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Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationSun, 18 Oct 2009 09:12:48 -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/18/t12558792054y76guf9y0zvcnc.htm/, Retrieved Mon, 29 Apr 2024 09:34:06 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=47361, Retrieved Mon, 29 Apr 2024 09:34:06 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact126
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
F     [Univariate Data Series] [Gemiddelde renden...] [2008-10-13 19:42:56] [86c69698417c3ad89592e76776a2c65b]
-   PD  [Univariate Data Series] [Werkloosheid in BE] [2009-10-11 19:20:59] [5c968c05ca472afa314d272082b56b09]
-   PD    [Univariate Data Series] [Y[t]-X[t]=c+e[t]] [2009-10-18 14:49:48] [5c968c05ca472afa314d272082b56b09]
- RM          [Central Tendency] [Forecast] [2009-10-18 15:12:48] [b8ce264f75295a954feffaf60221d1b0] [Current]
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Post a new message
Dataseries X:
113
111
107
103
98
99
137
147
147
139
130
128
127
123
118
113
109
111
150
159
158
147
137
137
136
133
125
120
114
116
153
162
161
149
139
134
130
126
122
117
112
113
149
157
157
147
136
132
125
123
117
114
111
112
144
150
149
135
123
115
117
111
105
102
95
93
124
131
124
115
106
105




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24

\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 & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=47361&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]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=47361&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=47361&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'Sir Ronald Aylmer Fisher' @ 193.190.124.24







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean126.8611111111112.1061711208074960.2330503242651
Geometric Mean125.626780284036
Harmonic Mean124.404054679888
Quadratic Mean128.096426353136
Winsorized Mean ( 1 / 24 )126.8752.0968283579621660.5080523249435
Winsorized Mean ( 2 / 24 )126.9027777777782.0672534115429861.3871415421
Winsorized Mean ( 3 / 24 )126.9027777777782.0501497828999761.899271378246
Winsorized Mean ( 4 / 24 )127.0138888888892.0077600876265563.2614871027926
Winsorized Mean ( 5 / 24 )127.0833333333331.9957652742078663.6764929101065
Winsorized Mean ( 6 / 24 )126.9166666666671.9005754420581766.7780209393982
Winsorized Mean ( 7 / 24 )126.6251.8463512955058968.5812067877936
Winsorized Mean ( 8 / 24 )126.7361111111111.8283107743969769.3186918142582
Winsorized Mean ( 9 / 24 )126.7361111111111.7864243160771870.944013676108
Winsorized Mean ( 10 / 24 )127.0138888888891.7445974123795872.804125460467
Winsorized Mean ( 11 / 24 )127.3194444444441.7017236025395274.8179341547843
Winsorized Mean ( 12 / 24 )126.9861111111111.6432025602381577.2796453607684
Winsorized Mean ( 13 / 24 )126.9861111111111.6432025602381577.2796453607684
Winsorized Mean ( 14 / 24 )126.9861111111111.6432025602381577.2796453607684
Winsorized Mean ( 15 / 24 )127.1944444444441.6151230335467778.7521704554785
Winsorized Mean ( 16 / 24 )126.5277777777781.5028627119843284.1911751278437
Winsorized Mean ( 17 / 24 )125.5833333333331.2864026462924197.6236590427439
Winsorized Mean ( 18 / 24 )125.5833333333331.2864026462924197.6236590427439
Winsorized Mean ( 19 / 24 )125.0555555555561.21091296422185103.273777100833
Winsorized Mean ( 20 / 24 )125.3333333333331.17252052512808106.892229728467
Winsorized Mean ( 21 / 24 )125.3333333333331.17252052512808106.892229728467
Winsorized Mean ( 22 / 24 )125.3333333333331.08878189247878115.113352085598
Winsorized Mean ( 23 / 24 )125.3333333333331.08878189247878115.113352085598
Winsorized Mean ( 24 / 24 )125.3333333333330.998825601473863125.480697679747
Trimmed Mean ( 1 / 24 )126.8428571428572.0498584220450161.8788379620453
Trimmed Mean ( 2 / 24 )126.8088235294121.9939831963293363.5957332854414
Trimmed Mean ( 3 / 24 )126.7575757575761.9461348468146565.1329870409786
Trimmed Mean ( 4 / 24 )126.7031251.8964617858811566.8102705487049
Trimmed Mean ( 5 / 24 )126.6129032258061.8520580172798468.3633568951397
Trimmed Mean ( 6 / 24 )126.51.8016784390506970.2123071787736
Trimmed Mean ( 7 / 24 )126.4137931034481.7673236372929671.528377958594
Trimmed Mean ( 8 / 24 )126.3751.7387042682605772.6834357670425
Trimmed Mean ( 9 / 24 )126.3148148148151.7068170289817674.0060666550594
Trimmed Mean ( 10 / 24 )126.251.6760388822582975.3264147606712
Trimmed Mean ( 11 / 24 )126.141.6455282632960576.6562342401443
Trimmed Mean ( 12 / 24 )125.9791666666671.6145640298548778.0267393161181
