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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 computationWed, 10 Dec 2008 05:45:44 -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/10/t1228913185bhkw44fqtsamvcp.htm/, Retrieved Sun, 26 May 2024 05:29:37 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=31928, Retrieved Sun, 26 May 2024 05:29:37 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact170
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [Central Tendency ...] [2008-12-10 12:45:44] [28deb8481dba3cc87d2d53a86e0e0d0b] [Current]
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Dataseries X:
98,5
97,0
103,3
99,6
100,1
102,9
95,9
94,5
107,4
116,0
102,8
99,8
109,6
103,0
111,6
106,3
97,9
108,8
103,9
101,2
122,9
123,9
111,7
120,9
99,6
103,3
119,4
106,5
101,9
124,6
106,5
107,8
127,4
120,1
118,5
127,7
107,7
104,5
118,8
110,3
109,6
119,1
96,5
106,7
126,3
116,2
118,8
115,2
110,0
111,4
129,6
108,1
117,8
122,9
100,6
111,8
127,0
128,6
124,8
118,5
114,7
112,6
128,7
111,0
115,8
126,0
111,1
113,2
120,1
130,6
124,0
119,4
116,7
116,5
119,6
126,5
111,3
123,5
114,2
103,7
129,5




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=31928&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=31928&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=31928&T=0

As an alternative you can also use a QR Code:  

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

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean112.9913580246911.08736599505136103.912903786691
Geometric Mean112.570828146094
Harmonic Mean112.149194482513
Quadratic Mean113.409153831776
Winsorized Mean ( 1 / 27 )112.9962962962961.08138634792127104.492068457778
Winsorized Mean ( 2 / 27 )113.0086419753091.07803146718037104.828704370650
Winsorized Mean ( 3 / 27 )112.9975308641981.06897316500266105.706611319767
Winsorized Mean ( 4 / 27 )113.0370370370371.05994182877368106.644566681379
Winsorized Mean ( 5 / 27 )113.0185185185191.04342904411178108.314522349458
Winsorized Mean ( 6 / 27 )113.0777777777781.02575476577307110.238608243321
Winsorized Mean ( 7 / 27 )113.0432098765431.01978111042712110.850464595483
Winsorized Mean ( 8 / 27 )113.0135802469141.00818219419234112.096385849632
Winsorized Mean ( 9 / 27 )113.0246913580250.999052839814467113.131845337644
Winsorized Mean ( 10 / 27 )113.0493827160490.983049430857173114.998675720178
Winsorized Mean ( 11 / 27 )112.9679012345680.944053558261247119.662597790142
Winsorized Mean ( 12 / 27 )113.0419753086420.923512925771184122.404323918093
Winsorized Mean ( 13 / 27 )113.090123456790.887206054500765127.467709314074
Winsorized Mean ( 14 / 27 )113.0901234567900.882052889112777128.212406367767
Winsorized Mean ( 15 / 27 )113.0345679012350.868122282757708130.205813335611
Winsorized Mean ( 16 / 27 )112.9753086419750.841919710520886134.187746444466
Winsorized Mean ( 17 / 27 )112.9753086419750.841919710520886134.187746444466
Winsorized Mean ( 18 / 27 )112.6197530864200.766178225553295146.988976363941
Winsorized Mean ( 19 / 27 )112.4790123456790.734485030080038153.139965743648
Winsorized Mean ( 20 / 27 )112.6271604938270.713113526937667157.937209489608
Winsorized Mean ( 21 / 27 )112.9641975308640.631970533385715178.749152948114
Winsorized Mean ( 22 / 27 )112.9641975308640.61773508206272182.868353783078
Winsorized Mean ( 23 / 27 )112.9641975308640.61773508206272182.868353783078
Winsorized Mean ( 24 / 27 )112.9345679012350.59848873586414188.699571326387
Winsorized Mean ( 25 / 27 )113.0580246913580.558828868539705202.312427034763
Winsorized Mean ( 26 / 27 )113.1543209876540.546730036364112206.965620071211
Winsorized Mean ( 27 / 27 )113.0876543209880.529731421338435213.481114703857
