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Description of Statistical Computation

Author's title

datareeks-prijsindexcijfers vd grondstoffen (levensmiddelen)-gaelle croonen...

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationMon, 13 Oct 2014 12:32:20 +0100
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2014/Oct/13/t1413200079kwyiske2ekyan4b.htm/, Retrieved Fri, 10 May 2024 14:16:28 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=240726, Retrieved Fri, 10 May 2024 14:16:28 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact107

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [datareeks-prijsin...] [2014-10-13 11:32:20] [3acc2e190882a8fff3240b97d842d2ea] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
103,1
113,5
115,7
113,1
112,7
121,9
120,3
108,7
102,8
83,4
79,4
77,8
85,7
83,2
82
86,9
95,7
97,9
89,3
91,5
86,8
91
93,8
96,8
95,7
91,4
88,7
88,2
87,7
89,5
95,6
100,5
106,3
112
117,7
125
132,4
138,1
134,7
136,7
134,3
131,6
129,8
131,9
129,8
119,4
116,7
112,8
116
117,5
118,8
118,7
116,3
115,2
131,7
133,7
132,5
126,9
122,2
120,2
117,9
117,2
116,4
112,3
113,6
114,2
108
102,8
102,8
101,6
100,3
101,7

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gertrude Mary Cox' @ cox.wessa.net

\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 & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=240726&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]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=240726&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=240726&T=0

As an alternative you can also use a QR Code:  
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'Gertrude Mary Cox' @ cox.wessa.net






Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean109.1388888888891.933771962905956.4383448423176
Geometric Mean107.890357023511
Harmonic Mean106.617055027476
Quadratic Mean110.348537472058
Winsorized Mean ( 1 / 24 )109.1416666666671.924805896357956.7026872024776
Winsorized Mean ( 2 / 24 )109.1583333333331.8988019758947957.4880028139287
Winsorized Mean ( 3 / 24 )109.1916666666671.8857703186856257.9029511625641
Winsorized Mean ( 4 / 24 )109.1694444444441.877425024278658.1484975605844
Winsorized Mean ( 5 / 24 )109.2458333333331.8324025993197459.6189032769816
Winsorized Mean ( 6 / 24 )109.3291666666671.8146006660071460.2497115286722
Winsorized Mean ( 7 / 24 )109.2902777777781.8042585250468760.5735133078773
Winsorized Mean ( 8 / 24 )109.3569444444441.7849744833077661.2652704378123
Winsorized Mean ( 9 / 24 )109.4069444444441.7721627309224361.7363984330585
Winsorized Mean ( 10 / 24 )109.2263888888891.7173103686894563.603173241331
Winsorized Mean ( 11 / 24 )109.3180555555561.702001406782364.2291217386393
Winsorized Mean ( 12 / 24 )108.8680555555561.6174467243343267.3085882320864
Winsorized Mean ( 13 / 24 )108.7958333333331.5195227165112571.5986882928101
Winsorized Mean ( 14 / 24 )108.3291666666671.4283862622423875.8402468087337
Winsorized Mean ( 15 / 24 )108.28751.416404197585976.4523998054817
Winsorized Mean ( 16 / 24 )108.4430555555561.2854546615760184.3616339004918
Winsorized Mean ( 17 / 24 )108.8444444444441.2156241737490989.5379071878428
Winsorized Mean ( 18 / 24 )108.6694444444441.1858741466701191.6365743781361
Winsorized Mean ( 19 / 24 )108.5111111111111.1659430276823593.0672498868223
Winsorized Mean ( 20 / 24 )108.7888888888891.1157019789932397.5071219171417
Winsorized Mean ( 21 / 24 )108.8763888888891.03864772491037104.825135873941
Winsorized Mean ( 22 / 24 )109.5486111111110.924721319639975118.466622088655
Winsorized Mean ( 23 / 24 )109.5486111111110.907829776119002120.670872439803
Winsorized Mean ( 24 / 24 )109.8152777777780.844629215819147130.015959335808
Trimmed Mean ( 1 / 24 )109.1728571428571.8922987886981257.6932447427961
Trimmed Mean ( 2 / 24 )109.2058823529411.8534426624640758.9205614851646
Trimmed Mean ( 3 / 24 )109.2318181818181.8232404860269259.9108121056748
Trimmed Mean ( 4 / 24 )109.2468751.7924803921106660.9473194132745
Trimmed Mean ( 5 / 24 )109.269354838711.758014944551262.1549635726248
Trimmed Mean ( 6 / 24 )109.2751.7298911252112863.1687153066663
Trimmed Mean ( 7 / 24 )109.2637931034481.699937186619164.2751943798325
Trimmed Mean ( 8 / 24 )109.2589285714291.6652576275582765.6108260747812
Trimmed Mean ( 9 / 24 )109.2425925925931.6266358252477467.1586048315115
Trimmed Mean ( 10 / 24 )109.2173076923081.5811405499088269.0750153100596
Trimmed Mean ( 11 / 24 )109.2161.5366817152154771.0726228591105
Trimmed Mean ( 12 / 24 )109.2020833333331.4835160744375773.6103135078829
Trimmed Mean ( 13 / 24 )109.2456521739131.4351646761096976.1206389708851
Trimmed Mean ( 14 / 24 )109.3022727272731.3950853355288578.3480909329738
Trimmed Mean ( 15 / 24 )109.4214285714291.3621076434900380.3324385516743
Trimmed Mean ( 16 / 24 )109.55751.3197847896629483.0116401235236
Trimmed Mean ( 17 / 24 )109.6894736842111.2936258518504884.7922709083961
Trimmed Mean ( 18 / 24 )109.7888888888891.2735263988375686.2085693622853
Trimmed Mean ( 19 / 24 )109.9205882352941.2496329543945487.962299528626
Trimmed Mean ( 20 / 24 )110.08751.2173704971861990.4305634598951
Trimmed Mean ( 21 / 24 )110.2433333333331.1835431253240993.1468663663145
Trimmed Mean ( 22 / 24 )110.4107142857141.1540742102182495.6703765738212
Trimmed Mean ( 23 / 24 )110.5192307692311.1443778186053796.5758239738679
Trimmed Mean ( 24 / 24 )110.6458333333331.1275049273112398.1333479377256
Median112.75
Midrange107.95
Midmean - Weighted Average at Xnp109.405405405405
Midmean - Weighted Average at X(n+1)p109.788888888889
Midmean - Empirical Distribution Function109.405405405405
Midmean - Empirical Distribution Function - Averaging109.788888888889
Midmean - Empirical Distribution Function - Interpolation109.788888888889
Midmean - Closest Observation109.405405405405
Midmean - True Basic - Statistics Graphics Toolkit109.788888888889
Midmean - MS Excel (old versions)109.68947368421
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 109.138888888889 & 1.9337719629059 & 56.4383448423176 \tabularnewline
Geometric Mean & 107.890357023511 &  &  \tabularnewline
Harmonic Mean & 106.617055027476 &  &  \tabularnewline
Quadratic Mean & 110.348537472058 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 109.141666666667 & 1.9248058963579 & 56.7026872024776 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 109.158333333333 & 1.89880197589479 & 57.4880028139287 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 109.191666666667 & 1.88577031868562 & 57.9029511625641 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 109.169444444444 & 1.8774250242786 & 58.1484975605844 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 109.245833333333 & 1.83240259931974 & 59.6189032769816 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 109.329166666667 & 1.81460066600714 & 60.2497115286722 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 109.290277777778 & 1.80425852504687 & 60.5735133078773 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 109.356944444444 & 1.78497448330776 & 61.2652704378123 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 109.406944444444 & 1.77216273092243 & 61.7363984330585 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 109.226388888889 & 1.71731036868945 & 63.603173241331 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 109.318055555556 & 1.7020014067823 & 64.2291217386393 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 