Trimmed Mean ( 13 / 24 )125.8478260869571.5870756357918279.2954180940273
Trimmed Mean ( 14 / 24 )125.7045454545451.5499367597596681.1030157604867
Trimmed Mean ( 15 / 24 )125.5476190476191.4999815643282083.6994414020335
Trimmed Mean ( 16 / 24 )125.351.4387271796403687.1256217119177
Trimmed Mean ( 17 / 24 )125.2105263157891.3863579878461990.3161574524584
Trimmed Mean ( 18 / 24 )125.1666666666671.3694512862445491.3991376866807
Trimmed Mean ( 19 / 24 )125.1176470588241.3429453263342193.1665977797862
Trimmed Mean ( 20 / 24 )125.1251.3226851355261994.599233513139
Trimmed Mean ( 21 / 24 )125.11.3001768226341196.2176819507916
Trimmed Mean ( 22 / 24 )125.0714285714291.2629525449372399.0309802793462
Trimmed Mean ( 23 / 24 )125.0384615384621.23098555791162101.575896430979
Trimmed Mean ( 24 / 24 )1251.17645993175054106.250962422497
Median124.5
Midrange127.5
Midmean - Weighted Average at Xnp125.210526315789
Midmean - Weighted Average at X(n+1)p125.210526315789
Midmean - Empirical Distribution Function125.210526315789
Midmean - Empirical Distribution Function - Averaging125.210526315789
Midmean - Empirical Distribution Function - Interpolation125.210526315789
Midmean - Closest Observation125.210526315789
Midmean - True Basic - Statistics Graphics Toolkit125.210526315789
Midmean - MS Excel (old versions)125.210526315789
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 126.861111111111 & 2.10617112080749 & 60.2330503242651 \tabularnewline
Geometric Mean & 125.626780284036 &  &  \tabularnewline
Harmonic Mean & 124.404054679888 &  &  \tabularnewline
Quadratic Mean & 128.096426353136 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 126.875 & 2.09682835796216 & 60.5080523249435 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 126.902777777778 & 2.06725341154298 & 61.3871415421 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 126.902777777778 & 2.05014978289997 & 61.899271378246 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 127.013888888889 & 2.00776008762655 & 63.2614871027926 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 127.083333333333 & 1.99576527420786 & 63.6764929101065 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 126.916666666667 & 1.90057544205817 & 66.7780209393982 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 126.625 & 1.84635129550589 & 68.5812067877936 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 126.736111111111 & 1.82831077439697 & 69.3186918142582 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 126.736111111111 & 1.78642431607718 & 70.944013676108 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 127.013888888889 & 1.74459741237958 & 72.804125460467 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 127.319444444444 & 1.70172360253952 & 74.8179341547843 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 126.986111111111 & 1.64320256023815 & 77.2796453607684 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 126.986111111111 & 1.64320256023815 & 77.2796453607684 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 126.986111111111 & 1.64320256023815 & 77.2796453607684 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 127.194444444444 & 1.61512303354677 & 78.7521704554785 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 126.527777777778 & 1.50286271198432 & 84.1911751278437 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 125.583333333333 & 1.28640264629241 & 97.6236590427439 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 125.583333333333 & 1.28640264629241 & 97.6236590427439 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 125.055555555556 & 1.21091296422185 & 103.273777100833 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 125.333333333333 & 1.17252052512808 & 106.892229728467 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 125.333333333333 & 1.17252052512808 & 106.892229728467 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 125.333333333333 & 1.08878189247878 & 115.113352085598 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 125.333333333333 & 1.08878189247878 & 115.113352085598 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 125.333333333333 & 0.998825601473863 & 125.480697679747 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 126.842857142857 & 2.04985842204501 & 61.8788379620453 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 126.808823529412 & 1.99398319632933 & 63.5957332854414 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 126.757575757576 & 1.94613484681465 & 65.1329870409786 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 126.703125 & 1.89646178588115 & 66.8102705487049 