Trimmed Mean ( 1 / 27 )113.0025316455701.06657026709126105.949448556961
Trimmed Mean ( 2 / 27 )113.0090909090911.04917892874972107.711933410406
Trimmed Mean ( 3 / 27 )113.0093333333331.03080860997102109.631732059854
Trimmed Mean ( 4 / 27 )113.0136986301371.01311287531535111.550944997081
Trimmed Mean ( 5 / 27 )113.0070422535210.995299463431024113.540744675939
Trimmed Mean ( 6 / 27 )113.0043478260870.97900473754763115.427784455016
Trimmed Mean ( 7 / 27 )112.9895522388060.964090989080129117.198017115182
Trimmed Mean ( 8 / 27 )112.980.947484523924757119.242053191543
Trimmed Mean ( 9 / 27 )112.9746031746030.929964207268018121.482743412773
Trimmed Mean ( 10 / 27 )112.9672131147540.910580554952302124.060647353349
Trimmed Mean ( 11 / 27 )112.9559322033900.890219836344856126.885436149316
Trimmed Mean ( 12 / 27 )112.9543859649120.873126602364102129.367706423185
Trimmed Mean ( 13 / 27 )112.9436363636360.85587596113627131.962622496946
Trimmed Mean ( 14 / 27 )112.9264150943400.841253776728901134.235849179113
Trimmed Mean ( 15 / 27 )112.9078431372550.823544911151998137.099800640279
Trimmed Mean ( 16 / 27 )112.8938775510200.80366617517238140.473595926574
Trimmed Mean ( 17 / 27 )112.8851063829790.78342554519262144.091684367050
Trimmed Mean ( 18 / 27 )112.8755555555560.757042061169225149.100771734166
Trimmed Mean ( 19 / 27 )112.9023255813950.738945766453542152.788378669862
Trimmed Mean ( 20 / 27 )112.9463414634150.721288629696165156.589660245985
Trimmed Mean ( 21 / 27 )112.9794871794870.702157649106989160.903306149517
Trimmed Mean ( 22 / 27 )112.9810810810810.69436641067944162.711040372084
Trimmed Mean ( 23 / 27 )112.9828571428570.685387527188065164.845219180441
Trimmed Mean ( 24 / 27 )112.9848484848480.671245467397952168.321208816245
Trimmed Mean ( 25 / 27 )112.9903225806450.654929280245424172.522936428043
Trimmed Mean ( 26 / 27 )112.9827586206900.641255483570928176.189929778890
Trimmed Mean ( 27 / 27 )112.9629629629630.622629936968003181.428736808022
Median111.8
Midrange112.55
Midmean - Weighted Average at Xnp112.7675
Midmean - Weighted Average at X(n+1)p113.116666666667
Midmean - Empirical Distribution Function113.116666666667
Midmean - Empirical Distribution Function - Averaging113.116666666667
Midmean - Empirical Distribution Function - Interpolation113.116666666667
Midmean - Closest Observation112.902325581395
Midmean - True Basic - Statistics Graphics Toolkit113.116666666667
Midmean - MS Excel (old versions)113.116666666667
Number of observations81

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 112.991358024691 & 1.08736599505136 & 103.912903786691 \tabularnewline
Geometric Mean & 112.570828146094 &  &  \tabularnewline
Harmonic Mean & 112.149194482513 &  &  \tabularnewline
Quadratic Mean & 113.409153831776 &  &  \tabularnewline
Winsorized Mean ( 1 / 27 ) & 112.996296296296 & 1.08138634792127 & 104.492068457778 \tabularnewline
Winsorized Mean ( 2 / 27 ) & 113.008641975309 & 1.07803146718037 & 104.828704370650 \tabularnewline
Winsorized Mean ( 3 / 27 ) & 112.997530864198 & 1.06897316500266 & 105.706611319767 \tabularnewline
Winsorized Mean ( 4 / 27 ) & 113.037037037037 & 1.05994182877368 & 106.644566681379 \tabularnewline
Winsorized Mean ( 5 / 27 ) & 113.018518518519 & 1.04342904411178 & 108.314522349458 \tabularnewline
Winsorized Mean ( 6 / 27 ) & 113.077777777778 & 1.02575476577307 & 110.238608243321 \tabularnewline
Winsorized Mean ( 7 / 27 ) & 113.043209876543 & 1.01978111042712 & 110.850464595483 \tabularnewline
Winsorized Mean ( 8 / 27 ) & 113.013580246914 & 1.00818219419234 & 112.096385849632 \tabularnewline
Winsorized Mean ( 9 / 27 ) & 113.024691358025 & 0.999052839814467 & 113.131845337644 \tabularnewline
