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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 computationSun, 30 Nov 2008 11:25:17 -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/Nov/30/t1228069572d5x4hax3x9w23fv.htm/, Retrieved Mon, 13 May 2024 22:24:43 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=26676, Retrieved Mon, 13 May 2024 22:24:43 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact177
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
F     [Central Tendency] [Q1 central tenden...] [2007-10-18 09:40:43] [b731da8b544846036771bbf9bf2f34ce]
F    D  [Central Tendency] [task 3 Q1 Reprodu...] [2008-10-19 12:06:44] [86761fc994bdf34e4f4ab5b8e1d9e1c3]
-    D      [Central Tendency] [CT Bouwproductie] [2008-11-30 18:25:17] [8a1195ff8db4df756ce44b463a631c76] [Current]
- R           [Central Tendency] [Central Tendancy ...] [2008-11-30 18:59:06] [aa5573c1db401b164e448aef050955a1]
- R  D          [Central Tendency] [Central Tendancy ...] [2008-11-30 19:21:14] [aa5573c1db401b164e448aef050955a1]
-    D            [Central Tendency] [CT Investeringen] [2008-11-30 21:15:30] [aa5573c1db401b164e448aef050955a1]
- R                 [Central Tendency] [CT invest gemiddelde] [2008-11-30 21:32:45] [aa5573c1db401b164e448aef050955a1]
-    D              [Central Tendency] [CT omzet ] [2008-11-30 21:40:40] [aa5573c1db401b164e448aef050955a1]
- R                   [Central Tendency] [CT omzet gemiddelde] [2008-11-30 21:44:33] [aa5573c1db401b164e448aef050955a1]
- R                   [Central Tendency] [CT Gemiddelde omzet] [2008-11-30 22:36:39] [aa5573c1db401b164e448aef050955a1]
- RM D                [Univariate Explorative Data Analysis] [Univariate EDA Bo...] [2008-11-30 23:26:57] [aa5573c1db401b164e448aef050955a1]
- RM D                [Univariate Explorative Data Analysis] [Univariate EDA To...] [2008-11-30 23:51:28] [aa5573c1db401b164e448aef050955a1]
- RM D                [Univariate Explorative Data Analysis] [Univariate EDA In...] [2008-11-30 23:58:42] [aa5573c1db401b164e448aef050955a1]
- RM                  [Univariate Explorative Data Analysis] [Univariate EDA Omzet] [2008-12-01 00:05:10] [aa5573c1db401b164e448aef050955a1]
- RM D                [Univariate Explorative Data Analysis] [Univariate EDA In...] [2008-12-01 00:12:08] [aa5573c1db401b164e448aef050955a1]
- R  D            [Central Tendency] [CT gemiddelde invest] [2008-11-30 21:19:41] [aa5573c1db401b164e448aef050955a1]
- R  D          [Central Tendency] [Central Tendancy ...] [2008-11-30 19:24:23] [aa5573c1db401b164e448aef050955a1]
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Dataseries X:
82.7
88.9
105.9
100.8
94
105
58.5
87.6
113.1
112.5
89.6
74.5
82.7
90.1
109.4
96
89.2
109.1
49.1
92.9
107.7
103.5
91.1
79.8
71.9
82.9
90.1
100.7
90.7
108.8
44.1
93.6
107.4
96.5
93.6
76.5
76.7
84
103.3
88.5
99
105.9
44.7
94
107.1
104.8
102.5
77.7
85.2
91.3
106.5
92.4
97.5
107
51.1
98.6
102.2
114.3
99.4
72.5
92.3
99.4
85.9
109.4
97.6




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'George Udny Yule' @ 72.249.76.132

\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 & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=26676&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]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=26676&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=26676&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'George Udny Yule' @ 72.249.76.132







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean91.71230769230772.0154934828200145.5036488453373
Geometric Mean89.9530368565007
Harmonic Mean87.7295884550365
Quadratic Mean93.1188975284989
Winsorized Mean ( 1 / 21 )91.70307692307692.0089498898089345.6472694457295
Winsorized Mean ( 2 / 21 )91.821.9580457781244046.8936942260635
