Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationWed, 12 Oct 2016 13:49:08 +0100
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2016/Oct/12/t1476276894k1tl9jw623vqigl.htm/, Retrieved Sun, 05 May 2024 11:07:08 +0200
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=, Retrieved Sun, 05 May 2024 11:07:08 +0200
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact0
Dataseries X:
88
90
82
75
79
70
71
75
89
92
94
90
102
98
100
98
100
91
93
92
106
109
108
108
118
119
124
118
119
113
114
115
125
125
118
122
132
133
136
128
126
114
108
107
117
119
113
114
124
125
124
118
111
99
94
93
107
107
103
97




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

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

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

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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'Gertrude Mary Cox' @ cox.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean106.3166666666672.0984917460610350.6633713791004
Geometric Mean105.017556730004
Harmonic Mean103.637960491812
Quadratic Mean107.531623255673
Winsorized Mean ( 1 / 20 )106.2833333333332.0822211720699151.0432487955534
Winsorized Mean ( 2 / 20 )106.3833333333332.0384844911638752.1874626932255
Winsorized Mean ( 3 / 20 )106.1833333333331.9986565638607553.1273532698494
Winsorized Mean ( 4 / 20 )106.3166666666671.9069441444017655.7523758515852
Winsorized Mean ( 5 / 20 )106.4833333333331.8338455884246558.0655939657422
Winsorized Mean ( 6 / 20 )107.0833333333331.7087828401312262.6664376645484
Winsorized Mean ( 7 / 20 )107.21.6870728168237263.5420113056098
Winsorized Mean ( 8 / 20 )107.21.6395190144887265.3850300317683
Winsorized Mean ( 9 / 20 )107.21.6395190144887265.3850300317683
Winsorized Mean ( 10 / 20 )107.3666666666671.6103420464582566.6732057967477
Winsorized Mean ( 11 / 20 )107.1833333333331.5164804008052270.6790099472575
Winsorized Mean ( 12 / 20 )106.5833333333331.4222389579406174.940524402218
Winsorized Mean ( 13 / 20 )106.81.3851104914216577.1057620756179
Winsorized Mean ( 14 / 20 )106.81.3851104914216577.1057620756179
Winsorized Mean ( 15 / 20 )106.81.3063945294843681.7517201653886
Winsorized Mean ( 16 / 20 )106.81.3063945294843681.7517201653886
Winsorized Mean ( 17 / 20 )107.651.1699690951541592.01097742314
Winsorized Mean ( 18 / 20 )107.951.1243139779011796.0141047090041
Winsorized Mean ( 19 / 20 )107.6333333333331.0769717606594999.9407201423957
Winsorized Mean ( 20 / 20 )107.30.930433347795137115.322607744306
Trimmed Mean ( 1 / 20 )106.4310344827592.0123803251067952.8881311126468
Trimmed Mean ( 2 / 20 )106.5892857142861.9260309746727655.3414182408961
Trimmed Mean ( 3 / 20 )106.7037037037041.8486835230602357.7187508693055
Trimmed Mean ( 4 / 20 )106.9038461538461.7712850392681960.3538356525688
Trimmed Mean ( 5 / 20 )107.081.711388027184962.5690949679822
Trimmed Mean ( 6 / 20 )107.2291666666671.6610471530932164.5551611626341
Trimmed Mean ( 7 / 20 )107.2608695652171.635781892140865.5716205690732
Trimmed Mean ( 8 / 20 )107.2727272727271.6077782775661566.7210950474568
Trimmed Mean ( 9 / 20 )107.2857142857141.5825286350342967.793853400567
Trimmed Mean ( 10 / 20 )107.31.5472059183722669.3508205506898
Trimmed Mean ( 11 / 20 )107.2894736842111.5062260048610171.2306608290906
Trimmed Mean ( 12 / 20 )107.3055555555561.4745564005772272.7714148563937
Trimmed Mean ( 13 / 20 )107.4117647058821.4528340041445373.932578945335
Trimmed Mean ( 14 / 20 )107.51.4291041633405975.2219486567823
Trimmed Mean ( 15 / 20 )107.61.3909394823924477.3577868498821
Trimmed Mean ( 16 / 20 )107.7142857142861.355819460575479.4458914674172
Trimmed Mean ( 17 / 20 )107.8461538461541.2981552682910183.076467415281
Trimmed Mean ( 18 / 20 )107.8751.2587555678963885.6997202246973
Trimmed Mean ( 19 / 20 )107.8636363636361.2083681073583389.2638887991193
Trimmed Mean ( 20 / 20 )107.91.1399445969916894.6537228956114
Median108
Midrange103
Midmean - Weighted Average at Xnp106.6875
Midmean - Weighted Average at X(n+1)p107.6
Midmean - Empirical Distribution Function106.6875
Midmean - Empirical Distribution Function - Averaging107.6
Midmean - Empirical Distribution Function - Interpolation107.6
Midmean - Closest Observation106.6875
Midmean - True Basic - Statistics Graphics Toolkit107.6
Midmean - MS Excel (old versions)107.742857142857
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 106.316666666667 & 2.09849174606103 & 50.6633713791004 \tabularnewline
Geometric Mean & 105.017556730004 &  &  \tabularnewline
Harmonic Mean & 103.637960491812 &  &  \tabularnewline
