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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 computationThu, 17 Dec 2009 10:47:36 -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/2009/Dec/17/t1261072261026l665isfryoo6.htm/, Retrieved Tue, 30 Apr 2024 04:05:18 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=69016, Retrieved Tue, 30 Apr 2024 04:05:18 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact90
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [paper central ten...] [2009-12-17 17:47:36] [f47dffd5f5a8c03c3681db4cc9472742] [Current]
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Dataseries X:
110.75
110.64
110.46
110.66
110.48
110.5
110.96
111.17
111.07
111.75
111.45
111.24
111.09
111.29
111.15
110.88
111.22
110.62
110.2
109.49
109.32
108.71
107.85
107.44
106.93
106.19
105.71
105.67
105.7
105.28
105.34
105.58
105.23
105.46
104.92
104.68
104.58
104.32
104.36
104.38
104.25
103.93
103.95
103.6
103.23
103.31
102.82
102.76
102.68
102.37
102.54
102.65
102.63
102.22
102.04
101.85
101.88
101.33
100.8




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\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 & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=69016&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]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=69016&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=69016&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 time2 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean106.5349152542370.459892204791659231.651926569401
Geometric Mean106.477502861679
Harmonic Mean106.420281911683
Quadratic Mean106.592472609229
Winsorized Mean ( 1 / 19 )106.5388135593220.457075620671908233.087937183585
Winsorized Mean ( 2 / 19 )106.5510169491530.452773626057502235.329557237993
Winsorized Mean ( 3 / 19 )106.550.452044449902128235.706908962314
Winsorized Mean ( 4 / 19 )106.5594915254240.449896567353769236.853310866967
Winsorized Mean ( 5 / 19 )106.5705084745760.446539550387342238.658610154764
Winsorized Mean ( 6 / 19 )106.5837288135590.44364819719003240.243800129556
Winsorized Mean ( 7 / 19 )106.5967796610170.439130659219583242.745017736769
Winsorized Mean ( 8 / 19 )106.6062711864410.436722751901422244.105146164915
Winsorized Mean ( 9 / 19 )106.5925423728810.433307424325354245.997498286217
Winsorized Mean ( 10 / 19 )106.5840677966100.430165186397949247.77474134787
Winsorized Mean ( 11 / 19 )106.5747457627120.423694636844965251.536688206202
Winsorized Mean ( 12 / 19 )106.5686440677970.418708491151852254.517513544161
Winsorized Mean ( 13 / 19 )106.6545762711860.404388862309412263.742615615317
Winsorized Mean ( 14 / 19 )106.6688135593220.400825134093078266.123065861812
Winsorized Mean ( 15 / 19 )106.7120338983050.385180836765232277.043984831847
Winsorized Mean ( 16 / 19 )106.7961016949150.372077351685110287.026612104295
Winsorized Mean ( 17 / 19 )106.7961016949150.370329517992425288.381283441467
Winsorized Mean ( 18 / 19 )106.8083050847460.344914896672163309.665677288115
Winsorized Mean ( 19 / 19 )106.6022033898300.303859074409359350.827776320466
Trimmed Mean ( 1 / 19 )106.5440350877190.455977004683427233.660982885946
Trimmed Mean ( 2 / 19 )106.5496363636360.454090422745718234.644095154815
Trimmed Mean ( 3 / 19 )106.5488679245280.453918087242388234.731487726842
Trimmed Mean ( 4 / 19 )106.5484313725490.453330020681295235.035021974545
Trimmed Mean ( 5 / 19 )106.5451020408160.452645109822631235.383305218002
Trimmed Mean ( 6 / 19 )106.5387234042550.45204721056048235.680523881922
Trimmed Mean ( 7 / 19 )106.5288888888890.45123346352892236.083751536883
Trimmed Mean ( 8 / 19 )106.5155813953490.450438730674246236.470743170573
Trimmed Mean ( 9 / 19 )106.4992682926830.448967024461858237.209555468657
Trimmed Mean ( 10 / 19 )106.4835897435900.446800363777219238.324760623257
Trimmed Mean ( 11 / 19 )106.4675675675680.443545029285432240.037787683228