Winsorized Mean ( 3 / 21 )91.76923076923081.9047371652380448.1794719208737
Winsorized Mean ( 4 / 21 )92.22461538461541.7603075981875152.3911931525910
Winsorized Mean ( 5 / 21 )93.23230769230771.4832512166176162.856720862777
Winsorized Mean ( 6 / 21 )93.261.4662940596042763.6025218742068
Winsorized Mean ( 7 / 21 )93.3569230769231.4004926489501266.6600593347694
Winsorized Mean ( 8 / 21 )93.56615384615391.3442314020027169.6056896950582
Winsorized Mean ( 9 / 21 )93.55230769230771.3321074030032670.2288024834876
Winsorized Mean ( 10 / 21 )93.69076923076921.2996555073825672.0889256411167
Winsorized Mean ( 11 / 21 )93.96153846153851.2196304853151577.040988719841
Winsorized Mean ( 12 / 21 )94.38615384615381.1088929790801585.1174600496154
Winsorized Mean ( 13 / 21 )94.38615384615381.1088929790801585.1174600496154
Winsorized Mean ( 14 / 21 )94.23538461538461.0708269422444988.0024408219165
Winsorized Mean ( 15 / 21 )94.4430769230771.0222805605012292.3846941555569
Winsorized Mean ( 16 / 21 )94.41846153846150.925807579660165101.984973565587
Winsorized Mean ( 17 / 21 )94.54923076923080.889625361612217106.279828396399
Winsorized Mean ( 18 / 21 )94.79846153846150.786073164985334120.597503847152
Winsorized Mean ( 19 / 21 )94.97384615384620.735701120736712129.092974683444
Winsorized Mean ( 20 / 21 )94.66615384615380.654060089434996144.736172372068
Winsorized Mean ( 21 / 21 )94.73076923076920.636063324877671148.932921496438
Trimmed Mean ( 1 / 21 )92.10952380952381.900745958458348.4596710042377
Trimmed Mean ( 2 / 21 )92.54262295081971.7657974854587452.4084011405066
Trimmed Mean ( 3 / 21 )92.94067796610171.6322583141867756.9399323368782
Trimmed Mean ( 4 / 21 )93.38596491228071.4897591910595662.6852752261672
Trimmed Mean ( 5 / 21 )93.7290909090911.3736718047334668.2325214699137
Trimmed Mean ( 6 / 21 )93.85094339622641.3321349851229870.4515266428216
Trimmed Mean ( 7 / 21 )93.97647058823531.2849981711600473.1335442317378
Trimmed Mean ( 8 / 21 )94.09387755102041.2444209106041575.6125815222273
Trimmed Mean ( 9 / 21 )94.18510638297871.2080671587958277.9634689158017
Trimmed Mean ( 10 / 21 )94.28666666666671.1639127670461181.0083619118266
Trimmed Mean ( 11 / 21 )94.37674418604651.1149832133240884.6440942412782
Trimmed Mean ( 12 / 21 )94.43658536585371.0722654163690088.0720238890508
Trimmed Mean ( 13 / 21 )94.44358974358971.0443718118566590.4310023225264
Trimmed Mean ( 14 / 21 )94.45135135135131.0057165555535293.914483986363
Trimmed Mean ( 15 / 21 )94.480.96254913658271798.1560279981414
Trimmed Mean ( 16 / 21 )94.48484848484850.91608233316589103.140127327113
Trimmed Mean ( 17 / 21 )94.49354838709680.879099435136572107.489033220021
Trimmed Mean ( 18 / 21 )94.48620689655170.83586072769731113.040610433809
Trimmed Mean ( 19 / 21 )94.44444444444440.80563070678041117.230442744516
Trimmed Mean ( 20 / 21 )94.3720.774607857779234121.831968333707
Trimmed Mean ( 21 / 21 )94.33043478260870.755361201523577124.881228467047
Median93.6
Midrange79.2
Midmean - Weighted Average at Xnp94.203125
Midmean - Weighted Average at X(n+1)p94.4848484848485
Midmean - Empirical Distribution Function94.4848484848485
Midmean - Empirical Distribution Function - Averaging94.4848484848485
Midmean - Empirical Distribution Function - Interpolation94.4848484848485
Midmean - Closest Observation94.1764705882353
Midmean - True Basic - Statistics Graphics Toolkit94.4848484848485
Midmean - MS Excel (old versions)94.4848484848485
Number of observations65

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 91.7123076923077 & 2.01549348282001 & 45.5036488453373 \tabularnewline
Geometric Mean & 89.9530368565007 &  &  \tabularnewline
Harmonic Mean & 87.7295884550365 &  &  \tabularnewline
Quadratic Mean & 93.1188975284989 &  &  \tabularnewline
Winsorized Mean ( 1 / 21 ) & 91.7030769230769 & 2.00894988980893 & 45.6472694457295 \tabularnewline
