Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationSun, 16 Dec 2007 04:37:09 -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/2007/Dec/16/t1197804299xhdkdxiuibhfm4p.htm/, Retrieved Thu, 02 May 2024 10:03:48 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=4138, Retrieved Thu, 02 May 2024 10:03:48 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact266
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [Central tendency ...] [2007-12-16 11:37:09] [908a52009ae83f013a8231794220d3ac] [Current]
Feedback Forum

Post a new message
Dataseries X:
106,9
107,1
99,3
99,2
108,3
105,6
99,5
107,4
93,1
88,1
110,7
113,1
99,6
93,6
98,6
99,6
114,3
107,8
101,2
112,5
100,5
93,9
116,2
112,0
106,4
95,7
96,0
95,8
103,0
102,2
98,4
111,4
86,6
91,3
107,9
101,8
104,4
93,4
100,1
98,5
112,9
101,4
107,1
110,8
90,3
95,5
111,4
113,0
107,5
95,9
106,3
105,2
117,2
106,9
108,2
113,0
97,2
100,2
109,7
119,1




Summary of compuational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Herman Ole Andreas Wold' @ 193.190.124.10:1001

\begin{tabular}{lllllllll}
\hline
Summary of compuational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 3 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ 193.190.124.10:1001 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=4138&T=0

[TABLE]
[ROW][C]Summary of compuational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Herman Ole Andreas Wold' @ 193.190.124.10:1001[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=4138&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=4138&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 compuational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Herman Ole Andreas Wold' @ 193.190.124.10:1001







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean103.4966666666670.989606914675917104.583613080918
Geometric Mean103.214720968916
Harmonic Mean102.930119750870
Quadratic Mean103.775430618234
Winsorized Mean ( 1 / 20 )103.490.97463219195988106.183646357805
Winsorized Mean ( 2 / 20 )103.530.948383400026765109.164711230794
Winsorized Mean ( 3 / 20 )103.4850.916557749050562112.906142692261
Winsorized Mean ( 4 / 20 )103.5250.875467994297649118.251039072027
Winsorized Mean ( 5 / 20 )103.5416666666670.86893106507759119.159816961339
Winsorized Mean ( 6 / 20 )103.5616666666670.865000870861606119.724349599222
Winsorized Mean ( 7 / 20 )103.5850.856074423212781120.999993915545
Winsorized Mean ( 8 / 20 )103.7450.807277719489508128.512155724556
Winsorized Mean ( 9 / 20 )103.70.788515733607702131.512911639113
Winsorized Mean ( 10 / 20 )103.6166666666670.768133575758251134.894073032002
Winsorized Mean ( 11 / 20 )103.6350.764981536648061135.473857910480
Winsorized Mean ( 12 / 20 )103.5350.741249612951376139.676295529873
Winsorized Mean ( 13 / 20 )103.7733333333330.694310480487297149.462432513622
Winsorized Mean ( 14 / 20 )103.820.611965436046231169.650104213005
Winsorized Mean ( 15 / 20 )103.4950.553807697763127186.878948086176
Winsorized Mean ( 16 / 20 )103.4950.545833861646357189.608976782488
Winsorized Mean ( 17 / 20 )103.580.508141623570162203.840809718077
Winsorized Mean ( 18 / 20 )103.580.499461857295085207.383203516188
Winsorized Mean ( 19 / 20 )103.5483333333330.476827389836911217.161043053231
Winsorized Mean ( 20 / 20 )103.5483333333330.467373304785763221.553803507880
Trimmed Mean ( 1 / 20 )103.5189655172410.942671471567069109.814467329911
Trimmed Mean ( 2 / 20 )103.550.90324810703214114.641812358999
Trimmed Mean ( 3 / 20 )103.5611111111110.872206198359934118.734665387432
Trimmed Mean ( 4 / 20 )103.5903846153850.848995767414282122.015195589115
Trimmed Mean ( 5 / 20 )103.610.835694749466403123.980676037699
Trimmed Mean ( 6 / 20 )103.6270833333330.820454053839808126.304553982454
Trimmed Mean ( 7 / 20 )103.6413043478260.801632248421759129.287843087492
Trimmed Mean ( 8 / 20 )103.6522727272730.77949059527504132.974372437039
Trimmed Mean ( 9 / 20 )103.6357142857140.763890505350468135.668284341572
Trimmed Mean ( 10 / 20 )103.6250.74760086361778138.610059248112
Trimmed Mean ( 11 / 20 )103.6263157894740.730465704357292141.863355351707
Trimmed Mean ( 12 / 20 )103.6250.707155884119226146.537704524748
Trimmed Mean ( 13 / 20 )103.6382352941180.681078816899015152.167756099048
Trimmed Mean ( 14 / 20 )103.618750.657715337912844157.543459954603
Trimmed Mean ( 15 / 20 )103.590.647618981213172159.955163460384
Trimmed Mean ( 16 / 20 )103.6035714285710.647328293158275160.047957927339
Trimmed Mean ( 17 / 20 )103.6192307692310.64524340620764160.589367938285
Trimmed Mean ( 18 / 20 )103.6250.649365632473479159.578817876895
Trimmed Mean ( 19 / 20 )103.6318181818180.652381131918267158.851648387038
Trimmed Mean ( 20 / 20 )103.6450.65812632765898157.484962451928
Median103.7
Midrange102.85
Midmean - Weighted Average at Xnp103.422580645161
Midmean - Weighted Average at X(n+1)p103.59