Quadratic Mean & 107.531623255673 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 106.283333333333 & 2.08222117206991 & 51.0432487955534 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 106.383333333333 & 2.03848449116387 & 52.1874626932255 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 106.183333333333 & 1.99865656386075 & 53.1273532698494 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 106.316666666667 & 1.90694414440176 & 55.7523758515852 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 106.483333333333 & 1.83384558842465 & 58.0655939657422 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 107.083333333333 & 1.70878284013122 & 62.6664376645484 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 107.2 & 1.68707281682372 & 63.5420113056098 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 107.2 & 1.63951901448872 & 65.3850300317683 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 107.2 & 1.63951901448872 & 65.3850300317683 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 107.366666666667 & 1.61034204645825 & 66.6732057967477 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 107.183333333333 & 1.51648040080522 & 70.6790099472575 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 106.583333333333 & 1.42223895794061 & 74.940524402218 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 106.8 & 1.38511049142165 & 77.1057620756179 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 106.8 & 1.38511049142165 & 77.1057620756179 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 106.8 & 1.30639452948436 & 81.7517201653886 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 106.8 & 1.30639452948436 & 81.7517201653886 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 107.65 & 1.16996909515415 & 92.01097742314 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 107.95 & 1.12431397790117 & 96.0141047090041 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 107.633333333333 & 1.07697176065949 & 99.9407201423957 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 107.3 & 0.930433347795137 & 115.322607744306 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 106.431034482759 & 2.01238032510679 & 52.8881311126468 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 106.589285714286 & 1.92603097467276 & 55.3414182408961 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 106.703703703704 & 1.84868352306023 & 57.7187508693055 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 106.903846153846 & 1.77128503926819 & 60.3538356525688 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 107.08 & 1.7113880271849 & 62.5690949679822 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 107.229166666667 & 1.66104715309321 & 64.5551611626341 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 107.260869565217 & 1.6357818921408 & 65.5716205690732 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 107.272727272727 & 1.60777827756615 & 66.7210950474568 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 107.285714285714 & 1.58252863503429 & 67.793853400567 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 107.3 & 1.54720591837226 & 69.3508205506898 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 107.289473684211 & 1.50622600486101 & 71.2306608290906 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 107.305555555556 & 1.47455640057722 & 72.7714148563937 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 107.411764705882 & 1.45283400414453 & 73.932578945335 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 107.5 & 1.42910416334059 & 75.2219486567823 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 107.6 & 1.39093948239244 & 77.3577868498821 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 107.714285714286 & 1.3558194605754 & 79.4458914674172 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 107.846153846154 & 1.29815526829101 & 83.076467415281 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 107.875 & 1.25875556789638 & 85.6997202246973 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 107.863636363636 & 1.20836810735833 & 89.2638887991193 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 107.9 & 1.13994459699168 & 94.6537228956114 \tabularnewline
Median & 108 &  &  \tabularnewline
Midrange & 103 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 106.6875 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 107.6 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 106.6875 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 107.6 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 107.6 &  &  \tabularnewline