Winsorized Mean ( 2 / 21 ) & 91.82 & 1.95804577812440 & 46.8936942260635 \tabularnewline
Winsorized Mean ( 3 / 21 ) & 91.7692307692308 & 1.90473716523804 & 48.1794719208737 \tabularnewline
Winsorized Mean ( 4 / 21 ) & 92.2246153846154 & 1.76030759818751 & 52.3911931525910 \tabularnewline
Winsorized Mean ( 5 / 21 ) & 93.2323076923077 & 1.48325121661761 & 62.856720862777 \tabularnewline
Winsorized Mean ( 6 / 21 ) & 93.26 & 1.46629405960427 & 63.6025218742068 \tabularnewline
Winsorized Mean ( 7 / 21 ) & 93.356923076923 & 1.40049264895012 & 66.6600593347694 \tabularnewline
Winsorized Mean ( 8 / 21 ) & 93.5661538461539 & 1.34423140200271 & 69.6056896950582 \tabularnewline
Winsorized Mean ( 9 / 21 ) & 93.5523076923077 & 1.33210740300326 & 70.2288024834876 \tabularnewline
Winsorized Mean ( 10 / 21 ) & 93.6907692307692 & 1.29965550738256 & 72.0889256411167 \tabularnewline
Winsorized Mean ( 11 / 21 ) & 93.9615384615385 & 1.21963048531515 & 77.040988719841 \tabularnewline
Winsorized Mean ( 12 / 21 ) & 94.3861538461538 & 1.10889297908015 & 85.1174600496154 \tabularnewline
Winsorized Mean ( 13 / 21 ) & 94.3861538461538 & 1.10889297908015 & 85.1174600496154 \tabularnewline
Winsorized Mean ( 14 / 21 ) & 94.2353846153846 & 1.07082694224449 & 88.0024408219165 \tabularnewline
Winsorized Mean ( 15 / 21 ) & 94.443076923077 & 1.02228056050122 & 92.3846941555569 \tabularnewline
Winsorized Mean ( 16 / 21 ) & 94.4184615384615 & 0.925807579660165 & 101.984973565587 \tabularnewline
Winsorized Mean ( 17 / 21 ) & 94.5492307692308 & 0.889625361612217 & 106.279828396399 \tabularnewline
Winsorized Mean ( 18 / 21 ) & 94.7984615384615 & 0.786073164985334 & 120.597503847152 \tabularnewline
Winsorized Mean ( 19 / 21 ) & 94.9738461538462 & 0.735701120736712 & 129.092974683444 \tabularnewline
Winsorized Mean ( 20 / 21 ) & 94.6661538461538 & 0.654060089434996 & 144.736172372068 \tabularnewline
Winsorized Mean ( 21 / 21 ) & 94.7307692307692 & 0.636063324877671 & 148.932921496438 \tabularnewline
Trimmed Mean ( 1 / 21 ) & 92.1095238095238 & 1.9007459584583 & 48.4596710042377 \tabularnewline
Trimmed Mean ( 2 / 21 ) & 92.5426229508197 & 1.76579748545874 & 52.4084011405066 \tabularnewline
Trimmed Mean ( 3 / 21 ) & 92.9406779661017 & 1.63225831418677 & 56.9399323368782 \tabularnewline
Trimmed Mean ( 4 / 21 ) & 93.3859649122807 & 1.48975919105956 & 62.6852752261672 \tabularnewline
Trimmed Mean ( 5 / 21 ) & 93.729090909091 & 1.37367180473346 & 68.2325214699137 \tabularnewline
Trimmed Mean ( 6 / 21 ) & 93.8509433962264 & 1.33213498512298 & 70.4515266428216 \tabularnewline
Trimmed Mean ( 7 / 21 ) & 93.9764705882353 & 1.28499817116004 & 73.1335442317378 \tabularnewline
Trimmed Mean ( 8 / 21 ) & 94.0938775510204 & 1.24442091060415 & 75.6125815222273 \tabularnewline
Trimmed Mean ( 9 / 21 ) & 94.1851063829787 & 1.20806715879582 & 77.9634689158017 \tabularnewline
Trimmed Mean ( 10 / 21 ) & 94.2866666666667 & 1.16391276704611 & 81.0083619118266 \tabularnewline
Trimmed Mean ( 11 / 21 ) & 94.3767441860465 & 1.11498321332408 & 84.6440942412782 \tabularnewline
Trimmed Mean ( 12 / 21 ) & 94.4365853658537 & 1.07226541636900 & 88.0720238890508 \tabularnewline
Trimmed Mean ( 13 / 21 ) & 94.4435897435897 & 1.04437181185665 & 90.4310023225264 \tabularnewline
Trimmed Mean ( 14 / 21 ) & 94.4513513513513 & 1.00571655555352 & 93.914483986363 \tabularnewline
Trimmed Mean ( 15 / 21 ) & 94.48 & 0.962549136582717 & 98.1560279981414 \tabularnewline
Trimmed Mean ( 16 / 21 ) & 94.4848484848485 & 0.91608233316589 & 103.140127327113 \tabularnewline
Trimmed Mean ( 17 / 21 ) & 94.4935483870968 & 0.879099435136572 & 107.489033220021 \tabularnewline
Trimmed Mean ( 18 / 21 ) & 94.4862068965517 & 0.83586072769731 & 113.040610433809 \tabularnewline