Midmean - Empirical Distribution Function103.422580645161
Midmean - Empirical Distribution Function - Averaging103.59
Midmean - Empirical Distribution Function - Interpolation103.59
Midmean - Closest Observation103.422580645161
Midmean - True Basic - Statistics Graphics Toolkit103.59
Midmean - MS Excel (old versions)103.61875
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 103.496666666667 & 0.989606914675917 & 104.583613080918 \tabularnewline
Geometric Mean & 103.214720968916 &  &  \tabularnewline
Harmonic Mean & 102.930119750870 &  &  \tabularnewline
Quadratic Mean & 103.775430618234 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 103.49 & 0.97463219195988 & 106.183646357805 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 103.53 & 0.948383400026765 & 109.164711230794 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 103.485 & 0.916557749050562 & 112.906142692261 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 103.525 & 0.875467994297649 & 118.251039072027 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 103.541666666667 & 0.86893106507759 & 119.159816961339 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 103.561666666667 & 0.865000870861606 & 119.724349599222 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 103.585 & 0.856074423212781 & 120.999993915545 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 103.745 & 0.807277719489508 & 128.512155724556 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 103.7 & 0.788515733607702 & 131.512911639113 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 103.616666666667 & 0.768133575758251 & 134.894073032002 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 103.635 & 0.764981536648061 & 135.473857910480 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 103.535 & 0.741249612951376 & 139.676295529873 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 103.773333333333 & 0.694310480487297 & 149.462432513622 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 103.82 & 0.611965436046231 & 169.650104213005 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 103.495 & 0.553807697763127 & 186.878948086176 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 103.495 & 0.545833861646357 & 189.608976782488 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 103.58 & 0.508141623570162 & 203.840809718077 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 103.58 & 0.499461857295085 & 207.383203516188 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 103.548333333333 & 0.476827389836911 & 217.161043053231 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 103.548333333333 & 0.467373304785763 & 221.553803507880 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 103.518965517241 & 0.942671471567069 & 109.814467329911 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 103.55 & 0.90324810703214 & 114.641812358999 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 103.561111111111 & 0.872206198359934 & 118.734665387432 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 103.590384615385 & 0.848995767414282 & 122.015195589115 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 103.61 & 0.835694749466403 & 123.980676037699 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 103.627083333333 & 0.820454053839808 & 126.304553982454 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 103.641304347826 & 0.801632248421759 & 129.287843087492 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 103.652272727273 & 0.77949059527504 & 132.974372437039 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 103.635714285714 & 0.763890505350468 & 135.668284341572 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 103.625 & 0.74760086361778 & 138.610059248112 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 103.626315789474 & 0.730465704357292 & 141.863355351707 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 103.625 & 0.707155884119226 & 146.537704524748 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 103.638235294118 & 0.681078816899015 & 152.167756099048 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 103.61875 & 0.657715337912844 & 157.543459954603 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 103.59 & 0.647618981213172 & 159.955163460384 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 103.603571428571 & 0.647328293158275 & 160.047957927339 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 103.619230769231 & 0.64524340620764 & 160.589367938285 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 103.625 & 0.649365632473479 & 159.578817876895 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 103.631818181818 & 0.652381131918267 & 158.851648387038 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 103.645 & 0.65812632765898 & 157.484962451928 \tabularnewline
Median & 103.7 &  &  \tabularnewline
