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Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationFri, 04 Mar 2016 16:40:40 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2016/Mar/04/t1457109693hl6v6tw2nrn6cae.htm/, Retrieved Sat, 18 May 2024 14:39:56 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=293398, Retrieved Sat, 18 May 2024 14:39:56 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact52
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [centrummaten - we...] [2016-03-04 16:40:40] [214f5f03d61b6cc2dcf3be3cf135b694] [Current]
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Dataseries X:
78,21
75,50
79,87
85,76
77,02
75,47
75,29
77,52
78,44
83,50
86,29
92,14
96,91
104,23
114,60
122,09
114,52
113,77
117,03
109,84
109,90
108,74
110,49
107,82
111,26
119,06
124,54
120,60
110,28
95,93
102,72
112,68
113,03
111,48
109,56
109,16
112,32
116,08
109,63
109,63
103,27
103,32
107,38
110,45
111,24
109,44
107,94
110,58
107,31
108,70
107,70
108,08
109,32
111,95
108,07
103,38
98,54
88,16
79,70
63,30




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Herman Ole Andreas Wold' @ wold.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 & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=293398&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]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=293398&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=293398&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'Herman Ole Andreas Wold' @ wold.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean102.3456666666671.8688434800482954.7641724731393
Geometric Mean101.22210304016
Harmonic Mean99.9743123327272
Quadratic Mean103.347459894603
Winsorized Mean ( 1 / 20 )102.5046666666671.7997879107107356.9537477480822
Winsorized Mean ( 2 / 20 )102.4611.7894042138873957.2598405686149
Winsorized Mean ( 3 / 20 )102.38551.7762778868622857.6404743634227
Winsorized Mean ( 4 / 20 )102.35151.7301915054352359.1561683654513
Winsorized Mean ( 5 / 20 )102.3141.7087996447766259.8747783643031
Winsorized Mean ( 6 / 20 )102.2351.6725291836187861.1259887129734
Winsorized Mean ( 7 / 20 )102.25251.6648425151594661.418722232839
Winsorized Mean ( 8 / 20 )102.32051.6122302240057863.4651915566824
Winsorized Mean ( 9 / 20 )102.2351.5931081531304264.1732953278223
Winsorized Mean ( 10 / 20 )102.7816666666671.4458489806867571.0874151032339
Winsorized Mean ( 11 / 20 )103.131.3460075301373576.6191850274988
Winsorized Mean ( 12 / 20 )103.1621.3144078772575278.4855308500169
Winsorized Mean ( 13 / 20 )103.4653333333331.2156058791746685.1142093879816
Winsorized Mean ( 14 / 20 )104.3426666666671.01573960325449102.725803279056
Winsorized Mean ( 15 / 20 )105.2851666666670.827303990190158127.262974571737
Winsorized Mean ( 16 / 20 )105.37050.756449460785824139.296153229507
Winsorized Mean ( 17 / 20 )105.8068333333330.666956935042665158.641177224681
Winsorized Mean ( 18 / 20 )107.0488333333330.443542817738726241.349491079781
Winsorized Mean ( 19 / 20 )107.1691666666670.408043650848922262.641426827019
Winsorized Mean ( 20 / 20 )107.0591666666670.389312612515513274.995371906685
Trimmed Mean ( 1 / 20 )102.6362068965521.7686582359777358.0305481345941
Trimmed Mean ( 2 / 20 )102.7771428571431.7296397176509659.421127884786
Trimmed Mean ( 3 / 20 )102.9527777777781.6874276010903461.0116710851798
Trimmed Mean ( 4 / 20 )103.1709615384621.6401035370789962.9051515383035
Trimmed Mean ( 5 / 20 )103.41681.5977985222020464.7245560456984
Trimmed Mean ( 6 / 20 )103.69251.5500089939112266.8979989195722
Trimmed Mean ( 7 / 20 )104.0093478260871.4983329674573269.4167118291413
Trimmed Mean ( 8 / 20 )104.3515909090911.4316223275390972.8904466644271
Trimmed Mean ( 9 / 20 )104.7142857142861.3580324182847577.107353480224
Trimmed Mean ( 10 / 20 )105.12751.2615066668523183.3348746878306
Trimmed Mean ( 11 / 20 )105.4978947368421.1784516904030389.5224603570824
Trimmed Mean ( 12 / 20 )105.8566666666671.0953801978207396.6392005965324
Trimmed Mean ( 13 / 20 )106.2529411764710.984052203719696107.974902931813
Trimmed Mean ( 14 / 20 )106.6550.855867438672979124.616260860874
Trimmed Mean ( 15 / 20 )106.9853333333330.751614466673846142.340705344298
Trimmed Mean ( 16 / 20 )107.2282142857140.679937176830982157.70312014042
Trimmed Mean ( 17 / 20 )107.4961538461540.59477625448517180.733768430619
Trimmed Mean ( 18 / 20 )107.7445833333330.502324660867311214.491924699261
Trimmed Mean ( 19 / 20 )107.850.480070341166305224.65457819782
Trimmed Mean ( 20 / 20 )107.95750.457002749617434236.229432077539
Median108.39
Midrange93.92
Midmean - Weighted Average at Xnp106.506451612903
Midmean - Weighted Average at X(n+1)p106.985333333333
Midmean - Empirical Distribution Function106.506451612903
Midmean - Empirical Distribution Function - Averaging106.985333333333
Midmean - Empirical Distribution Function - Interpolation106.985333333333