Trimmed Mean ( 12 / 19 )106.4511428571430.439587807583684242.161272493614
Trimmed Mean ( 13 / 19 )106.4336363636360.434151431605077245.153254407446
Trimmed Mean ( 14 / 19 )106.4012903225810.428868915465777248.097464016534
Trimmed Mean ( 15 / 19 )106.3624137931030.420614333481577252.873963929625
Trimmed Mean ( 16 / 19 )106.3114814814810.411438205647679258.389911345563
Trimmed Mean ( 17 / 19 )106.240.399290620976751266.071864498379
Trimmed Mean ( 18 / 19 )106.1560869565220.37838158538997280.552994795226
Trimmed Mean ( 19 / 19 )106.0542857142860.352681274854014300.708581021731
Median105.58
Midrange106.275
Midmean - Weighted Average at Xnp106.260666666667
Midmean - Weighted Average at X(n+1)p106.401290322581
Midmean - Empirical Distribution Function106.401290322581
Midmean - Empirical Distribution Function - Averaging106.401290322581
Midmean - Empirical Distribution Function - Interpolation106.362413793103
Midmean - Closest Observation106.260666666667
Midmean - True Basic - Statistics Graphics Toolkit106.401290322581
Midmean - MS Excel (old versions)106.401290322581
Number of observations59

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 106.534915254237 & 0.459892204791659 & 231.651926569401 \tabularnewline
Geometric Mean & 106.477502861679 &  &  \tabularnewline
Harmonic Mean & 106.420281911683 &  &  \tabularnewline
Quadratic Mean & 106.592472609229 &  &  \tabularnewline
Winsorized Mean ( 1 / 19 ) & 106.538813559322 & 0.457075620671908 & 233.087937183585 \tabularnewline
Winsorized Mean ( 2 / 19 ) & 106.551016949153 & 0.452773626057502 & 235.329557237993 \tabularnewline
Winsorized Mean ( 3 / 19 ) & 106.55 & 0.452044449902128 & 235.706908962314 \tabularnewline
Winsorized Mean ( 4 / 19 ) & 106.559491525424 & 0.449896567353769 & 236.853310866967 \tabularnewline
Winsorized Mean ( 5 / 19 ) & 106.570508474576 & 0.446539550387342 & 238.658610154764 \tabularnewline
Winsorized Mean ( 6 / 19 ) & 106.583728813559 & 0.44364819719003 & 240.243800129556 \tabularnewline
Winsorized Mean ( 7 / 19 ) & 106.596779661017 & 0.439130659219583 & 242.745017736769 \tabularnewline
Winsorized Mean ( 8 / 19 ) & 106.606271186441 & 0.436722751901422 & 244.105146164915 \tabularnewline
Winsorized Mean ( 9 / 19 ) & 106.592542372881 & 0.433307424325354 & 245.997498286217 \tabularnewline
Winsorized Mean ( 10 / 19 ) & 106.584067796610 & 0.430165186397949 & 247.77474134787 \tabularnewline
Winsorized Mean ( 11 / 19 ) & 106.574745762712 & 0.423694636844965 & 251.536688206202 \tabularnewline
Winsorized Mean ( 12 / 19 ) & 106.568644067797 & 0.418708491151852 & 254.517513544161 \tabularnewline
Winsorized Mean ( 13 / 19 ) & 106.654576271186 & 0.404388862309412 & 263.742615615317 \tabularnewline
Winsorized Mean ( 14 / 19 ) & 106.668813559322 & 0.400825134093078 & 266.123065861812 \tabularnewline
Winsorized Mean ( 15 / 19 ) & 106.712033898305 & 0.385180836765232 & 277.043984831847 \tabularnewline
Winsorized Mean ( 16 / 19 ) & 106.796101694915 & 0.372077351685110 & 287.026612104295 \tabularnewline
Winsorized Mean ( 17 / 19 ) & 106.796101694915 & 0.370329517992425 & 288.381283441467 \tabularnewline
Winsorized Mean ( 18 / 19 ) & 106.808305084746 & 0.344914896672163 & 309.665677288115 \tabularnewline
Winsorized Mean ( 19 / 19 ) & 106.602203389830 & 0.303859074409359 & 350.827776320466 \tabularnewline
Trimmed Mean ( 1 / 19 ) & 106.544035087719 & 0.455977004683427 & 233.660982885946 \tabularnewline
Trimmed Mean ( 2 / 19 ) & 106.549636363636 & 0.454090422745718 & 234.644095154815 \tabularnewline
Trimmed Mean ( 3 / 19 ) & 106.548867924528 & 0.453918087242388 & 234.731487726842 \tabularnewline
Trimmed Mean ( 4 / 19 ) & 106.548431372549 & 0.453330020681295 & 235.035021974545 \tabularnewline
Trimmed Mean ( 5 / 19 ) & 106.545102040816 & 0.452645109822631 & 235.383305218002 \tabularnewline
Trimmed Mean ( 6 / 19 ) & 106.538723404255 & 0.45204721056048 & 235.680523881922 \tabularnewline