Midrange & 102.85 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 103.422580645161 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 103.59 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 103.422580645161 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 103.59 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 103.59 &  &  \tabularnewline
Midmean - Closest Observation & 103.422580645161 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 103.59 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 103.61875 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=4138&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]103.496666666667[/C][C]0.989606914675917[/C][C]104.583613080918[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]103.214720968916[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]102.930119750870[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]103.775430618234[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]103.49[/C][C]0.97463219195988[/C][C]106.183646357805[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]103.53[/C][C]0.948383400026765[/C][C]109.164711230794[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]103.485[/C][C]0.916557749050562[/C][C]112.906142692261[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]103.525[/C][C]0.875467994297649[/C][C]118.251039072027[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]103.541666666667[/C][C]0.86893106507759[/C][C]119.159816961339[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]103.561666666667[/C][C]0.865000870861606[/C][C]119.724349599222[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]103.585[/C][C]0.856074423212781[/C][C]120.999993915545[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]103.745[/C][C]0.807277719489508[/C][C]128.512155724556[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]103.7[/C][C]0.788515733607702[/C][C]131.512911639113[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]103.616666666667[/C][C]0.768133575758251[/C][C]134.894073032002[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]103.635[/C][C]0.764981536648061[/C][C]135.473857910480[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]103.535[/C][C]0.741249612951376[/C][C]139.676295529873[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]103.773333333333[/C][C]0.694310480487297[/C][C]149.462432513622[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]103.82[/C][C]0.611965436046231[/C][C]169.650104213005[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]103.495[/C][C]0.553807697763127[/C][C]186.878948086176[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]103.495[/C][C]0.545833861646357[/C][C]189.608976782488[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]103.58[/C][C]0.508141623570162[/C][C]203.840809718077[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]103.58[/C][C]0.499461857295085[/C][C]207.383203516188[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]103.548333333333[/C][C]0.476827389836911[/C][C]217.161043053231[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]103.548333333333[/C][C]0.467373304785763[/C][C]221.553803507880[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]103.518965517241[/C][C]0.942671471567069[/C][C]109.814467329911[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]103.55[/C][C]0.90324810703214[/C][C]114.641812358999[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]103.561111111111[/C][C]0.872206198359934[/C][C]118.734665387432[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]103.590384615385[/C][C]0.848995767414282[/C][C]122.015195589115[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]103.61[/C][C]0.835694749466403[/C][C]123.980676037699[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]103.627083333333[/C][C]0.820454053839808[/C][C]126.304553982454[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]103.641304347826[/C][C]0.801632248421759[/C][C]129.287843087492[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]103.652272727273[/C][C]0.77949059527504[/C][C]132.974372437039[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]103.635714285714[/C][C]0.763890505350468[/C][C]135.668284341572[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]103.625[/C][C]0.74760086361778[/C][C]138.610059248112[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]103.626315789474[/C][C]0.730465704357292[/C][C]141.863355351707[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]103.625[/C][C]0.707155884119226[/C][C]146.537704524748[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]103.638235294118[/C][C]0.681078816899015[/C][C]152.167756099048[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]103.61875[/C][C]0.657715337912844[/C][C]157.543459954603[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]103.59[/C][C]0.647618981213172[/C][C]159.955163460384[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]103.603571428571[/C][C]0.647328293158275[/C][C]160.047957927339[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]103.619230769231[/C][C]0.64524340620764[/C][C]160.589367938285[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]103.625[/C][C]0.649365632473479[/C][C]159.578817876895[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]103.631818181818[/C][C]0.652381131918267[/C][C]158.851648387038[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]103.645[/C][C]0.65812632765898[/C][C]157.484962451928[/C][/ROW]