Trimmed Mean ( 19 / 21 ) & 94.4444444444444 & 0.80563070678041 & 117.230442744516 \tabularnewline
Trimmed Mean ( 20 / 21 ) & 94.372 & 0.774607857779234 & 121.831968333707 \tabularnewline
Trimmed Mean ( 21 / 21 ) & 94.3304347826087 & 0.755361201523577 & 124.881228467047 \tabularnewline
Median & 93.6 &  &  \tabularnewline
Midrange & 79.2 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 94.203125 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 94.4848484848485 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 94.4848484848485 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 94.4848484848485 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 94.4848484848485 &  &  \tabularnewline
Midmean - Closest Observation & 94.1764705882353 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 94.4848484848485 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 94.4848484848485 &  &  \tabularnewline
Number of observations & 65 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=26676&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]91.7123076923077[/C][C]2.01549348282001[/C][C]45.5036488453373[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]89.9530368565007[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]87.7295884550365[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]93.1188975284989[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 21 )[/C][C]91.7030769230769[/C][C]2.00894988980893[/C][C]45.6472694457295[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 21 )[/C][C]91.82[/C][C]1.95804577812440[/C][C]46.8936942260635[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 21 )[/C][C]91.7692307692308[/C][C]1.90473716523804[/C][C]48.1794719208737[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 21 )[/C][C]92.2246153846154[/C][C]1.76030759818751[/C][C]52.3911931525910[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 21 )[/C][C]93.2323076923077[/C][C]1.48325121661761[/C][C]62.856720862777[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 21 )[/C][C]93.26[/C][C]1.46629405960427[/C][C]63.6025218742068[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 21 )[/C][C]93.356923076923[/C][C]1.40049264895012[/C][C]66.6600593347694[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 21 )[/C][C]93.5661538461539[/C][C]1.34423140200271[/C][C]69.6056896950582[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 21 )[/C][C]93.5523076923077[/C][C]1.33210740300326[/C][C]70.2288024834876[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 21 )[/C][C]93.6907692307692[/C][C]1.29965550738256[/C][C]72.0889256411167[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 21 )[/C][C]93.9615384615385[/C][C]1.21963048531515[/C][C]77.040988719841[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 21 )[/C][C]94.3861538461538[/C][C]1.10889297908015[/C][C]85.1174600496154[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 21 )[/C][C]94.3861538461538[/C][C]1.10889297908015[/C][C]85.1174600496154[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 21 )[/C][C]94.2353846153846[/C][C]1.07082694224449[/C][C]88.0024408219165[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 21 )[/C][C]94.443076923077[/C][C]1.02228056050122[/C][C]92.3846941555569[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 21 )[/C][C]94.4184615384615[/C][C]0.925807579660165[/C][C]101.984973565587[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 21 )[/C][C]94.5492307692308[/C][C]0.889625361612217[/C][C]106.279828396399[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 21 )[/C][C]94.7984615384615[/C][C]0.786073164985334[/C][C]120.597503847152[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 21 )[/C][C]94.9738461538462[/C][C]0.735701120736712[/C][C]129.092974683444[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 