108.868055555556 & 1.61744672433432 & 67.3085882320864 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 108.795833333333 & 1.51952271651125 & 71.5986882928101 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 108.329166666667 & 1.42838626224238 & 75.8402468087337 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 108.2875 & 1.4164041975859 & 76.4523998054817 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 108.443055555556 & 1.28545466157601 & 84.3616339004918 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 108.844444444444 & 1.21562417374909 & 89.5379071878428 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 108.669444444444 & 1.18587414667011 & 91.6365743781361 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 108.511111111111 & 1.16594302768235 & 93.0672498868223 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 108.788888888889 & 1.11570197899323 & 97.5071219171417 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 108.876388888889 & 1.03864772491037 & 104.825135873941 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 109.548611111111 & 0.924721319639975 & 118.466622088655 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 109.548611111111 & 0.907829776119002 & 120.670872439803 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 109.815277777778 & 0.844629215819147 & 130.015959335808 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 109.172857142857 & 1.89229878869812 & 57.6932447427961 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 109.205882352941 & 1.85344266246407 & 58.9205614851646 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 109.231818181818 & 1.82324048602692 & 59.9108121056748 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 109.246875 & 1.79248039211066 & 60.9473194132745 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 109.26935483871 & 1.7580149445512 & 62.1549635726248 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 109.275 & 1.72989112521128 & 63.1687153066663 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 109.263793103448 & 1.6999371866191 & 64.2751943798325 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 109.258928571429 & 1.66525762755827 & 65.6108260747812 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 109.242592592593 & 1.62663582524774 & 67.1586048315115 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 109.217307692308 & 1.58114054990882 & 69.0750153100596 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 109.216 & 1.53668171521547 & 71.0726228591105 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 109.202083333333 & 1.48351607443757 & 73.6103135078829 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 109.245652173913 & 1.43516467610969 & 76.1206389708851 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 109.302272727273 & 1.39508533552885 & 78.3480909329738 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 109.421428571429 & 1.36210764349003 & 80.3324385516743 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 109.5575 & 1.31978478966294 & 83.0116401235236 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 109.689473684211 & 1.29362585185048 & 84.7922709083961 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 109.788888888889 & 1.27352639883756 & 86.2085693622853 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 109.920588235294 & 1.24963295439454 & 87.962299528626 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 110.0875 & 1.21737049718619 & 90.4305634598951 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 110.243333333333 & 1.18354312532409 & 93.1468663663145 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 110.410714285714 & 1.15407421021824 & 95.6703765738212 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 110.519230769231 & 1.14437781860537 & 96.5758239738679 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 110.645833333333 & 1.12750492731123 & 98.1333479377256 \tabularnewline
Median & 112.75 &  &  \tabularnewline
Midrange & 107.95 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 109.405405405405 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 109.788888888889 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 109.405405405405 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 109.788888888889 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 109.788888888889 &  &  \tabularnewline
Midmean - Closest Observation & 109.405405405405 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 109.788888888889 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 109.68947368421 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=240726&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]109.138888888889[/C][C]1.9337719629059[/C][C]56.4383448423176[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]107.890357023511[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]106.617055027476[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]110.348537472058[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]109.141666666667[/C][C]1.9248058963579[/C][C]56.7026872024776[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]109.158333333333[/C][C]1.89880197589479[/C][C]57.4880028139287[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]109.191666666667[/C][C]1.88577031868562[/C][C]57.9029511625641[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]109.169444444444[/C][C]1.8774250242786[/C][C]58.1484975605844[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]109.245833333333[/C][C]1.83240259931974[/C][C]59.6189032769816[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]109.329166666667[/C][C]1.81460066600714[/C][C]60.2497115286722[