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 126.612903225806 & 1.85205801727984 & 68.3633568951397 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 126.5 & 1.80167843905069 & 70.2123071787736 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 126.413793103448 & 1.76732363729296 & 71.528377958594 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 126.375 & 1.73870426826057 & 72.6834357670425 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 126.314814814815 & 1.70681702898176 & 74.0060666550594 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 126.25 & 1.67603888225829 & 75.3264147606712 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 126.14 & 1.64552826329605 & 76.6562342401443 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 125.979166666667 & 1.61456402985487 & 78.0267393161181 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 125.847826086957 & 1.58707563579182 & 79.2954180940273 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 125.704545454545 & 1.54993675975966 & 81.1030157604867 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 125.547619047619 & 1.49998156432820 & 83.6994414020335 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 125.35 & 1.43872717964036 & 87.1256217119177 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 125.210526315789 & 1.38635798784619 & 90.3161574524584 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 125.166666666667 & 1.36945128624454 & 91.3991376866807 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 125.117647058824 & 1.34294532633421 & 93.1665977797862 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 125.125 & 1.32268513552619 & 94.599233513139 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 125.1 & 1.30017682263411 & 96.2176819507916 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 125.071428571429 & 1.26295254493723 & 99.0309802793462 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 125.038461538462 & 1.23098555791162 & 101.575896430979 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 125 & 1.17645993175054 & 106.250962422497 \tabularnewline
Median & 124.5 &  &  \tabularnewline
Midrange & 127.5 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 125.210526315789 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 125.210526315789 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 125.210526315789 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 125.210526315789 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 125.210526315789 &  &  \tabularnewline
Midmean - Closest Observation & 125.210526315789 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 125.210526315789 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 125.210526315789 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=47361&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]126.861111111111[/C][C]2.10617112080749[/C][C]60.2330503242651[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]125.626780284036[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]124.404054679888[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]128.096426353136[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]126.875[/C][C]2.09682835796216[/C][C]60.5080523249435[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]126.902777777778[/C][C]2.06725341154298[/C][C]61.3871415421[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]126.902777777778[/C][C]2.05014978289997[/C][C]61.899271378246[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]127.013888888889[/C][C]2.00776008762655[/C][C]63.2614871027926[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]127.083333333333[/C][C]1.99576527420786[/C][C]63.6764929101065[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]126.916666666667[/C][C]1.90057544205817[/C][C]66.7780209393982[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]126.625[/C][C]1.84635129550589[/C][C]68.5812067877936[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]126.736111111111[/C][C]1.82831077439697[/C][C]69.3186918142582[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]126.736111111111[/C][C]1.78642431607718[/C][C]70.944013676108[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]127.013888888889[/C][C]1.74459741237958[/C][C]72.804125460467[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]127.319444444444[/C][C]1.70172360253952[/C][C]74.8179341547843[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]126.986111111111[/C][C]1.64320256023815[/C][C]77.2796453607684[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]126.986111111111[/C][C]