Winsorized Mean ( 10 / 27 ) & 113.049382716049 & 0.983049430857173 & 114.998675720178 \tabularnewline
Winsorized Mean ( 11 / 27 ) & 112.967901234568 & 0.944053558261247 & 119.662597790142 \tabularnewline
Winsorized Mean ( 12 / 27 ) & 113.041975308642 & 0.923512925771184 & 122.404323918093 \tabularnewline
Winsorized Mean ( 13 / 27 ) & 113.09012345679 & 0.887206054500765 & 127.467709314074 \tabularnewline
Winsorized Mean ( 14 / 27 ) & 113.090123456790 & 0.882052889112777 & 128.212406367767 \tabularnewline
Winsorized Mean ( 15 / 27 ) & 113.034567901235 & 0.868122282757708 & 130.205813335611 \tabularnewline
Winsorized Mean ( 16 / 27 ) & 112.975308641975 & 0.841919710520886 & 134.187746444466 \tabularnewline
Winsorized Mean ( 17 / 27 ) & 112.975308641975 & 0.841919710520886 & 134.187746444466 \tabularnewline
Winsorized Mean ( 18 / 27 ) & 112.619753086420 & 0.766178225553295 & 146.988976363941 \tabularnewline
Winsorized Mean ( 19 / 27 ) & 112.479012345679 & 0.734485030080038 & 153.139965743648 \tabularnewline
Winsorized Mean ( 20 / 27 ) & 112.627160493827 & 0.713113526937667 & 157.937209489608 \tabularnewline
Winsorized Mean ( 21 / 27 ) & 112.964197530864 & 0.631970533385715 & 178.749152948114 \tabularnewline
Winsorized Mean ( 22 / 27 ) & 112.964197530864 & 0.61773508206272 & 182.868353783078 \tabularnewline
Winsorized Mean ( 23 / 27 ) & 112.964197530864 & 0.61773508206272 & 182.868353783078 \tabularnewline
Winsorized Mean ( 24 / 27 ) & 112.934567901235 & 0.59848873586414 & 188.699571326387 \tabularnewline
Winsorized Mean ( 25 / 27 ) & 113.058024691358 & 0.558828868539705 & 202.312427034763 \tabularnewline
Winsorized Mean ( 26 / 27 ) & 113.154320987654 & 0.546730036364112 & 206.965620071211 \tabularnewline
Winsorized Mean ( 27 / 27 ) & 113.087654320988 & 0.529731421338435 & 213.481114703857 \tabularnewline
Trimmed Mean ( 1 / 27 ) & 113.002531645570 & 1.06657026709126 & 105.949448556961 \tabularnewline
Trimmed Mean ( 2 / 27 ) & 113.009090909091 & 1.04917892874972 & 107.711933410406 \tabularnewline
Trimmed Mean ( 3 / 27 ) & 113.009333333333 & 1.03080860997102 & 109.631732059854 \tabularnewline
Trimmed Mean ( 4 / 27 ) & 113.013698630137 & 1.01311287531535 & 111.550944997081 \tabularnewline
Trimmed Mean ( 5 / 27 ) & 113.007042253521 & 0.995299463431024 & 113.540744675939 \tabularnewline
Trimmed Mean ( 6 / 27 ) & 113.004347826087 & 0.97900473754763 & 115.427784455016 \tabularnewline
Trimmed Mean ( 7 / 27 ) & 112.989552238806 & 0.964090989080129 & 117.198017115182 \tabularnewline
Trimmed Mean ( 8 / 27 ) & 112.98 & 0.947484523924757 & 119.242053191543 \tabularnewline
Trimmed Mean ( 9 / 27 ) & 112.974603174603 & 0.929964207268018 & 121.482743412773 \tabularnewline
Trimmed Mean ( 10 / 27 ) & 112.967213114754 & 0.910580554952302 & 124.060647353349 \tabularnewline
Trimmed Mean ( 11 / 27 ) & 112.955932203390 & 0.890219836344856 & 126.885436149316 \tabularnewline
Trimmed Mean ( 12 / 27 ) & 112.954385964912 & 0.873126602364102 & 129.367706423185 \tabularnewline
Trimmed Mean ( 13 / 27 ) & 112.943636363636 & 0.85587596113627 & 131.962622496946 \tabularnewline
Trimmed Mean ( 14 / 27 ) & 112.926415094340 & 0.841253776728901 & 134.235849179113 \tabularnewline
Trimmed Mean ( 15 / 27 ) & 112.907843137255 & 0.823544911151998 & 137.099800640279 \tabularnewline
Trimmed Mean ( 16 / 27 ) & 112.893877551020 & 0.80366617517238 & 140.473595926574 \tabularnewline
Trimmed Mean ( 17 / 27 ) & 112.885106382979 & 0.78342554519262 & 144.091684367050 \tabularnewline
Trimmed Mean ( 18 / 27 ) & 112.875555555556 & 0.757042061169225 & 149.100771734166 \tabularnewline