Midmean - Closest Observation & 106.6875 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 107.6 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 107.742857142857 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]106.316666666667[/C][C]2.09849174606103[/C][C]50.6633713791004[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]105.017556730004[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]103.637960491812[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]107.531623255673[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]106.283333333333[/C][C]2.08222117206991[/C][C]51.0432487955534[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]106.383333333333[/C][C]2.03848449116387[/C][C]52.1874626932255[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]106.183333333333[/C][C]1.99865656386075[/C][C]53.1273532698494[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]106.316666666667[/C][C]1.90694414440176[/C][C]55.7523758515852[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]106.483333333333[/C][C]1.83384558842465[/C][C]58.0655939657422[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]107.083333333333[/C][C]1.70878284013122[/C][C]62.6664376645484[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]107.2[/C][C]1.68707281682372[/C][C]63.5420113056098[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]107.2[/C][C]1.63951901448872[/C][C]65.3850300317683[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]107.2[/C][C]1.63951901448872[/C][C]65.3850300317683[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]107.366666666667[/C][C]1.61034204645825[/C][C]66.6732057967477[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]107.183333333333[/C][C]1.51648040080522[/C][C]70.6790099472575[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]106.583333333333[/C][C]1.42223895794061[/C][C]74.940524402218[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]106.8[/C][C]1.38511049142165[/C][C]77.1057620756179[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]106.8[/C][C]1.38511049142165[/C][C]77.1057620756179[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]106.8[/C][C]1.30639452948436[/C][C]81.7517201653886[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]106.8[/C][C]1.30639452948436[/C][C]81.7517201653886[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]107.65[/C][C]1.16996909515415[/C][C]92.01097742314[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]107.95[/C][C]1.12431397790117[/C][C]96.0141047090041[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]107.633333333333[/C][C]1.07697176065949[/C][C]99.9407201423957[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]107.3[/C][C]0.930433347795137[/C][C]115.322607744306[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]106.431034482759[/C][C]2.01238032510679[/C][C]52.8881311126468[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]106.589285714286[/C][C]1.92603097467276[/C][C]55.3414182408961[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]106.703703703704[/C][C]1.84868352306023[/C][C]57.7187508693055[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]106.903846153846[/C][C]1.77128503926819[/C][C]60.3538356525688[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]107.08[/C][C]1.7113880271849[/C][C]62.5690949679822[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]107.229166666667[/C][C]1.66104715309321[/C][C]64.5551611626341[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]107.260869565217[/C][C]1.6357818921408[/C][C]65.5716205690732[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]107.272727272727[/C][C]1.60777827756615[/C][C]66.7210950474568[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]107.285714285714[/C][C]1.58252863503429[/C][C]67.793853400567[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]107.3[/C][C]1.54720591837226[/C][C]69.3508205506898[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]107.289473684211[/C][C]1.50622600486101[/C][C]71.2306608290906[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]107.305555555556[/C][C]1.47455640057722[/C][C]72.7714148563937[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]107.411764705882[/C][C]1.45283400414453[/C][C]73.932578945335[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]107.5[/C][C]1.42910416334059[/C][C]75.2219486567823[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]107.6[/C][C]1.39093948239244[/C][C]77.3577868498821[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]107.714285714286[/C][C]1.3558194605754[/C][C]79.4458914674172[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]107.846153846154[/C][C]1.29815526829101[/C][C]83.076467415281[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]107.875[/C][C]1.25875556789638[/C][C]85.6997202246973[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]107.863636363636[/C][C]1.20836810735833[/C][C]89.2638887991193[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]107.9[/C][C]1.13994459699168[/C][C]94.6537228956114[/C][/ROW]
