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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 computationMon, 19 Oct 2009 12:39:01 -0600
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/Oct/19/t1255977735z3dctdtd5jwltwb.htm/, Retrieved Mon, 29 Apr 2024 17:46:36 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=48083, Retrieved Mon, 29 Apr 2024 17:46:36 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact91
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Bivariate Data Series] [Bivariate dataset] [2008-01-05 23:51:08] [74be16979710d4c4e7c6647856088456]
F RMPD  [Univariate Explorative Data Analysis] [Colombia Coffee] [2008-01-07 14:21:11] [74be16979710d4c4e7c6647856088456]
F RMPD    [Univariate Data Series] [] [2009-10-14 08:30:28] [74be16979710d4c4e7c6647856088456]
- RMPD        [Central Tendency] [SHWWS3Centraltend] [2009-10-19 18:39:01] [db49399df1e4a3dbe31268849cebfd7f] [Current]
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Dataseries X:
161
149
139
135
130
127
122
117
112
113
149
157
157
147
137
132
125
123
117
114
111
112
144
150
149
134
123
116
117
111
105
102
95
93
124
130
124
115
106
105
105
101
95
93
84
87
116
120
117
109
105
107
109
109
108
107
99
103
131
137




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time4 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 & 4 seconds \tabularnewline
R Server & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=48083&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]4 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=48083&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=48083&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 time4 seconds
R Server'George Udny Yule' @ 72.249.76.132







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean119.5166666666672.3770907142247450.2785467763041
Geometric Mean118.150128732689
Harmonic Mean116.812290902038
Quadratic Mean120.903336044406
Winsorized Mean ( 1 / 20 )119.52.3459906897479850.9379685615196
Winsorized Mean ( 2 / 20 )119.72.3028231261394151.9796760078019
Winsorized Mean ( 3 / 20 )119.352.2135720295358653.9173780692491
Winsorized Mean ( 4 / 20 )119.4166666666672.1718917873526554.9827884437215
Winsorized Mean ( 5 / 20 )119.4166666666672.1718917873526554.9827884437215
Winsorized Mean ( 6 / 20 )119.8166666666672.1001064899912157.0526624424498
Winsorized Mean ( 7 / 20 )119.8166666666672.0076818105352459.6791115195312
Winsorized Mean ( 8 / 20 )119.551.8969831833045163.0211174522623
Winsorized Mean ( 9 / 20 )118.951.7168860591527369.2824077438784
Winsorized Mean ( 10 / 20 )118.951.6010986693994074.2927355280483
Winsorized Mean ( 11 / 20 )118.951.6010986693994074.2927355280483
Winsorized Mean ( 12 / 20 )118.551.5263088298466377.6710438161536
Winsorized Mean ( 13 / 20 )118.3333333333331.4871704955594479.5694466012242
Winsorized Mean ( 14 / 20 )118.11.3701210305728886.1967646395589
Winsorized Mean ( 15 / 20 )118.11.2904910815803591.515549146898
Winsorized Mean ( 16 / 20 )117.8333333333331.2458216417643994.5828274153695
Winsorized Mean ( 17 / 20 )118.1166666666671.2047672880916698.0410638919006
Winsorized Mean ( 18 / 20 )117.5166666666671.01527644134691115.748442375718
Winsorized Mean ( 19 / 20 )116.8833333333330.917529126884663127.38923474854
Winsorized Mean ( 20 / 20 )116.550.868281307744518134.230691091065
Trimmed Mean ( 1 / 20 )119.4137931034482.2689725046183952.6290172579823
Trimmed Mean ( 2 / 20 )119.3214285714292.1739465493102454.8870111867689
Trimmed Mean ( 3 / 20 )119.1111111111112.0849644208918357.1286060891926
Trimmed Mean ( 4 / 20 )119.0192307692312.0184836655659158.9646737299021
Trimmed Mean ( 5 / 20 )118.91.9512947036283860.9339018749493
Trimmed Mean ( 6 / 20 )118.7708333333331.865428188285563.6694749651525
Trimmed Mean ( 7 / 20 )118.5434782608701.7779395667821866.674638708568
Trimmed Mean ( 8 / 20 )118.2954545454551.6930337137433569.8718835810418
Trimmed Mean ( 9 / 20 )118.0714285714291.6156151700309073.081406241791
Trimmed Mean ( 10 / 20 )117.9251.5666342740786575.272832945872
Trimmed Mean ( 11 / 20 )117.7631578947371.5312924702625176.9044190980371
Trimmed Mean ( 12 / 20 )117.5833333333331.4807628878921679.4072665480637
Trimmed Mean ( 13 / 20 )117.4411764705881.4318699841335982.0194415498212
Trimmed Mean ( 14 / 20 )117.31251.3733035722712285.4235744876015
Trimmed Mean ( 15 / 20 )117.21.3247424386406788.4700275173942
Trimmed Mean ( 16 / 20 )117.0714285714291.2764954622539691.7131568683455
Trimmed Mean ( 17 / 20 )116.9615384615381.2171603386328596.0937805391468
Trimmed Mean ( 18 / 20 )116.7916666666671.13568463464642102.838114652337
Trimmed Mean ( 19 / 20 )116.6818181818181.08788361127125107.255791863129
Trimmed Mean ( 20 / 20 )116.651.04949862716492111.14831118466
Median116.5
Midrange122.5
Midmean - Weighted Average at Xnp116.838709677419
Midmean - Weighted Average at X(n+1)p117.2
