( 18 / 20 )112.9816666666670.96325569546197117.291459784706
Winsorized Mean ( 19 / 20 )112.7283333333330.926700884422912121.644788764320
Winsorized Mean ( 20 / 20 )112.8616666666670.896720615645442125.860457200966
Trimmed Mean ( 1 / 20 )113.6948275862071.8638186224288961.0010149153045
Trimmed Mean ( 2 / 20 )113.4751.7518862746995164.7730401446657
Trimmed Mean ( 3 / 20 )113.4296296296301.6852996789574267.3053172951417
Trimmed Mean ( 4 / 20 )113.4269230769231.6174508260983670.1269684658873
Trimmed Mean ( 5 / 20 )113.4241.5418106503824273.5654536903525
Trimmed Mean ( 6 / 20 )113.3583333333331.4805620977505576.5643896365854
Trimmed Mean ( 7 / 20 )113.2847826086961.4367837384335578.8460918497059
Trimmed Mean ( 8 / 20 )113.2022727272731.3815244538016981.9401150777767
Trimmed Mean ( 9 / 20 )113.1476190476191.3243201665553485.4382662932069
Trimmed Mean ( 10 / 20 )113.1151.2818183698688988.245731734653
Trimmed Mean ( 11 / 20 )113.1184210526321.2572852014209389.9703749990776
Trimmed Mean ( 12 / 20 )113.0888888888891.2318380754351291.80499543249
Trimmed Mean ( 13 / 20 )113.0764705882351.2133912555727293.1904446063138
Trimmed Mean ( 14 / 20 )113.0781251.1949552425735694.6295902735781
Trimmed Mean ( 15 / 20 )113.1033333333331.1784022236767495.9802443179707
Trimmed Mean ( 16 / 20 )113.1107142857141.1615003443334197.3832808897094
Trimmed Mean ( 17 / 20 )113.151.1484739037924798.5220470629402
Trimmed Mean ( 18 / 20 )113.1791666666671.1361800219465899.613762326819
Trimmed Mean ( 19 / 20 )113.2090909090911.11030024196705101.962592306137
Trimmed Mean ( 20 / 20 )113.2851.07442212129909105.438074807159
Median113.05
Midrange118.3
Midmean - Weighted Average at Xnp112.761290322581
Midmean - Weighted Average at X(n+1)p113.103333333333
Midmean - Empirical Distribution Function112.761290322581
Midmean - Empirical Distribution Function - Averaging113.103333333333
Midmean - Empirical Distribution Function - Interpolation113.103333333333
Midmean - Closest Observation112.761290322581
Midmean - True Basic - Statistics Graphics Toolkit113.103333333333
Midmean - MS Excel (old versions)113.078125
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 113.848333333333 & 2.02102157373606 & 56.3320722612937 \tabularnewline
Geometric Mean & 112.800144606646 &  &  \tabularnewline
Harmonic Mean & 111.758674672239 &  &  \tabularnewline
Quadratic Mean & 114.901828386961 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 113.9 & 1.95361608797866 & 58.3021406820255 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 113.556666666667 & 1.84883589373383 & 61.420630706889 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 113.436666666667 & 1.81806218104936 & 62.3942722361633 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 113.436666666667 & 1.79403746704048 & 63.2298203079319 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 113.686666666667 & 1.69852788814824 & 66.9324698522374 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 113.696666666667 & 1.59177967179522 & 71.4273895321448 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 113.708333333333 & 1.58516300765209 & 71.7328961024366 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 113.508333333333 & 1.53421485038971 & 73.9846399638884 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 113.343333333333 & 1.41916137937714 & 79.8664161669047 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 113.093333333333 & 1.29855170664857 & 87.0918984236796 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 113.313333333333 & 1.26184213528791 & 89.7999283464086 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 113.173333333333 & 1.19221075248580 & 94.9272878955029 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 113.065 & 1.15381172518533 & 97.9925905865095 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 112.901666666667 & 1.10619082667025 & 102.063463142713 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 113.051666666667 & 1.06709514257844 & 105.943380450124 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 112.838333333333 & 1.01064976488856 & 111.649294595913 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 112.951666666667 & 0.967793493832404 & 116.710504241339 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 112.981666666667 & 0.96325569546197 & 117.291459784706 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 112.728333333333 & 0.926700884422912 & 121.644788764320 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 112.861666666667 & 0.896720615645442 & 125.860457200966 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 113.694827586207 & 1.86381862242889 & 61.0010149153045 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 113.475 & 1.75188627469951 & 64.7730401446657 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 113.429629629630 & 1.68529967895742 & 67.3053172951417 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 113.426923076923 & 1.61745082609836 & 70.1269684658873 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 113.424 & 1.54181065038242 & 73.5654536903525 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 113.358333333333 & 1.48056209775055 & 76.5643896365854 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 113.284782608696 & 1.43678373843355 & 78.8460918497059 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 113.202272727273 & 1.38152445380169 & 81.9401150777767 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 113.147619047619 & 1.32432016655534 & 85.4382662932069 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 113.115 & 1.28181836986889 & 88.245731734653 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 113.118421052632 & 1.25728520142093 & 89.9703749990776 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 113.088888888889 & 1.23183807543512 & 91.80499543249 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 113.076470588235 & 1.21339125557272 & 93.1904446063138 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 113.078125 & 1.19495524257356 & 94.6295902735781 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 113.103333333333 & 1.17840222367674 & 95.9802443179707 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 113.110714285714 & 1.16150034433341 & 97.3832808897094 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 113.15 & 1.14847390379247 & 98.5220470629402 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 113.179166666667 & 1.13618002194658 & 99.613762326819 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 113.209090909091 & 1.11030024196705 & 101.962592306137 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 113.285 & 1.07442212129909 & 105.438074807159 \tabularnewline
Median & 113.05 &  &  \tabularnewline
Midrange & 118.3 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 112.761290322581 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 113.103333333333 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 112.761290322581 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 113.103333333333 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 113.103333333333 &  &  \tabularnewline
Midmean - Closest Observation & 112.761290322581 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 113.103333333333 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 113.078125 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=28188&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]113.848333333333[/C][C]2.02102157373606[/C][C]56.3320722612937[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]112.800144606646[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]111.758674672239[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]114.901828386961[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]113.9[/C][C]1.95361608797866[/C][C]58.3021406820255[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]113.556666666667[/C][C]1.84883589373383[/C][C]61.420630706889[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]113.436666666667[/C][C]1.81806218104936[/C][C]62.3942722361633[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]113.436666666667[/C][C]1.79403746704048[/C][C]63.2298203079319[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]113.686666666667[/C][C]1.69852788814824[/C][C]66.9324698522374[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]113.696666666667[/C][C]1.59177967179522[/C][C]71.4273895321448[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]113.708333333333[/C][C]1.58516300765209[/C][C]71.7328961024366[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]113.508333333333[/C][C]1.53421485038971[/C][C]73.9846399638884[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]113.343333333333[/C][C]1.41916137937714[/C][C]79.8664161669047[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]113.093333333333[/C][C]1.29855170664857[/C][C]87.0918984236796[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]113.313333333333[/C][C]1.26184213528791[/C][C]89.7999283464086[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]113.173333333333[/C][C]1.19221075248580[/C][C]94.9272878955029[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]113.065[/C][C]1.15381172518533[/C][C]97.9925905865095[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]112.901666666667[/C][C]1.10619082667025[/C][C]102.063463142713[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]113.051666666667[/C][C]1.06709514257844[/C][C]105.943380450124[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]112.838333333333[/C][C]1.01064976488856[/C][C]111.649294595913[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]112.951666666667[/C][C]0.967793493832404[/C][C]116.710504241339[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]112.981666666667[/C][C]0.96325569546197[/C][C]117.291459784706[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]112.728333333333[/C][C]0.926700884422912[/C][C]121.644788764320[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]112.861666666667[/C][C]0.896720615645442[/C][C]125.860457200966[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]113.694827586207[/C][C]1.86381862242889[/C][C]61.0010149153045[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]113.475[/C][C]1.75188627469951[/C][C]64.7730401446657[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]113.429629629630[/C][C]1.68529967895742[/C][C]67.3053172951417[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]113.426923076923[/C][C]1.61745082609836[/C][C]70.1269684658873[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]113.424[/C][C]1.54181065038242[/C][C]73.5654536903525[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]113.358333333333[/C][C]1.48056209775055[/C][C]76.5643896365854[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]113.284782608696[/C][C]1.43678373843355[/C][C]78.8460918497059[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]113.202272727273[/C][C]1.38152445380169[/C][C]81.9401150777767[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]113.147619047619[/C][C]1.32432016655534[/C][C]85.4382662932069[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]113.115[/C][C]1.28181836