Trimmed Mean ( 19 / 27 ) & 112.902325581395 & 0.738945766453542 & 152.788378669862 \tabularnewline
Trimmed Mean ( 20 / 27 ) & 112.946341463415 & 0.721288629696165 & 156.589660245985 \tabularnewline
Trimmed Mean ( 21 / 27 ) & 112.979487179487 & 0.702157649106989 & 160.903306149517 \tabularnewline
Trimmed Mean ( 22 / 27 ) & 112.981081081081 & 0.69436641067944 & 162.711040372084 \tabularnewline
Trimmed Mean ( 23 / 27 ) & 112.982857142857 & 0.685387527188065 & 164.845219180441 \tabularnewline
Trimmed Mean ( 24 / 27 ) & 112.984848484848 & 0.671245467397952 & 168.321208816245 \tabularnewline
Trimmed Mean ( 25 / 27 ) & 112.990322580645 & 0.654929280245424 & 172.522936428043 \tabularnewline
Trimmed Mean ( 26 / 27 ) & 112.982758620690 & 0.641255483570928 & 176.189929778890 \tabularnewline
Trimmed Mean ( 27 / 27 ) & 112.962962962963 & 0.622629936968003 & 181.428736808022 \tabularnewline
Median & 111.8 &  &  \tabularnewline
Midrange & 112.55 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 112.7675 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 113.116666666667 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 113.116666666667 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 113.116666666667 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 113.116666666667 &  &  \tabularnewline
Midmean - Closest Observation & 112.902325581395 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 113.116666666667 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 113.116666666667 &  &  \tabularnewline
Number of observations & 81 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=31928&T=1

[TABLE]
[ROW][C]Central Tendency - Ungrouped Data[/C][/ROW]
[ROW][C]Measure[/C][C]Value[/C][C]S.E.[/C][C]Value/S.E.[/C][/ROW]
[ROW][C]Arithmetic Mean[/C][C]112.991358024691[/C][C]1.08736599505136[/C][C]103.912903786691[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]112.570828146094[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]112.149194482513[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]113.409153831776[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 27 )[/C][C]112.996296296296[/C][C]1.08138634792127[/C][C]104.492068457778[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 27 )[/C][C]113.008641975309[/C][C]1.07803146718037[/C][C]104.828704370650[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 27 )[/C][C]112.997530864198[/C][C]1.06897316500266[/C][C]105.706611319767[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 27 )[/C][C]113.037037037037[/C][C]1.05994182877368[/C][C]106.644566681379[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 27 )[/C][C]113.018518518519[/C][C]1.04342904411178[/C][C]108.314522349458[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 27 )[/C][C]113.077777777778[/C][C]1.02575476577307[/C][C]110.238608243321[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 27 )[/C][C]113.043209876543[/C][C]1.01978111042712[/C][C]110.850464595483[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 27 )[/C][C]113.013580246914[/C][C]1.00818219419234[/C][C]112.096385849632[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 27 )[/C][C]113.024691358025[/C][C]0.999052839814467[/C][C]113.131845337644[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 27 )[/C][C]113.049382716049[/C][C]0.983049430857173[/C][C]114.998675720178[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 27 )[/C][C]112.967901234568[/C][C]0.944053558261247[/C][C]119.662597790142[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 27 )[/C][C]113.041975308642[/C][C]0.923512925771184[/C][C]122.404323918093[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 27 )[/C][C]113.09012345679[/C][C]0.887206054500765[/C][C]127.467709314074[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 27 )[/C][C]113.090123456790[/C][C]0.882052889112777[/C][C]128.212406367767[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 27 )[/C][C]113.034567901235[/C][C]0.868122282757708[/C][C]130.205813335611[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 27 )[/C][C]112.975308641975[/C][C]0.841919710520886[/C][C]134.187746444466[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 27 )[/C][C]112.975308641975[/C][C]0.841919710520886[/C][C]134.187746444466[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 27 )[/C][C]112.619753086420[/C][C]0.766178225553295[/C][C]146.988976363941[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 27 )[/C][C]112.479012345679[/C][C]0.734485030080038[/C][C]153.139965743648[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 27 )[/C][C]112.627160493827[/C][C]0.713113526937667[/C][C]157.937209489608[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 27 )[/C][C]112.964197530864[/C][C]0.631970533385715[/C][C]178.749152948114[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 27 )[/C][C]112.964197530864[/C][C]0.61773508206272[/C][C]182.868353783078[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 27 )[/C][C]112.964197530864[/C][C]0.61773508206272[/C][C]182.868353783078[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 27 )[/C][C]112.934567901235[/C][C]0.59848873586414[/C][C]188.699571326387[/C][/ROW]
[ROW][C]Winsorized Mean ( 25 / 27 )[/C][C]113.058024691358[/C][C]0.558828868539705[/C][C]202.312427034763[/C][/ROW]
[ROW][C]Winsorized Mean ( 26 / 27 )[/C][C]113.154320987654[/C][C]0.546730036364112[/C][C]206.965620071211[/C][/ROW]
[ROW][C]Winsorized Mean ( 27 / 27 )[/C][C]113.087654320988[/C][C]0.529731421338435[/C][C]213.481114703857[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 27 )[/C][C]113.002531645570[/C][C]1.06657026709126[/C][C]105.949448556961[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 27 )[/C][C]113.009090909091[/C][C]1.04917892874972[/C][C]107.711933410406[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 27 )[/C][C]113.009333333333[/C][C]1.03080860997102[/C][C]109.631732059854[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 27 )[/C][C]113.013698630137[/C][C]1.01311287531535[/C][C]111.550944997081[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 27 )[/C][C]113.007042253521[/C][C]0.995299463431024[/C][C]113.540744675939[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 27 )[/C][C]113.004347826087[/C][C]0.97900473754763[/C][C]115.427784455016[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 27 )[/C][C]112.989552238806[/C][C]0.964090989080129[/C][C]117.198017115182[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 27 )[/C][C]112.98[/C][C]0.947484523924757[/C][C]119.242053191543[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 27 )[/C][C]112.974603174603[/C][C]0.929964207268018[/C][C]121.482743412773[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 27 )[/C][C]112.967213114754[/C][C]0.910580554952302[/C][C]124.060647353349[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 27 )[/C][C]112.955932203390[/C][C]0.890219836344856[/C][C]126.885436149316[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 27 )[/C][C]112.954385964912[/C][C]0.873126602364102[/C][C]129.367706423185[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 27 )[/C][C]112.943636363636[/C][C]0.85587596113627[/C][C]131.962622496946[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 27 )[/C][C]112.926415094340[/C][C]0.841253776728901[/C][C]134.235849179113[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 