Midmean - Empirical Distribution Function116.838709677419
Midmean - Empirical Distribution Function - Averaging117.2
Midmean - Empirical Distribution Function - Interpolation117.2
Midmean - Closest Observation116.838709677419
Midmean - True Basic - Statistics Graphics Toolkit117.2
Midmean - MS Excel (old versions)117.3125
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 119.516666666667 & 2.37709071422474 & 50.2785467763041 \tabularnewline
Geometric Mean & 118.150128732689 &  &  \tabularnewline
Harmonic Mean & 116.812290902038 &  &  \tabularnewline
Quadratic Mean & 120.903336044406 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 119.5 & 2.34599068974798 & 50.9379685615196 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 119.7 & 2.30282312613941 & 51.9796760078019 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 119.35 & 2.21357202953586 & 53.9173780692491 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 119.416666666667 & 2.17189178735265 & 54.9827884437215 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 119.416666666667 & 2.17189178735265 & 54.9827884437215 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 119.816666666667 & 2.10010648999121 & 57.0526624424498 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 119.816666666667 & 2.00768181053524 & 59.6791115195312 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 119.55 & 1.89698318330451 & 63.0211174522623 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 118.95 & 1.71688605915273 & 69.2824077438784 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 118.95 & 1.60109866939940 & 74.2927355280483 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 118.95 & 1.60109866939940 & 74.2927355280483 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 118.55 & 1.52630882984663 & 77.6710438161536 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 118.333333333333 & 1.48717049555944 & 79.5694466012242 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 118.1 & 1.37012103057288 & 86.1967646395589 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 118.1 & 1.29049108158035 & 91.515549146898 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 117.833333333333 & 1.24582164176439 & 94.5828274153695 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 118.116666666667 & 1.20476728809166 & 98.0410638919006 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 117.516666666667 & 1.01527644134691 & 115.748442375718 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 116.883333333333 & 0.917529126884663 & 127.38923474854 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 116.55 & 0.868281307744518 & 134.230691091065 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 119.413793103448 & 2.26897250461839 & 52.6290172579823 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 119.321428571429 & 2.17394654931024 & 54.8870111867689 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 119.111111111111 & 2.08496442089183 & 57.1286060891926 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 119.019230769231 & 2.01848366556591 & 58.9646737299021 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 118.9 & 1.95129470362838 & 60.9339018749493 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 118.770833333333 & 1.8654281882855 & 63.6694749651525 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 118.543478260870 & 1.77793956678218 & 66.674638708568 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 118.295454545455 & 1.69303371374335 & 69.8718835810418 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 118.071428571429 & 1.61561517003090 & 73.081406241791 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 117.925 & 1.56663427407865 & 75.272832945872 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 117.763157894737 & 1.53129247026251 & 76.9044190980371 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 117.583333333333 & 1.48076288789216 & 79.4072665480637 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 117.441176470588 & 1.43186998413359 & 82.0194415498212 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 117.3125 & 1.37330357227122 & 85.4235744876015 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 117.2 & 1.32474243864067 & 88.4700275173942 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 117.071428571429 & 1.27649546225396 & 91.7131568683455 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 116.961538461538 & 1.21716033863285 & 96.0937805391468 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 116.791666666667 & 1.13568463464642 & 102.838114652337 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 116.681818181818 & 1.08788361127125 & 107.255791863129 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 116.65 & 1.04949862716492 & 111.14831118466 \tabularnewline
Median & 116.5 &  &  \tabularnewline