986889[/C][C]88.245731734653[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]113.118421052632[/C][C]1.25728520142093[/C][C]89.9703749990776[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]113.088888888889[/C][C]1.23183807543512[/C][C]91.80499543249[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]113.076470588235[/C][C]1.21339125557272[/C][C]93.1904446063138[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]113.078125[/C][C]1.19495524257356[/C][C]94.6295902735781[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]113.103333333333[/C][C]1.17840222367674[/C][C]95.9802443179707[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]113.110714285714[/C][C]1.16150034433341[/C][C]97.3832808897094[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]113.15[/C][C]1.14847390379247[/C][C]98.5220470629402[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]113.179166666667[/C][C]1.13618002194658[/C][C]99.613762326819[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]113.209090909091[/C][C]1.11030024196705[/C][C]101.962592306137[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]113.285[/C][C]1.07442212129909[/C][C]105.438074807159[/C][/ROW]
[ROW][C]Median[/C][C]113.05[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]118.3[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]112.761290322581[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]113.103333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]112.761290322581[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]113.103333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]113.103333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]112.761290322581[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]113.103333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]113.078125[/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=28188&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=28188&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 Mean113.8483333333332.0210215737360656.3320722612937
Geometric Mean112.800144606646
Harmonic Mean111.758674672239
Quadratic Mean114.901828386961
Winsorized Mean ( 1 / 20 )113.91.9536160879786658.3021406820255
Winsorized Mean ( 2 / 20 )113.5566666666671.8488358937338361.420630706889
Winsorized Mean ( 3 / 20 )113.4366666666671.8180621810493662.3942722361633
Winsorized Mean ( 4 / 20 )113.4366666666671.7940374670404863.2298203079319
Winsorized Mean ( 5 / 20 )113.6866666666671.6985278881482466.9324698522374
Winsorized Mean ( 6 / 20 )113.6966666666671.5917796717952271.4273895321448
Winsorized Mean ( 7 / 20 )113.7083333333331.5851630076520971.7328961024366
Winsorized Mean ( 8 / 20 )113.5083333333331.5342148503897173.9846399638884
Winsorized Mean ( 9 / 20 )113.3433333333331.4191613793771479.8664161669047
Winsorized Mean ( 10 / 20 )113.0933333333331.2985517066485787.0918984236796
Winsorized Mean ( 11 / 20 )113.3133333333331.2618421352879189.7999283464086
Winsorized Mean ( 12 / 20 )113.1733333333331.1922107524858094.9272878955029
Winsorized Mean ( 13 / 20 )113.0651.1538117251853397.9925905865095
Winsorized Mean ( 14 / 20 )112.9016666666671.10619082667025102.063463142713
Winsorized Mean ( 15 / 20 )113.0516666666671.06709514257844105.943380450124
Winsorized Mean ( 16 / 20 )112.8383333333331.01064976488856111.649294595913
Winsorized Mean ( 17 / 20 )112.9516666666670.967793493832404116.710504241339
Winsorized Mean ( 18 / 20 )112.9816666666670.96325569546197117.291459784706
Winsorized Mean ( 19 / 20 )112.7283333333330.926700884422912121.644788764320
Winsorized Mean ( 20 / 20 )112.8616666666670.896720615645442125.860457200966
Trimmed Mean ( 1 / 20 )113.6948275862071.8638186224288961.0010149153045
Trimmed Mean ( 2 / 20 )113.4751.7518862746995164.7730401446657
Trimmed Mean ( 3 / 20 )113.4296296296301.6852996789574267.3053172951417
Trimmed Mean ( 4 / 20 )113.4269230769231.6174508260983670.1269684658873
Trimmed Mean ( 5 / 20 )113.4241.5418106503824273.5654536903525
Trimmed Mean ( 6 / 20 )113.3583333333331.4805620977505576.5643896365854
Trimmed Mean ( 7 / 20 )113.2847826086961.4367837384335578.8460918497059
Trimmed Mean ( 8 / 20 )113.2022727272731.3815244538016981.9401150777767
Trimmed Mean ( 9 / 20 )113.1476190476191.3243201665553485.4382662932069
Trimmed Mean ( 10 / 20 )113.1151.2818183698688988.245731734653
Trimmed Mean ( 11 / 20 )113.1184210526321.2572852014209389.9703749990776
Trimmed Mean ( 12 / 20 )113.0888888888891.2318380754351291.80499543249
Trimmed Mean ( 13 / 20 )113.0764705882351.2133912555727293.1904446063138
Trimmed Mean ( 14 / 20 )113.0781251.1949552425735694.6295902735781
Trimmed Mean ( 15 / 20 )113.1033333333331.1784022236767495.9802443179707
Trimmed Mean ( 16 / 20 )113.1107142857141.1615003443334197.3832808897094
Trimmed Mean ( 17 / 20 )113.151.1484739037924798.5220470629402
Trimmed Mean ( 18 / 20 )113.1791666666671.1361800219465899.613762326819
Trimmed Mean ( 19 / 20 )113.2090909090911.11030024196705101.962592306137
Trimmed Mean ( 20 / 20 )113.2851.07442212129909105.438074807159
Median113.05
Midrange118.3
Midmean - Weighted Average at Xnp112.761290322581
Midmean - Weighted Average at X(n+1)p113.103333333333
Midmean - Empirical Distribution Function112.761290322581
Midmean - Empirical Distribution Function - Averaging113.103333333333
Midmean - Empirical Distribution Function - Interpolation113.103333333333
Midmean - Closest Observation112.761290322581
Midmean - True Basic - Statistics Graphics Toolkit113.103333333333
Midmean - MS Excel (old versions)113.078125
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')