Trimmed Mean ( 7 / 19 ) & 106.528888888889 & 0.45123346352892 & 236.083751536883 \tabularnewline
Trimmed Mean ( 8 / 19 ) & 106.515581395349 & 0.450438730674246 & 236.470743170573 \tabularnewline
Trimmed Mean ( 9 / 19 ) & 106.499268292683 & 0.448967024461858 & 237.209555468657 \tabularnewline
Trimmed Mean ( 10 / 19 ) & 106.483589743590 & 0.446800363777219 & 238.324760623257 \tabularnewline
Trimmed Mean ( 11 / 19 ) & 106.467567567568 & 0.443545029285432 & 240.037787683228 \tabularnewline
Trimmed Mean ( 12 / 19 ) & 106.451142857143 & 0.439587807583684 & 242.161272493614 \tabularnewline
Trimmed Mean ( 13 / 19 ) & 106.433636363636 & 0.434151431605077 & 245.153254407446 \tabularnewline
Trimmed Mean ( 14 / 19 ) & 106.401290322581 & 0.428868915465777 & 248.097464016534 \tabularnewline
Trimmed Mean ( 15 / 19 ) & 106.362413793103 & 0.420614333481577 & 252.873963929625 \tabularnewline
Trimmed Mean ( 16 / 19 ) & 106.311481481481 & 0.411438205647679 & 258.389911345563 \tabularnewline
Trimmed Mean ( 17 / 19 ) & 106.24 & 0.399290620976751 & 266.071864498379 \tabularnewline
Trimmed Mean ( 18 / 19 ) & 106.156086956522 & 0.37838158538997 & 280.552994795226 \tabularnewline
Trimmed Mean ( 19 / 19 ) & 106.054285714286 & 0.352681274854014 & 300.708581021731 \tabularnewline
Median & 105.58 &  &  \tabularnewline
Midrange & 106.275 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 106.260666666667 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 106.401290322581 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 106.401290322581 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 106.401290322581 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 106.362413793103 &  &  \tabularnewline
Midmean - Closest Observation & 106.260666666667 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 106.401290322581 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 106.401290322581 &  &  \tabularnewline
Number of observations & 59 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=69016&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]106.534915254237[/C][C]0.459892204791659[/C][C]231.651926569401[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]106.477502861679[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]106.420281911683[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]106.592472609229[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 19 )[/C][C]106.538813559322[/C][C]0.457075620671908[/C][C]233.087937183585[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 19 )[/C][C]106.551016949153[/C][C]0.452773626057502[/C][C]235.329557237993[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 19 )[/C][C]106.55[/C][C]0.452044449902128[/C][C]235.706908962314[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 19 )[/C][C]106.559491525424[/C][C]0.449896567353769[/C][C]236.853310866967[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 19 )[/C][C]106.570508474576[/C][C]0.446539550387342[/C][C]238.658610154764[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 19 )[/C][C]106.583728813559[/C][C]0.44364819719003[/C][C]240.243800129556[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 19 )[/C][C]106.596779661017[/C][C]0.439130659219583[/C][C]242.745017736769[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 19 )[/C][C]106.606271186441[/C][C]0.436722751901422[/C][C]244.105146164915[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 19 )[/C][C]106.592542372881[/C][C]0.433307424325354[/C][C]245.997498286217[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 19 )[/C][C]106.584067796610[/C][C]0.430165186397949[/C][C]247.77474134787[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 19 )[/C][C]106.574745762712[/C][C]0.423694636844965[/C][C]251.536688206202[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 19 )[/C][C]106.568644067797[/C][C]0.418708491151852[/C][C]254.517513544161[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 