21 )[/C][C]94.6661538461538[/C][C]0.654060089434996[/C][C]144.736172372068[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 21 )[/C][C]94.7307692307692[/C][C]0.636063324877671[/C][C]148.932921496438[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 21 )[/C][C]92.1095238095238[/C][C]1.9007459584583[/C][C]48.4596710042377[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 21 )[/C][C]92.5426229508197[/C][C]1.76579748545874[/C][C]52.4084011405066[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 21 )[/C][C]92.9406779661017[/C][C]1.63225831418677[/C][C]56.9399323368782[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 21 )[/C][C]93.3859649122807[/C][C]1.48975919105956[/C][C]62.6852752261672[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 21 )[/C][C]93.729090909091[/C][C]1.37367180473346[/C][C]68.2325214699137[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 21 )[/C][C]93.8509433962264[/C][C]1.33213498512298[/C][C]70.4515266428216[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 21 )[/C][C]93.9764705882353[/C][C]1.28499817116004[/C][C]73.1335442317378[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 21 )[/C][C]94.0938775510204[/C][C]1.24442091060415[/C][C]75.6125815222273[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 21 )[/C][C]94.1851063829787[/C][C]1.20806715879582[/C][C]77.9634689158017[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 21 )[/C][C]94.2866666666667[/C][C]1.16391276704611[/C][C]81.0083619118266[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 21 )[/C][C]94.3767441860465[/C][C]1.11498321332408[/C][C]84.6440942412782[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 21 )[/C][C]94.4365853658537[/C][C]1.07226541636900[/C][C]88.0720238890508[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 21 )[/C][C]94.4435897435897[/C][C]1.04437181185665[/C][C]90.4310023225264[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 21 )[/C][C]94.4513513513513[/C][C]1.00571655555352[/C][C]93.914483986363[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 21 )[/C][C]94.48[/C][C]0.962549136582717[/C][C]98.1560279981414[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 21 )[/C][C]94.4848484848485[/C][C]0.91608233316589[/C][C]103.140127327113[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 21 )[/C][C]94.4935483870968[/C][C]0.879099435136572[/C][C]107.489033220021[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 21 )[/C][C]94.4862068965517[/C][C]0.83586072769731[/C][C]113.040610433809[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 21 )[/C][C]94.4444444444444[/C][C]0.80563070678041[/C][C]117.230442744516[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 21 )[/C][C]94.372[/C][C]0.774607857779234[/C][C]121.831968333707[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 21 )[/C][C]94.3304347826087[/C][C]0.755361201523577[/C][C]124.881228467047[/C][/ROW]
[ROW][C]Median[/C][C]93.6[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]79.2[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]94.203125[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]94.4848484848485[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]94.4848484848485[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]94.4848484848485[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]94.4848484848485[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]94.1764705882353[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]94.4848484848485[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]94.4848484848485[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]65[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=26676&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=26676&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 Mean91.71230769230772.0154934828200145.5036488453373