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]109.290277777778[/C][C]1.80425852504687[/C][C]60.5735133078773[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]109.356944444444[/C][C]1.78497448330776[/C][C]61.2652704378123[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]109.406944444444[/C][C]1.77216273092243[/C][C]61.7363984330585[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]109.226388888889[/C][C]1.71731036868945[/C][C]63.603173241331[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]109.318055555556[/C][C]1.7020014067823[/C][C]64.2291217386393[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]108.868055555556[/C][C]1.61744672433432[/C][C]67.3085882320864[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]108.795833333333[/C][C]1.51952271651125[/C][C]71.5986882928101[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]108.329166666667[/C][C]1.42838626224238[/C][C]75.8402468087337[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]108.2875[/C][C]1.4164041975859[/C][C]76.4523998054817[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]108.443055555556[/C][C]1.28545466157601[/C][C]84.3616339004918[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]108.844444444444[/C][C]1.21562417374909[/C][C]89.5379071878428[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]108.669444444444[/C][C]1.18587414667011[/C][C]91.6365743781361[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]108.511111111111[/C][C]1.16594302768235[/C][C]93.0672498868223[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]108.788888888889[/C][C]1.11570197899323[/C][C]97.5071219171417[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]108.876388888889[/C][C]1.03864772491037[/C][C]104.825135873941[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]109.548611111111[/C][C]0.924721319639975[/C][C]118.466622088655[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]109.548611111111[/C][C]0.907829776119002[/C][C]120.670872439803[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]109.815277777778[/C][C]0.844629215819147[/C][C]130.015959335808[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]109.172857142857[/C][C]1.89229878869812[/C][C]57.6932447427961[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]109.205882352941[/C][C]1.85344266246407[/C][C]58.9205614851646[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]109.231818181818[/C][C]1.82324048602692[/C][C]59.9108121056748[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]109.246875[/C][C]1.79248039211066[/C][C]60.9473194132745[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]109.26935483871[/C][C]1.7580149445512[/C][C]62.1549635726248[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]109.275[/C][C]1.72989112521128[/C][C]63.1687153066663[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]109.263793103448[/C][C]1.6999371866191[/C][C]64.2751943798325[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]109.258928571429[/C][C]1.66525762755827[/C][C]65.6108260747812[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]109.242592592593[/C][C]1.62663582524774[/C][C]67.1586048315115[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]109.217307692308[/C][C]1.58114054990882[/C][C]69.0750153100596[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]109.216[/C][C]1.53668171521547[/C][C]71.0726228591105[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]109.202083333333[/C][C]1.48351607443757[/C][C]73.6103135078829[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]109.245652173913[/C][C]1.43516467610969[/C][C]76.1206389708851[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]109.302272727273[/C][C]1.39508533552885[/C][C]78.3480909329738[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]109.421428571429[/C][C]1.36210764349003[/C][C]80.3324385516743[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]109.5575[/C][C]1.31978478966294[/C][C]83.0116401235236[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]109.689473684211[/C][C]1.29362585185048[/C][C]84.7922709083961[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]109.788888888889[/C][C]1.27352639883756[/C][C]86.2085693622853[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]109.920588235294[/C][C]1.24963295439454[/C][C]87.962299528626[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]110.0875[/C][C]1.21737049718619[/C][C]90.4305634598951[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]110.243333333333[/C][C]1.18354312532409[/C][C]93.1468663663145[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]110.410714285714[/C][C]1.15407421021824[/C][C]95.6703765738212[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]110.519230769231[/C][C]1.14437781860537[/C][C]96.5758239738679[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]110.645833333333[/C][C]1.12750492731123[/C][C]98.1333479377256[/C][/ROW]
[ROW][C]Median[/C][C]112.75[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]107.95[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]109.405405405405[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]109.788888888889[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]109.405405405405[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]109.788888888889[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]109.788888888889[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]109.405405405405[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]109.788888888889[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]109.68947368421[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]72[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=240726&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=240726&T=1