[ROW][C]Median[/C][C]108[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]103[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]106.6875[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]107.6[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]106.6875[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]107.6[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]107.6[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]106.6875[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]107.6[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]107.742857142857[/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=&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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 Mean106.3166666666672.0984917460610350.6633713791004
Geometric Mean105.017556730004
Harmonic Mean103.637960491812
Quadratic Mean107.531623255673
Winsorized Mean ( 1 / 20 )106.2833333333332.0822211720699151.0432487955534
Winsorized Mean ( 2 / 20 )106.3833333333332.0384844911638752.1874626932255
Winsorized Mean ( 3 / 20 )106.1833333333331.9986565638607553.1273532698494
Winsorized Mean ( 4 / 20 )106.3166666666671.9069441444017655.7523758515852
Winsorized Mean ( 5 / 20 )106.4833333333331.8338455884246558.0655939657422
Winsorized Mean ( 6 / 20 )107.0833333333331.7087828401312262.6664376645484
Winsorized Mean ( 7 / 20 )107.21.6870728168237263.5420113056098
Winsorized Mean ( 8 / 20 )107.21.6395190144887265.3850300317683
Winsorized Mean ( 9 / 20 )107.21.6395190144887265.3850300317683
Winsorized Mean ( 10 / 20 )107.3666666666671.6103420464582566.6732057967477
Winsorized Mean ( 11 / 20 )107.1833333333331.5164804008052270.6790099472575
Winsorized Mean ( 12 / 20 )106.5833333333331.4222389579406174.940524402218
Winsorized Mean ( 13 / 20 )106.81.3851104914216577.1057620756179
Winsorized Mean ( 14 / 20 )106.81.3851104914216577.1057620756179
Winsorized Mean ( 15 / 20 )106.81.3063945294843681.7517201653886
Winsorized Mean ( 16 / 20 )106.81.3063945294843681.7517201653886
Winsorized Mean ( 17 / 20 )107.651.1699690951541592.01097742314
Winsorized Mean ( 18 / 20 )107.951.1243139779011796.0141047090041
Winsorized Mean ( 19 / 20 )107.6333333333331.0769717606594999.9407201423957
Winsorized Mean ( 20 / 20 )107.30.930433347795137115.322607744306
Trimmed Mean ( 1 / 20 )106.4310344827592.0123803251067952.8881311126468
Trimmed Mean ( 2 / 20 )106.5892857142861.9260309746727655.3414182408961
Trimmed Mean ( 3 / 20 )106.7037037037041.8486835230602357.7187508693055
Trimmed Mean ( 4 / 20 )106.9038461538461.7712850392681960.3538356525688
Trimmed Mean ( 5 / 20 )107.081.711388027184962.5690949679822
Trimmed Mean ( 6 / 20 )107.2291666666671.6610471530932164.5551611626341
Trimmed Mean ( 7 / 20 )107.2608695652171.635781892140865.5716205690732
Trimmed Mean ( 8 / 20 )107.2727272727271.6077782775661566.7210950474568
Trimmed Mean ( 9 / 20 )107.2857142857141.5825286350342967.793853400567
Trimmed Mean ( 10 / 20 )107.31.5472059183722669.3508205506898
Trimmed Mean ( 11 / 20 )107.2894736842111.5062260048610171.2306608290906
Trimmed Mean ( 12 / 20 )107.3055555555561.4745564005772272.7714148563937
Trimmed Mean ( 13 / 20 )107.4117647058821.4528340041445373.932578945335
Trimmed Mean ( 14 / 20 )107.51.4291041633405975.2219486567823
Trimmed Mean ( 15 / 20 )107.61.3909394823924477.3577868498821
Trimmed Mean ( 16 / 20 )107.7142857142861.355819460575479.4458914674172
Trimmed Mean ( 17 / 20 )107.8461538461541.2981552682910183.076467415281
Trimmed Mean ( 18 / 20 )107.8751.2587555678963885.6997202246973
Trimmed Mean ( 19 / 20 )107.8636363636361.2083681073583389.2638887991193
Trimmed Mean ( 20 / 20 )107.91.1399445969916894.6537228956114
Median108
Midrange103
Midmean - Weighted Average at Xnp106.6875
Midmean - Weighted Average at X(n+1)p107.6
Midmean - Empirical Distribution Function106.6875
Midmean - Empirical Distribution Function - Averaging107.6
Midmean - Empirical Distribution Function - Interpolation107.6
Midmean - Closest Observation106.6875
Midmean - True Basic - Statistics Graphics Toolkit107.6
Midmean - MS Excel (old versions)107.742857142857
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')