Midmean - Closest Observation106.506451612903
Midmean - True Basic - Statistics Graphics Toolkit106.985333333333
Midmean - MS Excel (old versions)106.655
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 102.345666666667 & 1.86884348004829 & 54.7641724731393 \tabularnewline
Geometric Mean & 101.22210304016 &  &  \tabularnewline
Harmonic Mean & 99.9743123327272 &  &  \tabularnewline
Quadratic Mean & 103.347459894603 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 102.504666666667 & 1.79978791071073 & 56.9537477480822 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 102.461 & 1.78940421388739 & 57.2598405686149 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 102.3855 & 1.77627788686228 & 57.6404743634227 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 102.3515 & 1.73019150543523 & 59.1561683654513 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 102.314 & 1.70879964477662 & 59.8747783643031 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 102.235 & 1.67252918361878 & 61.1259887129734 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 102.2525 & 1.66484251515946 & 61.418722232839 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 102.3205 & 1.61223022400578 & 63.4651915566824 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 102.235 & 1.59310815313042 & 64.1732953278223 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 102.781666666667 & 1.44584898068675 & 71.0874151032339 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 103.13 & 1.34600753013735 & 76.6191850274988 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 103.162 & 1.31440787725752 & 78.4855308500169 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 103.465333333333 & 1.21560587917466 & 85.1142093879816 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 104.342666666667 & 1.01573960325449 & 102.725803279056 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 105.285166666667 & 0.827303990190158 & 127.262974571737 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 105.3705 & 0.756449460785824 & 139.296153229507 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 105.806833333333 & 0.666956935042665 & 158.641177224681 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 107.048833333333 & 0.443542817738726 & 241.349491079781 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 107.169166666667 & 0.408043650848922 & 262.641426827019 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 107.059166666667 & 0.389312612515513 & 274.995371906685 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 102.636206896552 & 1.76865823597773 & 58.0305481345941 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 102.777142857143 & 1.72963971765096 & 59.421127884786 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 102.952777777778 & 1.68742760109034 & 61.0116710851798 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 103.170961538462 & 1.64010353707899 & 62.9051515383035 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 103.4168 & 1.59779852220204 & 64.7245560456984 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 103.6925 & 1.55000899391122 & 66.8979989195722 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 104.009347826087 & 1.49833296745732 & 69.4167118291413 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 104.351590909091 & 1.43162232753909 & 72.8904466644271 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 104.714285714286 & 1.35803241828475 & 77.107353480224 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 105.1275 & 1.26150666685231 & 83.3348746878306 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 105.497894736842 & 1.17845169040303 & 89.5224603570824 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 105.856666666667 & 1.09538019782073 & 96.6392005965324 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 106.252941176471 & 0.984052203719696 & 107.974902931813 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 106.655 & 0.855867438672979 & 124.616260860874 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 106.985333333333 & 0.751614466673846 & 142.340705344298 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 107.228214285714 & 0.679937176830982 & 157.70312014042 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 107.496153846154 & 0.59477625448517 & 180.733768430619 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 107.744583333333 & 0.502324660867311 & 214.491924699261 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 107.85 & 0.480070341166305 & 224.65457819782 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 107.9575 & 0.457002749617434 & 236.229432077539 \tabularnewline
Median & 108.39 &  &  \tabularnewline