19 )[/C][C]106.654576271186[/C][C]0.404388862309412[/C][C]263.742615615317[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 19 )[/C][C]106.668813559322[/C][C]0.400825134093078[/C][C]266.123065861812[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 19 )[/C][C]106.712033898305[/C][C]0.385180836765232[/C][C]277.043984831847[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 19 )[/C][C]106.796101694915[/C][C]0.372077351685110[/C][C]287.026612104295[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 19 )[/C][C]106.796101694915[/C][C]0.370329517992425[/C][C]288.381283441467[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 19 )[/C][C]106.808305084746[/C][C]0.344914896672163[/C][C]309.665677288115[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 19 )[/C][C]106.602203389830[/C][C]0.303859074409359[/C][C]350.827776320466[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 19 )[/C][C]106.544035087719[/C][C]0.455977004683427[/C][C]233.660982885946[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 19 )[/C][C]106.549636363636[/C][C]0.454090422745718[/C][C]234.644095154815[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 19 )[/C][C]106.548867924528[/C][C]0.453918087242388[/C][C]234.731487726842[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 19 )[/C][C]106.548431372549[/C][C]0.453330020681295[/C][C]235.035021974545[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 19 )[/C][C]106.545102040816[/C][C]0.452645109822631[/C][C]235.383305218002[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 19 )[/C][C]106.538723404255[/C][C]0.45204721056048[/C][C]235.680523881922[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 19 )[/C][C]106.528888888889[/C][C]0.45123346352892[/C][C]236.083751536883[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 19 )[/C][C]106.515581395349[/C][C]0.450438730674246[/C][C]236.470743170573[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 19 )[/C][C]106.499268292683[/C][C]0.448967024461858[/C][C]237.209555468657[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 19 )[/C][C]106.483589743590[/C][C]0.446800363777219[/C][C]238.324760623257[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 19 )[/C][C]106.467567567568[/C][C]0.443545029285432[/C][C]240.037787683228[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 19 )[/C][C]106.451142857143[/C][C]0.439587807583684[/C][C]242.161272493614[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 19 )[/C][C]106.433636363636[/C][C]0.434151431605077[/C][C]245.153254407446[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 19 )[/C][C]106.401290322581[/C][C]0.428868915465777[/C][C]248.097464016534[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 19 )[/C][C]106.362413793103[/C][C]0.420614333481577[/C][C]252.873963929625[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 19 )[/C][C]106.311481481481[/C][C]0.411438205647679[/C][C]258.389911345563[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 19 )[/C][C]106.24[/C][C]0.399290620976751[/C][C]266.071864498379[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 19 )[/C][C]106.156086956522[/C][C]0.37838158538997[/C][C]280.552994795226[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 19 )[/C][C]106.054285714286[/C][C]0.352681274854014[/C][C]300.708581021731[/C][/ROW]
[ROW][C]Median[/C][C]105.58[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]106.275[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]106.260666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]106.401290322581[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]106.401290322581[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]106.401290322581[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]106.362413793103[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]106.260666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]106.401290322581[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]106.401290322581[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]59[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=69016&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=69016&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 Mean106.5349152542370.459892204791659231.651926569401