27 )[/C][C]112.907843137255[/C][C]0.823544911151998[/C][C]137.099800640279[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 27 )[/C][C]112.893877551020[/C][C]0.80366617517238[/C][C]140.473595926574[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 27 )[/C][C]112.885106382979[/C][C]0.78342554519262[/C][C]144.091684367050[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 27 )[/C][C]112.875555555556[/C][C]0.757042061169225[/C][C]149.100771734166[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 27 )[/C][C]112.902325581395[/C][C]0.738945766453542[/C][C]152.788378669862[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 27 )[/C][C]112.946341463415[/C][C]0.721288629696165[/C][C]156.589660245985[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 27 )[/C][C]112.979487179487[/C][C]0.702157649106989[/C][C]160.903306149517[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 27 )[/C][C]112.981081081081[/C][C]0.69436641067944[/C][C]162.711040372084[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 27 )[/C][C]112.982857142857[/C][C]0.685387527188065[/C][C]164.845219180441[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 27 )[/C][C]112.984848484848[/C][C]0.671245467397952[/C][C]168.321208816245[/C][/ROW]
[ROW][C]Trimmed Mean ( 25 / 27 )[/C][C]112.990322580645[/C][C]0.654929280245424[/C][C]172.522936428043[/C][/ROW]
[ROW][C]Trimmed Mean ( 26 / 27 )[/C][C]112.982758620690[/C][C]0.641255483570928[/C][C]176.189929778890[/C][/ROW]
[ROW][C]Trimmed Mean ( 27 / 27 )[/C][C]112.962962962963[/C][C]0.622629936968003[/C][C]181.428736808022[/C][/ROW]
[ROW][C]Median[/C][C]111.8[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]112.55[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]112.7675[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]113.116666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]113.116666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]113.116666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]113.116666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]112.902325581395[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]113.116666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]113.116666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]81[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=31928&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=31928&T=1

As an alternative you can also use a QR Code:  

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

Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean112.9913580246911.08736599505136103.912903786691
Geometric Mean112.570828146094
Harmonic Mean112.149194482513
Quadratic Mean113.409153831776
Winsorized Mean ( 1 / 27 )112.9962962962961.08138634792127104.492068457778
Winsorized Mean ( 2 / 27 )113.0086419753091.07803146718037104.828704370650
Winsorized Mean ( 3 / 27 )112.9975308641981.06897316500266105.706611319767
Winsorized Mean ( 4 / 27 )113.0370370370371.05994182877368106.644566681379
Winsorized Mean ( 5 / 27 )113.0185185185191.04342904411178108.314522349458
Winsorized Mean ( 6 / 27 )113.0777777777781.02575476577307110.238608243321
Winsorized Mean ( 7 / 27 )113.0432098765431.01978111042712110.850464595483
Winsorized Mean ( 8 / 27 )113.0135802469141.00818219419234112.096385849632
Winsorized Mean ( 9 / 27 )113.0246913580250.999052839814467113.131845337644
Winsorized Mean ( 10 / 27 )113.0493827160490.983049430857173114.998675720178
Winsorized Mean ( 11 / 27 )112.9679012345680.944053558261247119.662597790142
Winsorized Mean ( 12 / 27 )113.0419753086420.923512925771184122.404323918093
Winsorized Mean ( 13 / 27 )113.090123456790.887206054500765127.467709314074