[ROW][C]Median[/C][C]103.7[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]102.85[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]103.422580645161[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]103.59[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]103.422580645161[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]103.59[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]103.59[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]103.422580645161[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]103.59[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]103.61875[/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=4138&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=4138&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 Mean103.4966666666670.989606914675917104.583613080918
Geometric Mean103.214720968916
Harmonic Mean102.930119750870
Quadratic Mean103.775430618234
Winsorized Mean ( 1 / 20 )103.490.97463219195988106.183646357805
Winsorized Mean ( 2 / 20 )103.530.948383400026765109.164711230794
Winsorized Mean ( 3 / 20 )103.4850.916557749050562112.906142692261
Winsorized Mean ( 4 / 20 )103.5250.875467994297649118.251039072027
Winsorized Mean ( 5 / 20 )103.5416666666670.86893106507759119.159816961339
Winsorized Mean ( 6 / 20 )103.5616666666670.865000870861606119.724349599222
Winsorized Mean ( 7 / 20 )103.5850.856074423212781120.999993915545
Winsorized Mean ( 8 / 20 )103.7450.807277719489508128.512155724556
Winsorized Mean ( 9 / 20 )103.70.788515733607702131.512911639113
Winsorized Mean ( 10 / 20 )103.6166666666670.768133575758251134.894073032002
Winsorized Mean ( 11 / 20 )103.6350.764981536648061135.473857910480
Winsorized Mean ( 12 / 20 )103.5350.741249612951376139.676295529873
Winsorized Mean ( 13 / 20 )103.7733333333330.694310480487297149.462432513622
Winsorized Mean ( 14 / 20 )103.820.611965436046231169.650104213005
Winsorized Mean ( 15 / 20 )103.4950.553807697763127186.878948086176
Winsorized Mean ( 16 / 20 )103.4950.545833861646357189.608976782488
Winsorized Mean ( 17 / 20 )103.580.508141623570162203.840809718077
Winsorized Mean ( 18 / 20 )103.580.499461857295085207.383203516188
Winsorized Mean ( 19 / 20 )103.5483333333330.476827389836911217.161043053231
Winsorized Mean ( 20 / 20 )103.5483333333330.467373304785763221.553803507880
Trimmed Mean ( 1 / 20 )103.5189655172410.942671471567069109.814467329911
Trimmed Mean ( 2 / 20 )103.550.90324810703214114.641812358999
Trimmed Mean ( 3 / 20 )103.5611111111110.872206198359934118.734665387432
Trimmed Mean ( 4 / 20 )103.5903846153850.848995767414282122.015195589115
Trimmed Mean ( 5 / 20 )103.610.835694749466403123.980676037699
Trimmed Mean ( 6 / 20 )103.6270833333330.820454053839808126.304553982454
Trimmed Mean ( 7 / 20 )103.6413043478260.801632248421759129.287843087492
Trimmed Mean ( 8 / 20 )103.6522727272730.77949059527504132.974372437039
Trimmed Mean ( 9 / 20 )103.6357142857140.763890505350468135.668284341572
Trimmed Mean ( 10 / 20 )103.6250.74760086361778138.610059248112
Trimmed Mean ( 11 / 20 )103.6263157894740.730465704357292141.863355351707
Trimmed Mean ( 12 / 20 )103.6250.707155884119226146.537704524748
Trimmed Mean ( 13 / 20 )103.6382352941180.681078816899015152.167756099048
Trimmed Mean ( 14 / 20 )103.618750.657715337912844157.543459954603
Trimmed Mean ( 15 / 20 )103.590.647618981213172159.955163460384
Trimmed Mean ( 16 / 20 )103.6035714285710.647328293158275160.047957927339
Trimmed Mean ( 17 / 20 )103.6192307692310.64524340620764160.589367938285
Trimmed Mean ( 18 / 20 )103.6250.649365632473479159.578817876895
Trimmed Mean ( 19 / 20 )103.6318181818180.652381131918267158.851648387038
Trimmed Mean ( 20 / 20 )103.6450.65812632765898157.484962451928
Median103.7
Midrange102.85
Midmean - Weighted Average at Xnp103.422580645161
Midmean - Weighted Average at X(n+1)p103.59
Midmean - Empirical Distribution Function103.422580645161
Midmean - Empirical Distribution Function - Averaging103.59
Midmean - Empirical Distribution Function - Interpolation103.59
Midmean - Closest Observation103.422580645161
Midmean - True Basic - Statistics Graphics Toolkit103.59
Midmean - MS Excel (old versions)103.61875
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')