Geometric Mean106.477502861679
Harmonic Mean106.420281911683
Quadratic Mean106.592472609229
Winsorized Mean ( 1 / 19 )106.5388135593220.457075620671908233.087937183585
Winsorized Mean ( 2 / 19 )106.5510169491530.452773626057502235.329557237993
Winsorized Mean ( 3 / 19 )106.550.452044449902128235.706908962314
Winsorized Mean ( 4 / 19 )106.5594915254240.449896567353769236.853310866967
Winsorized Mean ( 5 / 19 )106.5705084745760.446539550387342238.658610154764
Winsorized Mean ( 6 / 19 )106.5837288135590.44364819719003240.243800129556
Winsorized Mean ( 7 / 19 )106.5967796610170.439130659219583242.745017736769
Winsorized Mean ( 8 / 19 )106.6062711864410.436722751901422244.105146164915
Winsorized Mean ( 9 / 19 )106.5925423728810.433307424325354245.997498286217
Winsorized Mean ( 10 / 19 )106.5840677966100.430165186397949247.77474134787
Winsorized Mean ( 11 / 19 )106.5747457627120.423694636844965251.536688206202
Winsorized Mean ( 12 / 19 )106.5686440677970.418708491151852254.517513544161
Winsorized Mean ( 13 / 19 )106.6545762711860.404388862309412263.742615615317
Winsorized Mean ( 14 / 19 )106.6688135593220.400825134093078266.123065861812
Winsorized Mean ( 15 / 19 )106.7120338983050.385180836765232277.043984831847
Winsorized Mean ( 16 / 19 )106.7961016949150.372077351685110287.026612104295
Winsorized Mean ( 17 / 19 )106.7961016949150.370329517992425288.381283441467
Winsorized Mean ( 18 / 19 )106.8083050847460.344914896672163309.665677288115
Winsorized Mean ( 19 / 19 )106.6022033898300.303859074409359350.827776320466
Trimmed Mean ( 1 / 19 )106.5440350877190.455977004683427233.660982885946
Trimmed Mean ( 2 / 19 )106.5496363636360.454090422745718234.644095154815
Trimmed Mean ( 3 / 19 )106.5488679245280.453918087242388234.731487726842
Trimmed Mean ( 4 / 19 )106.5484313725490.453330020681295235.035021974545
Trimmed Mean ( 5 / 19 )106.5451020408160.452645109822631235.383305218002
Trimmed Mean ( 6 / 19 )106.5387234042550.45204721056048235.680523881922
Trimmed Mean ( 7 / 19 )106.5288888888890.45123346352892236.083751536883
Trimmed Mean ( 8 / 19 )106.5155813953490.450438730674246236.470743170573
Trimmed Mean ( 9 / 19 )106.4992682926830.448967024461858237.209555468657
Trimmed Mean ( 10 / 19 )106.4835897435900.446800363777219238.324760623257
Trimmed Mean ( 11 / 19 )106.4675675675680.443545029285432240.037787683228
Trimmed Mean ( 12 / 19 )106.4511428571430.439587807583684242.161272493614
Trimmed Mean ( 13 / 19 )106.4336363636360.434151431605077245.153254407446
Trimmed Mean ( 14 / 19 )106.4012903225810.428868915465777248.097464016534
Trimmed Mean ( 15 / 19 )106.3624137931030.420614333481577252.873963929625
Trimmed Mean ( 16 / 19 )106.3114814814810.411438205647679258.389911345563
Trimmed Mean ( 17 / 19 )106.240.399290620976751266.071864498379
Trimmed Mean ( 18 / 19 )106.1560869565220.37838158538997280.552994795226
Trimmed Mean ( 19 / 19 )106.0542857142860.352681274854014300.708581021731
Median105.58
Midrange106.275
Midmean - Weighted Average at Xnp106.260666666667
Midmean - Weighted Average at X(n+1)p106.401290322581
Midmean - Empirical Distribution Function106.401290322581
Midmean - Empirical Distribution Function - Averaging106.401290322581
Midmean - Empirical Distribution Function - Interpolation106.362413793103
Midmean - Closest Observation106.260666666667
Midmean - True Basic - Statistics Graphics Toolkit106.401290322581
Midmean - MS Excel (old versions)106.401290322581
Number of observations59



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')