Winsorized Mean ( 14 / 27 )113.0901234567900.882052889112777128.212406367767
Winsorized Mean ( 15 / 27 )113.0345679012350.868122282757708130.205813335611
Winsorized Mean ( 16 / 27 )112.9753086419750.841919710520886134.187746444466
Winsorized Mean ( 17 / 27 )112.9753086419750.841919710520886134.187746444466
Winsorized Mean ( 18 / 27 )112.6197530864200.766178225553295146.988976363941
Winsorized Mean ( 19 / 27 )112.4790123456790.734485030080038153.139965743648
Winsorized Mean ( 20 / 27 )112.6271604938270.713113526937667157.937209489608
Winsorized Mean ( 21 / 27 )112.9641975308640.631970533385715178.749152948114
Winsorized Mean ( 22 / 27 )112.9641975308640.61773508206272182.868353783078
Winsorized Mean ( 23 / 27 )112.9641975308640.61773508206272182.868353783078
Winsorized Mean ( 24 / 27 )112.9345679012350.59848873586414188.699571326387
Winsorized Mean ( 25 / 27 )113.0580246913580.558828868539705202.312427034763
Winsorized Mean ( 26 / 27 )113.1543209876540.546730036364112206.965620071211
Winsorized Mean ( 27 / 27 )113.0876543209880.529731421338435213.481114703857
Trimmed Mean ( 1 / 27 )113.0025316455701.06657026709126105.949448556961
Trimmed Mean ( 2 / 27 )113.0090909090911.04917892874972107.711933410406
Trimmed Mean ( 3 / 27 )113.0093333333331.03080860997102109.631732059854
Trimmed Mean ( 4 / 27 )113.0136986301371.01311287531535111.550944997081
Trimmed Mean ( 5 / 27 )113.0070422535210.995299463431024113.540744675939
Trimmed Mean ( 6 / 27 )113.0043478260870.97900473754763115.427784455016
Trimmed Mean ( 7 / 27 )112.9895522388060.964090989080129117.198017115182
Trimmed Mean ( 8 / 27 )112.980.947484523924757119.242053191543
Trimmed Mean ( 9 / 27 )112.9746031746030.929964207268018121.482743412773
Trimmed Mean ( 10 / 27 )112.9672131147540.910580554952302124.060647353349
Trimmed Mean ( 11 / 27 )112.9559322033900.890219836344856126.885436149316
Trimmed Mean ( 12 / 27 )112.9543859649120.873126602364102129.367706423185
Trimmed Mean ( 13 / 27 )112.9436363636360.85587596113627131.962622496946
Trimmed Mean ( 14 / 27 )112.9264150943400.841253776728901134.235849179113
Trimmed Mean ( 15 / 27 )112.9078431372550.823544911151998137.099800640279
Trimmed Mean ( 16 / 27 )112.8938775510200.80366617517238140.473595926574
Trimmed Mean ( 17 / 27 )112.8851063829790.78342554519262144.091684367050
Trimmed Mean ( 18 / 27 )112.8755555555560.757042061169225149.100771734166
Trimmed Mean ( 19 / 27 )112.9023255813950.738945766453542152.788378669862
Trimmed Mean ( 20 / 27 )112.9463414634150.721288629696165156.589660245985
Trimmed Mean ( 21 / 27 )112.9794871794870.702157649106989160.903306149517
Trimmed Mean ( 22 / 27 )112.9810810810810.69436641067944162.711040372084
Trimmed Mean ( 23 / 27 )112.9828571428570.685387527188065164.845219180441
Trimmed Mean ( 24 / 27 )112.9848484848480.671245467397952168.321208816245
Trimmed Mean ( 25 / 27 )112.9903225806450.654929280245424172.522936428043
Trimmed Mean ( 26 / 27 )112.9827586206900.641255483570928176.189929778890
Trimmed Mean ( 27 / 27 )112.9629629629630.622629936968003181.428736808022
Median111.8
Midrange112.55
Midmean - Weighted Average at Xnp112.7675
Midmean - Weighted Average at X(n+1)p113.116666666667
Midmean - Empirical Distribution Function113.116666666667
Midmean - Empirical Distribution Function - Averaging113.116666666667
Midmean - Empirical Distribution Function - Interpolation113.116666666667
Midmean - Closest Observation112.902325581395
Midmean - True Basic - Statistics Graphics Toolkit113.116666666667
Midmean - MS Excel (old versions)113.116666666667
Number of observations81



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')