Midrange & 93.92 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 106.506451612903 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 106.985333333333 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 106.506451612903 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 106.985333333333 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 106.985333333333 &  &  \tabularnewline
Midmean - Closest Observation & 106.506451612903 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 106.985333333333 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 106.655 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=293398&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]102.345666666667[/C][C]1.86884348004829[/C][C]54.7641724731393[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]101.22210304016[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]99.9743123327272[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]103.347459894603[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]102.504666666667[/C][C]1.79978791071073[/C][C]56.9537477480822[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]102.461[/C][C]1.78940421388739[/C][C]57.2598405686149[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]102.3855[/C][C]1.77627788686228[/C][C]57.6404743634227[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]102.3515[/C][C]1.73019150543523[/C][C]59.1561683654513[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]102.314[/C][C]1.70879964477662[/C][C]59.8747783643031[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]102.235[/C][C]1.67252918361878[/C][C]61.1259887129734[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]102.2525[/C][C]1.66484251515946[/C][C]61.418722232839[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]102.3205[/C][C]1.61223022400578[/C][C]63.4651915566824[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]102.235[/C][C]1.59310815313042[/C][C]64.1732953278223[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]102.781666666667[/C][C]1.44584898068675[/C][C]71.0874151032339[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]103.13[/C][C]1.34600753013735[/C][C]76.6191850274988[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]103.162[/C][C]1.31440787725752[/C][C]78.4855308500169[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]103.465333333333[/C][C]1.21560587917466[/C][C]85.1142093879816[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]104.342666666667[/C][C]1.01573960325449[/C][C]102.725803279056[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]105.285166666667[/C][C]0.827303990190158[/C][C]127.262974571737[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]105.3705[/C][C]0.756449460785824[/C][C]139.296153229507[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]105.806833333333[/C][C]0.666956935042665[/C][C]158.641177224681[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]107.048833333333[/C][C]0.443542817738726[/C][C]241.349491079781[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]107.169166666667[/C][C]0.408043650848922[/C][C]262.641426827019[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]107.059166666667[/C][C]0.389312612515513[/C][C]274.995371906685[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]102.636206896552[/C][C]1.76865823597773[/C][C]58.0305481345941[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]102.777142857143[/C][C]1.72963971765096[/C][C]59.421127884786[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]102.952777777778[/C][C]1.68742760109034[/C][C]61.0116710851798[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]103.170961538462[/C][C]1.64010353707899[/C][C]62.9051515383035[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]103.4168[/C][C]1.59779852220204[/C][C]64.7245560456984[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]103.6925[/C][C]1.55000899391122[/C][C]66.8979989195722[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]104.009347826087[/C][C]1.49833296745732[/C][C]69.4167118291413[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]104.351590909091[/C][C]1.43162232753909[/C][C]72.8904466644271[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]104.714285714286[/C][C]1.35803241828475[/C][C]77.107353480224[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]105.1275[/C][C]1.26150666685231[/C][C]83.3348746878306[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]105.497894736842[/C][C]1.17845169040303[/C][C]89.5224603570824[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]105.856666666667[/C][C]1.09538019782073[/C][C]96.6392005965324[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]106.252941176471[/C][C]0.984052203719696[/C][C]107.974902931813[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]106.655[/C][C]0.855867438672979[/C][C]124.616260860874[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]106.985333333333[/C][C]0.751614466673846[/C][C]142.340705344298[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]107.228214285714[/C][C]0.679937176830982[/C][C]157.70312014042[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]107.496153846154[/C][C]0.59477625448517[/C][C]180.733768430619[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]107.744583333333[/C][C]0.502324660867311[/C][C]214.491924699261[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]107.85[/C][C]0.480070341166305[/C][C]224.65457819782[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]107.9575[/C][C]0.457002749617434[/C][C]236.229432077539[/C][/ROW]