1.64320256023815[/C][C]77.2796453607684[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]126.986111111111[/C][C]1.64320256023815[/C][C]77.2796453607684[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]127.194444444444[/C][C]1.61512303354677[/C][C]78.7521704554785[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]126.527777777778[/C][C]1.50286271198432[/C][C]84.1911751278437[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]125.583333333333[/C][C]1.28640264629241[/C][C]97.6236590427439[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]125.583333333333[/C][C]1.28640264629241[/C][C]97.6236590427439[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]125.055555555556[/C][C]1.21091296422185[/C][C]103.273777100833[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]125.333333333333[/C][C]1.17252052512808[/C][C]106.892229728467[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]125.333333333333[/C][C]1.17252052512808[/C][C]106.892229728467[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]125.333333333333[/C][C]1.08878189247878[/C][C]115.113352085598[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]125.333333333333[/C][C]1.08878189247878[/C][C]115.113352085598[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]125.333333333333[/C][C]0.998825601473863[/C][C]125.480697679747[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]126.842857142857[/C][C]2.04985842204501[/C][C]61.8788379620453[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]126.808823529412[/C][C]1.99398319632933[/C][C]63.5957332854414[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]126.757575757576[/C][C]1.94613484681465[/C][C]65.1329870409786[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]126.703125[/C][C]1.89646178588115[/C][C]66.8102705487049[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]126.612903225806[/C][C]1.85205801727984[/C][C]68.3633568951397[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]126.5[/C][C]1.80167843905069[/C][C]70.2123071787736[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]126.413793103448[/C][C]1.76732363729296[/C][C]71.528377958594[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]126.375[/C][C]1.73870426826057[/C][C]72.6834357670425[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]126.314814814815[/C][C]1.70681702898176[/C][C]74.0060666550594[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]126.25[/C][C]1.67603888225829[/C][C]75.3264147606712[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]126.14[/C][C]1.64552826329605[/C][C]76.6562342401443[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]125.979166666667[/C][C]1.61456402985487[/C][C]78.0267393161181[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]125.847826086957[/C][C]1.58707563579182[/C][C]79.2954180940273[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]125.704545454545[/C][C]1.54993675975966[/C][C]81.1030157604867[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]125.547619047619[/C][C]1.49998156432820[/C][C]83.6994414020335[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]125.35[/C][C]1.43872717964036[/C][C]87.1256217119177[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]125.210526315789[/C][C]1.38635798784619[/C][C]90.3161574524584[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]125.166666666667[/C][C]1.36945128624454[/C][C]91.3991376866807[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]125.117647058824[/C][C]1.34294532633421[/C][C]93.1665977797862[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]125.125[/C][C]1.32268513552619[/C][C]94.599233513139[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]125.1[/C][C]1.30017682263411[/C][C]96.2176819507916[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]125.071428571429[/C][C]1.26295254493723[/C][C]99.0309802793462[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]125.038461538462[/C][C]1.23098555791162[/C][C]101.575896430979[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]125[/C][C]1.17645993175054[/C][C]106.250962422497[/C][/ROW]
[ROW][C]Median[/C][C]124.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]127.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]125.210526315789[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]125.210526315789[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]125.210526315789[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]125.210526315789[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]125.210526315789[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]125.210526315789[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]125.210526315789[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]125.210526315789[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]72[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=47361&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=47361&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 Mean126.8611111111112.1061711208074960.2330503242651