Midrange & 122.5 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 116.838709677419 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 117.2 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 116.838709677419 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 117.2 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 117.2 &  &  \tabularnewline
Midmean - Closest Observation & 116.838709677419 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 117.2 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 117.3125 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=48083&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]119.516666666667[/C][C]2.37709071422474[/C][C]50.2785467763041[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]118.150128732689[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]116.812290902038[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]120.903336044406[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]119.5[/C][C]2.34599068974798[/C][C]50.9379685615196[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]119.7[/C][C]2.30282312613941[/C][C]51.9796760078019[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]119.35[/C][C]2.21357202953586[/C][C]53.9173780692491[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]119.416666666667[/C][C]2.17189178735265[/C][C]54.9827884437215[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]119.416666666667[/C][C]2.17189178735265[/C][C]54.9827884437215[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]119.816666666667[/C][C]2.10010648999121[/C][C]57.0526624424498[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]119.816666666667[/C][C]2.00768181053524[/C][C]59.6791115195312[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]119.55[/C][C]1.89698318330451[/C][C]63.0211174522623[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]118.95[/C][C]1.71688605915273[/C][C]69.2824077438784[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]118.95[/C][C]1.60109866939940[/C][C]74.2927355280483[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]118.95[/C][C]1.60109866939940[/C][C]74.2927355280483[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]118.55[/C][C]1.52630882984663[/C][C]77.6710438161536[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]118.333333333333[/C][C]1.48717049555944[/C][C]79.5694466012242[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]118.1[/C][C]1.37012103057288[/C][C]86.1967646395589[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]118.1[/C][C]1.29049108158035[/C][C]91.515549146898[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]117.833333333333[/C][C]1.24582164176439[/C][C]94.5828274153695[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]118.116666666667[/C][C]1.20476728809166[/C][C]98.0410638919006[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]117.516666666667[/C][C]1.01527644134691[/C][C]115.748442375718[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]116.883333333333[/C][C]0.917529126884663[/C][C]127.38923474854[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]116.55[/C][C]0.868281307744518[/C][C]134.230691091065[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]119.413793103448[/C][C]2.26897250461839[/C][C]52.6290172579823[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]119.321428571429[/C][C]2.17394654931024[/C][C]54.8870111867689[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]119.111111111111[/C][C]2.08496442089183[/C][C]57.1286060891926[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]119.019230769231[/C][C]2.01848366556591[/C][C]58.9646737299021[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]118.9[/C][C]1.95129470362838[/C][C]60.9339018749493[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]118.770833333333[/C][C]1.8654281882855[/C][C]63.6694749651525[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]118.543478260870[/C][C]1.77793956678218[/C][C]66.674638708568[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]118.295454545455[/C][C]1.69303371374335[/C][C]69.8718835810418[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]118.071428571429[/C][C]1.61561517003090[/C][C]73.081406241791[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]117.925[/C][C]1.56663427407865[/C][C]75.272832945872[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]117.763157894737[/C][C]1.53129247026251[/C][C]76.9044190980371[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]117.583333333333[/C][C]1.48076288789216[/C][C]79.4072665480637[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]117.441176470588[/C][C]1.43186998413359[/C][C]82.0194415498212[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]117.3125[/C][C]1.37330357227122[/C][C]85.4235744876015[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]117.2[/C][C]1.32474243864067[/C][C]88.4700275173942[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]117.071428571429[/C][C]1.27649546225396[/C][C]91.7131568683455[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]116.961538461538[/C][C]1.21716033863285[/C][C]96.0937805391468[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]116.791666666667[/C][C]1.13568463464642[/C][C]102.838114652337[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]116.681818181818[/C][C]1.08788361127125[/C][C]107.255791863129[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]116.65[/C][C]1.04949862716492[/C][C]111.14831118466[/C][/ROW]