As an alternative you can also use a QR Code:  
QR Code


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

Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean109.1388888888891.933771962905956.4383448423176
Geometric Mean107.890357023511
Harmonic Mean106.617055027476
Quadratic Mean110.348537472058
Winsorized Mean ( 1 / 24 )109.1416666666671.924805896357956.7026872024776
Winsorized Mean ( 2 / 24 )109.1583333333331.8988019758947957.4880028139287
Winsorized Mean ( 3 / 24 )109.1916666666671.8857703186856257.9029511625641
Winsorized Mean ( 4 / 24 )109.1694444444441.877425024278658.1484975605844
Winsorized Mean ( 5 / 24 )109.2458333333331.8324025993197459.6189032769816
Winsorized Mean ( 6 / 24 )109.3291666666671.8146006660071460.2497115286722
Winsorized Mean ( 7 / 24 )109.2902777777781.8042585250468760.5735133078773
Winsorized Mean ( 8 / 24 )109.3569444444441.7849744833077661.2652704378123
Winsorized Mean ( 9 / 24 )109.4069444444441.7721627309224361.7363984330585
Winsorized Mean ( 10 / 24 )109.2263888888891.7173103686894563.603173241331
Winsorized Mean ( 11 / 24 )109.3180555555561.702001406782364.2291217386393
Winsorized Mean ( 12 / 24 )108.8680555555561.6174467243343267.3085882320864
Winsorized Mean ( 13 / 24 )108.7958333333331.5195227165112571.5986882928101
Winsorized Mean ( 14 / 24 )108.3291666666671.4283862622423875.8402468087337
Winsorized Mean ( 15 / 24 )108.28751.416404197585976.4523998054817
Winsorized Mean ( 16 / 24 )108.4430555555561.2854546615760184.3616339004918
Winsorized Mean ( 17 / 24 )108.8444444444441.2156241737490989.5379071878428
Winsorized Mean ( 18 / 24 )108.6694444444441.1858741466701191.6365743781361
Winsorized Mean ( 19 / 24 )108.5111111111111.1659430276823593.0672498868223
Winsorized Mean ( 20 / 24 )108.7888888888891.1157019789932397.5071219171417
Winsorized Mean ( 21 / 24 )108.8763888888891.03864772491037104.825135873941
Winsorized Mean ( 22 / 24 )109.5486111111110.924721319639975118.466622088655
Winsorized Mean ( 23 / 24 )109.5486111111110.907829776119002120.670872439803
Winsorized Mean ( 24 / 24 )109.8152777777780.844629215819147130.015959335808
Trimmed Mean ( 1 / 24 )109.1728571428571.8922987886981257.6932447427961
Trimmed Mean ( 2 / 24 )109.2058823529411.8534426624640758.9205614851646
Trimmed Mean ( 3 / 24 )109.2318181818181.8232404860269259.9108121056748
Trimmed Mean ( 4 / 24 )109.2468751.7924803921106660.9473194132745
Trimmed Mean ( 5 / 24 )109.269354838711.758014944551262.1549635726248
Trimmed Mean ( 6 / 24 )109.2751.7298911252112863.1687153066663
Trimmed Mean ( 7 / 24 )109.2637931034481.699937186619164.2751943798325
Trimmed Mean ( 8 / 24 )109.2589285714291.6652576275582765.6108260747812
Trimmed Mean ( 9 / 24 )109.2425925925931.6266358252477467.1586048315115
Trimmed Mean ( 10 / 24 )109.2173076923081.5811405499088269.0750153100596
Trimmed Mean ( 11 / 24 )109.2161.5366817152154771.0726228591105
Trimmed Mean ( 12 / 24 )109.2020833333331.4835160744375773.6103135078829
Trimmed Mean ( 13 / 24 )109.2456521739131.4351646761096976.1206389708851
Trimmed Mean ( 14 / 24 )109.3022727272731.3950853355288578.3480909329738
Trimmed Mean ( 15 / 24 )109.4214285714291.3621076434900380.3324385516743
Trimmed Mean ( 16 / 24 )109.55751.3197847896629483.0116401235236
Trimmed Mean ( 17 / 24 )109.6894736842111.2936258518504884.7922709083961
Trimmed Mean ( 18 / 24 )109.7888888888891.2735263988375686.2085693622853
Trimmed Mean ( 19 / 24 )109.9205882352941.2496329543945487.962299528626
Trimmed Mean ( 20 / 24 )110.08751.2173704971861990.4305634598951
Trimmed Mean ( 21 / 24 )110.2433333333331.1835431253240993.1468663663145
Trimmed Mean ( 22 / 24 )110.4107142857141.1540742102182495.6703765738212
Trimmed Mean ( 23 / 24 )110.5192307692311.1443778186053796.5758239738679
Trimmed Mean ( 24 / 24 )110.6458333333331.1275049273112398.1333479377256
Median112.75
Midrange107.95
Midmean - Weighted Average at Xnp109.405405405405
Midmean - Weighted Average at X(n+1)p109.788888888889
Midmean - Empirical Distribution Function109.405405405405
Midmean - Empirical Distribution Function - Averaging109.788888888889
Midmean - Empirical Distribution Function - Interpolation109.788888888889
Midmean - Closest Observation109.405405405405
Midmean - True Basic - Statistics Graphics Toolkit109.788888888889
Midmean - MS Excel (old versions)109.68947368421
Number of observations72


Figures (Output of Computation)

Input Parameters & R Code

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')