Geometric Mean125.626780284036
Harmonic Mean124.404054679888
Quadratic Mean128.096426353136
Winsorized Mean ( 1 / 24 )126.8752.0968283579621660.5080523249435
Winsorized Mean ( 2 / 24 )126.9027777777782.0672534115429861.3871415421
Winsorized Mean ( 3 / 24 )126.9027777777782.0501497828999761.899271378246
Winsorized Mean ( 4 / 24 )127.0138888888892.0077600876265563.2614871027926
Winsorized Mean ( 5 / 24 )127.0833333333331.9957652742078663.6764929101065
Winsorized Mean ( 6 / 24 )126.9166666666671.9005754420581766.7780209393982
Winsorized Mean ( 7 / 24 )126.6251.8463512955058968.5812067877936
Winsorized Mean ( 8 / 24 )126.7361111111111.8283107743969769.3186918142582
Winsorized Mean ( 9 / 24 )126.7361111111111.7864243160771870.944013676108
Winsorized Mean ( 10 / 24 )127.0138888888891.7445974123795872.804125460467
Winsorized Mean ( 11 / 24 )127.3194444444441.7017236025395274.8179341547843
Winsorized Mean ( 12 / 24 )126.9861111111111.6432025602381577.2796453607684
Winsorized Mean ( 13 / 24 )126.9861111111111.6432025602381577.2796453607684
Winsorized Mean ( 14 / 24 )126.9861111111111.6432025602381577.2796453607684
Winsorized Mean ( 15 / 24 )127.1944444444441.6151230335467778.7521704554785
Winsorized Mean ( 16 / 24 )126.5277777777781.5028627119843284.1911751278437
Winsorized Mean ( 17 / 24 )125.5833333333331.2864026462924197.6236590427439
Winsorized Mean ( 18 / 24 )125.5833333333331.2864026462924197.6236590427439
Winsorized Mean ( 19 / 24 )125.0555555555561.21091296422185103.273777100833
Winsorized Mean ( 20 / 24 )125.3333333333331.17252052512808106.892229728467
Winsorized Mean ( 21 / 24 )125.3333333333331.17252052512808106.892229728467
Winsorized Mean ( 22 / 24 )125.3333333333331.08878189247878115.113352085598
Winsorized Mean ( 23 / 24 )125.3333333333331.08878189247878115.113352085598
Winsorized Mean ( 24 / 24 )125.3333333333330.998825601473863125.480697679747
Trimmed Mean ( 1 / 24 )126.8428571428572.0498584220450161.8788379620453
Trimmed Mean ( 2 / 24 )126.8088235294121.9939831963293363.5957332854414
Trimmed Mean ( 3 / 24 )126.7575757575761.9461348468146565.1329870409786
Trimmed Mean ( 4 / 24 )126.7031251.8964617858811566.8102705487049
Trimmed Mean ( 5 / 24 )126.6129032258061.8520580172798468.3633568951397
Trimmed Mean ( 6 / 24 )126.51.8016784390506970.2123071787736
Trimmed Mean ( 7 / 24 )126.4137931034481.7673236372929671.528377958594
Trimmed Mean ( 8 / 24 )126.3751.7387042682605772.6834357670425
Trimmed Mean ( 9 / 24 )126.3148148148151.7068170289817674.0060666550594
Trimmed Mean ( 10 / 24 )126.251.6760388822582975.3264147606712
Trimmed Mean ( 11 / 24 )126.141.6455282632960576.6562342401443
Trimmed Mean ( 12 / 24 )125.9791666666671.6145640298548778.0267393161181
Trimmed Mean ( 13 / 24 )125.8478260869571.5870756357918279.2954180940273
Trimmed Mean ( 14 / 24 )125.7045454545451.5499367597596681.1030157604867
Trimmed Mean ( 15 / 24 )125.5476190476191.4999815643282083.6994414020335
Trimmed Mean ( 16 / 24 )125.351.4387271796403687.1256217119177
Trimmed Mean ( 17 / 24 )125.2105263157891.3863579878461990.3161574524584
Trimmed Mean ( 18 / 24 )125.1666666666671.3694512862445491.3991376866807
Trimmed Mean ( 19 / 24 )125.1176470588241.3429453263342193.1665977797862
Trimmed Mean ( 20 / 24 )125.1251.3226851355261994.599233513139
Trimmed Mean ( 21 / 24 )125.11.3001768226341196.2176819507916
Trimmed Mean ( 22 / 24 )125.0714285714291.2629525449372399.0309802793462
Trimmed Mean ( 23 / 24 )125.0384615384621.23098555791162101.575896430979
Trimmed Mean ( 24 / 24 )1251.17645993175054106.250962422497
Median124.5
Midrange127.5
Midmean - Weighted Average at Xnp125.210526315789
Midmean - Weighted Average at X(n+1)p125.210526315789
Midmean - Empirical Distribution Function125.210526315789
Midmean - Empirical Distribution Function - Averaging125.210526315789
Midmean - Empirical Distribution Function - Interpolation125.210526315789
Midmean - Closest Observation125.210526315789
Midmean - True Basic - Statistics Graphics Toolkit125.210526315789
Midmean - MS Excel (old versions)125.210526315789
Number of observations72



Parameters (Session):
par1 = 0.01 ; par2 = 0.99 ; par3 = 0.005 ;
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')