[ROW][C]Median[/C][C]108.39[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]93.92[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]106.506451612903[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]106.985333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]106.506451612903[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]106.985333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]106.985333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]106.506451612903[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]106.985333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]106.655[/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=293398&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=293398&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 Mean102.3456666666671.8688434800482954.7641724731393
Geometric Mean101.22210304016
Harmonic Mean99.9743123327272
Quadratic Mean103.347459894603
Winsorized Mean ( 1 / 20 )102.5046666666671.7997879107107356.9537477480822
Winsorized Mean ( 2 / 20 )102.4611.7894042138873957.2598405686149
Winsorized Mean ( 3 / 20 )102.38551.7762778868622857.6404743634227
Winsorized Mean ( 4 / 20 )102.35151.7301915054352359.1561683654513
Winsorized Mean ( 5 / 20 )102.3141.7087996447766259.8747783643031
Winsorized Mean ( 6 / 20 )102.2351.6725291836187861.1259887129734
Winsorized Mean ( 7 / 20 )102.25251.6648425151594661.418722232839
Winsorized Mean ( 8 / 20 )102.32051.6122302240057863.4651915566824
Winsorized Mean ( 9 / 20 )102.2351.5931081531304264.1732953278223
Winsorized Mean ( 10 / 20 )102.7816666666671.4458489806867571.0874151032339
Winsorized Mean ( 11 / 20 )103.131.3460075301373576.6191850274988
Winsorized Mean ( 12 / 20 )103.1621.3144078772575278.4855308500169
Winsorized Mean ( 13 / 20 )103.4653333333331.2156058791746685.1142093879816
Winsorized Mean ( 14 / 20 )104.3426666666671.01573960325449102.725803279056
Winsorized Mean ( 15 / 20 )105.2851666666670.827303990190158127.262974571737
Winsorized Mean ( 16 / 20 )105.37050.756449460785824139.296153229507
Winsorized Mean ( 17 / 20 )105.8068333333330.666956935042665158.641177224681
Winsorized Mean ( 18 / 20 )107.0488333333330.443542817738726241.349491079781
Winsorized Mean ( 19 / 20 )107.1691666666670.408043650848922262.641426827019
Winsorized Mean ( 20 / 20 )107.0591666666670.389312612515513274.995371906685
Trimmed Mean ( 1 / 20 )102.6362068965521.7686582359777358.0305481345941
Trimmed Mean ( 2 / 20 )102.7771428571431.7296397176509659.421127884786
Trimmed Mean ( 3 / 20 )102.9527777777781.6874276010903461.0116710851798
Trimmed Mean ( 4 / 20 )103.1709615384621.6401035370789962.9051515383035
Trimmed Mean ( 5 / 20 )103.41681.5977985222020464.7245560456984
Trimmed Mean ( 6 / 20 )103.69251.5500089939112266.8979989195722
Trimmed Mean ( 7 / 20 )104.0093478260871.4983329674573269.4167118291413
Trimmed Mean ( 8 / 20 )104.3515909090911.4316223275390972.8904466644271
Trimmed Mean ( 9 / 20 )104.7142857142861.3580324182847577.107353480224
Trimmed Mean ( 10 / 20 )105.12751.2615066668523183.3348746878306
Trimmed Mean ( 11 / 20 )105.4978947368421.1784516904030389.5224603570824
Trimmed Mean ( 12 / 20 )105.8566666666671.0953801978207396.6392005965324
Trimmed Mean ( 13 / 20 )106.2529411764710.984052203719696107.974902931813
Trimmed Mean ( 14 / 20 )106.6550.855867438672979124.616260860874
Trimmed Mean ( 15 / 20 )106.9853333333330.751614466673846142.340705344298
Trimmed Mean ( 16 / 20 )107.2282142857140.679937176830982157.70312014042
Trimmed Mean ( 17 / 20 )107.4961538461540.59477625448517180.733768430619
Trimmed Mean ( 18 / 20 )107.7445833333330.502324660867311214.491924699261
Trimmed Mean ( 19 / 20 )107.850.480070341166305224.65457819782
Trimmed Mean ( 20 / 20 )107.95750.457002749617434236.229432077539
Median108.39
Midrange93.92
Midmean - Weighted Average at Xnp106.506451612903
Midmean - Weighted Average at X(n+1)p106.985333333333
Midmean - Empirical Distribution Function106.506451612903
Midmean - Empirical Distribution Function - Averaging106.985333333333
Midmean - Empirical Distribution Function - Interpolation106.985333333333
Midmean - Closest Observation106.506451612903
Midmean - True Basic - Statistics Graphics Toolkit106.985333333333
Midmean - MS Excel (old versions)106.655
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')