Geometric Mean89.9530368565007
Harmonic Mean87.7295884550365
Quadratic Mean93.1188975284989
Winsorized Mean ( 1 / 21 )91.70307692307692.0089498898089345.6472694457295
Winsorized Mean ( 2 / 21 )91.821.9580457781244046.8936942260635
Winsorized Mean ( 3 / 21 )91.76923076923081.9047371652380448.1794719208737
Winsorized Mean ( 4 / 21 )92.22461538461541.7603075981875152.3911931525910
Winsorized Mean ( 5 / 21 )93.23230769230771.4832512166176162.856720862777
Winsorized Mean ( 6 / 21 )93.261.4662940596042763.6025218742068
Winsorized Mean ( 7 / 21 )93.3569230769231.4004926489501266.6600593347694
Winsorized Mean ( 8 / 21 )93.56615384615391.3442314020027169.6056896950582
Winsorized Mean ( 9 / 21 )93.55230769230771.3321074030032670.2288024834876
Winsorized Mean ( 10 / 21 )93.69076923076921.2996555073825672.0889256411167
Winsorized Mean ( 11 / 21 )93.96153846153851.2196304853151577.040988719841
Winsorized Mean ( 12 / 21 )94.38615384615381.1088929790801585.1174600496154
Winsorized Mean ( 13 / 21 )94.38615384615381.1088929790801585.1174600496154
Winsorized Mean ( 14 / 21 )94.23538461538461.0708269422444988.0024408219165
Winsorized Mean ( 15 / 21 )94.4430769230771.0222805605012292.3846941555569
Winsorized Mean ( 16 / 21 )94.41846153846150.925807579660165101.984973565587
Winsorized Mean ( 17 / 21 )94.54923076923080.889625361612217106.279828396399
Winsorized Mean ( 18 / 21 )94.79846153846150.786073164985334120.597503847152
Winsorized Mean ( 19 / 21 )94.97384615384620.735701120736712129.092974683444
Winsorized Mean ( 20 / 21 )94.66615384615380.654060089434996144.736172372068
Winsorized Mean ( 21 / 21 )94.73076923076920.636063324877671148.932921496438
Trimmed Mean ( 1 / 21 )92.10952380952381.900745958458348.4596710042377
Trimmed Mean ( 2 / 21 )92.54262295081971.7657974854587452.4084011405066
Trimmed Mean ( 3 / 21 )92.94067796610171.6322583141867756.9399323368782
Trimmed Mean ( 4 / 21 )93.38596491228071.4897591910595662.6852752261672
Trimmed Mean ( 5 / 21 )93.7290909090911.3736718047334668.2325214699137
Trimmed Mean ( 6 / 21 )93.85094339622641.3321349851229870.4515266428216
Trimmed Mean ( 7 / 21 )93.97647058823531.2849981711600473.1335442317378
Trimmed Mean ( 8 / 21 )94.09387755102041.2444209106041575.6125815222273
Trimmed Mean ( 9 / 21 )94.18510638297871.2080671587958277.9634689158017
Trimmed Mean ( 10 / 21 )94.28666666666671.1639127670461181.0083619118266
Trimmed Mean ( 11 / 21 )94.37674418604651.1149832133240884.6440942412782
Trimmed Mean ( 12 / 21 )94.43658536585371.0722654163690088.0720238890508
Trimmed Mean ( 13 / 21 )94.44358974358971.0443718118566590.4310023225264
Trimmed Mean ( 14 / 21 )94.45135135135131.0057165555535293.914483986363
Trimmed Mean ( 15 / 21 )94.480.96254913658271798.1560279981414
Trimmed Mean ( 16 / 21 )94.48484848484850.91608233316589103.140127327113
Trimmed Mean ( 17 / 21 )94.49354838709680.879099435136572107.489033220021
Trimmed Mean ( 18 / 21 )94.48620689655170.83586072769731113.040610433809
Trimmed Mean ( 19 / 21 )94.44444444444440.80563070678041117.230442744516
Trimmed Mean ( 20 / 21 )94.3720.774607857779234121.831968333707
Trimmed Mean ( 21 / 21 )94.33043478260870.755361201523577124.881228467047
Median93.6
Midrange79.2
Midmean - Weighted Average at Xnp94.203125
Midmean - Weighted Average at X(n+1)p94.4848484848485
Midmean - Empirical Distribution Function94.4848484848485
Midmean - Empirical Distribution Function - Averaging94.4848484848485
Midmean - Empirical Distribution Function - Interpolation94.4848484848485
Midmean - Closest Observation94.1764705882353
Midmean - True Basic - Statistics Graphics Toolkit94.4848484848485
Midmean - MS Excel (old versions)94.4848484848485
Number of observations65



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')