[ROW][C]Median[/C][C]116.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]122.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]116.838709677419[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]117.2[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]116.838709677419[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]117.2[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]117.2[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]116.838709677419[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]117.2[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]117.3125[/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=48083&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=48083&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 Mean119.5166666666672.3770907142247450.2785467763041
Geometric Mean118.150128732689
Harmonic Mean116.812290902038
Quadratic Mean120.903336044406
Winsorized Mean ( 1 / 20 )119.52.3459906897479850.9379685615196
Winsorized Mean ( 2 / 20 )119.72.3028231261394151.9796760078019
Winsorized Mean ( 3 / 20 )119.352.2135720295358653.9173780692491
Winsorized Mean ( 4 / 20 )119.4166666666672.1718917873526554.9827884437215
Winsorized Mean ( 5 / 20 )119.4166666666672.1718917873526554.9827884437215
Winsorized Mean ( 6 / 20 )119.8166666666672.1001064899912157.0526624424498
Winsorized Mean ( 7 / 20 )119.8166666666672.0076818105352459.6791115195312
Winsorized Mean ( 8 / 20 )119.551.8969831833045163.0211174522623
Winsorized Mean ( 9 / 20 )118.951.7168860591527369.2824077438784
Winsorized Mean ( 10 / 20 )118.951.6010986693994074.2927355280483
Winsorized Mean ( 11 / 20 )118.951.6010986693994074.2927355280483
Winsorized Mean ( 12 / 20 )118.551.5263088298466377.6710438161536
Winsorized Mean ( 13 / 20 )118.3333333333331.4871704955594479.5694466012242
Winsorized Mean ( 14 / 20 )118.11.3701210305728886.1967646395589
Winsorized Mean ( 15 / 20 )118.11.2904910815803591.515549146898
Winsorized Mean ( 16 / 20 )117.8333333333331.2458216417643994.5828274153695
Winsorized Mean ( 17 / 20 )118.1166666666671.2047672880916698.0410638919006
Winsorized Mean ( 18 / 20 )117.5166666666671.01527644134691115.748442375718
Winsorized Mean ( 19 / 20 )116.8833333333330.917529126884663127.38923474854
Winsorized Mean ( 20 / 20 )116.550.868281307744518134.230691091065
Trimmed Mean ( 1 / 20 )119.4137931034482.2689725046183952.6290172579823
Trimmed Mean ( 2 / 20 )119.3214285714292.1739465493102454.8870111867689
Trimmed Mean ( 3 / 20 )119.1111111111112.0849644208918357.1286060891926
Trimmed Mean ( 4 / 20 )119.0192307692312.0184836655659158.9646737299021
Trimmed Mean ( 5 / 20 )118.91.9512947036283860.9339018749493
Trimmed Mean ( 6 / 20 )118.7708333333331.865428188285563.6694749651525
Trimmed Mean ( 7 / 20 )118.5434782608701.7779395667821866.674638708568
Trimmed Mean ( 8 / 20 )118.2954545454551.6930337137433569.8718835810418
Trimmed Mean ( 9 / 20 )118.0714285714291.6156151700309073.081406241791
Trimmed Mean ( 10 / 20 )117.9251.5666342740786575.272832945872
Trimmed Mean ( 11 / 20 )117.7631578947371.5312924702625176.9044190980371
Trimmed Mean ( 12 / 20 )117.5833333333331.4807628878921679.4072665480637
Trimmed Mean ( 13 / 20 )117.4411764705881.4318699841335982.0194415498212
Trimmed Mean ( 14 / 20 )117.31251.3733035722712285.4235744876015
Trimmed Mean ( 15 / 20 )117.21.3247424386406788.4700275173942
Trimmed Mean ( 16 / 20 )117.0714285714291.2764954622539691.7131568683455
Trimmed Mean ( 17 / 20 )116.9615384615381.2171603386328596.0937805391468
Trimmed Mean ( 18 / 20 )116.7916666666671.13568463464642102.838114652337
Trimmed Mean ( 19 / 20 )116.6818181818181.08788361127125107.255791863129
Trimmed Mean ( 20 / 20 )116.651.04949862716492111.14831118466
Median116.5
Midrange122.5
Midmean - Weighted Average at Xnp116.838709677419
Midmean - Weighted Average at X(n+1)p117.2
Midmean - Empirical Distribution Function116.838709677419
Midmean - Empirical Distribution Function - Averaging117.2
Midmean - Empirical Distribution Function - Interpolation117.2
Midmean - Closest Observation116.838709677419
Midmean - True Basic - Statistics Graphics Toolkit117.2
Midmean - MS Excel (old versions)117.3125
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')