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Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationMon, 10 Dec 2007 10:59:22 -0700
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2007/Dec/10/t11973089172tk47c1i4m6o9qq.htm/, Retrieved Mon, 06 May 2024 19:14:01 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=3003, Retrieved Mon, 06 May 2024 19:14:01 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact237
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [Central Tendency 2] [2007-12-10 17:59:22] [6b5c00822e2ce0f7cf73539c28d95782] [Current]
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Dataseries X:
106,22
106,31
107,38
109,31
110,82
111,22
110,66
110,76
110,69
111,08
110,97
110,24
112,51
111,52
112,13
112,23
112,92
111,89
111,99
111,51
112,33
112,04
112,09
111,41
112,61
113,14
113,65
114,26
114,4
114,93
114,86
114,95
116,17
114,6
114,62
113,82
115,02
115,18
115,59
116,6
117,07
116,96
116,66
116,07
116,04
115,81
116,22
115,85
116,43
117,39
119,17
119,24
120,03
119,34
118,49
118,59
117,5
117,56
118,25
118,01




Summary of compuational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\begin{tabular}{lllllllll}
\hline
Summary of compuational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=3003&T=0

[TABLE]
[ROW][C]Summary of compuational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]1 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=3003&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=3003&T=0

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Summary of compuational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean114.08850.418492439975185272.617827951121
Geometric Mean114.042928168590
Harmonic Mean113.997066300250
Quadratic Mean114.133776121123
Winsorized Mean ( 1 / 20 )114.07850.415397082170429274.625183701208
Winsorized Mean ( 2 / 20 )114.1108333333330.403983364572384282.464188727473
Winsorized Mean ( 3 / 20 )114.2038333333330.378933314920065301.382403807447
Winsorized Mean ( 4 / 20 )114.2271666666670.357972010052696319.095246161429
Winsorized Mean ( 5 / 20 )114.2538333333330.34990314169601326.529887041126
Winsorized Mean ( 6 / 20 )114.2328333333330.344546134903895331.545827281437
Winsorized Mean ( 7 / 20 )114.2130.337691088402464338.217394306478
Winsorized Mean ( 8 / 20 )114.1610.325263100805737350.980482314785
Winsorized Mean ( 9 / 20 )114.17450.319803296269886357.014769177509
Winsorized Mean ( 10 / 20 )114.17450.313503297903882364.189151321161
Winsorized Mean ( 11 / 20 )114.14150.299262259093114381.409604892695
Winsorized Mean ( 12 / 20 )114.15750.289429950640364394.421861826761
Winsorized Mean ( 13 / 20 )114.1141666666670.275521620514612414.174998149064
Winsorized Mean ( 14 / 20 )114.10250.272965781365742418.010270111901
Winsorized Mean ( 15 / 20 )114.15250.251941907145817453.090560809051
Winsorized Mean ( 16 / 20 )114.1231666666670.239449520725179476.606369146373
Winsorized Mean ( 17 / 20 )114.1231666666670.235220595065036485.175061457153
Winsorized Mean ( 18 / 20 )114.1081666666670.228577582876355499.209787901168
Winsorized Mean ( 19 / 20 )114.1113333333330.225305626284399506.47351872737
Winsorized Mean ( 20 / 20 )114.0813333333330.21125432054107540.01893566553
Trimmed Mean ( 1 / 20 )114.1217241379310.397626970131992287.007000807939
Trimmed Mean ( 2 / 20 )114.1680357142860.375520800230001304.025863931797
Trimmed Mean ( 3 / 20 )114.1998148148150.355879093895314320.894980272171
Trimmed Mean ( 4 / 20 )114.1982692307690.344017467850928331.954856665169
Trimmed Mean ( 5 / 20 )114.18960.337396993804882338.442849511684
Trimmed Mean ( 6 / 20 )114.1735416666670.331512824220476344.401583664632
Trimmed Mean ( 7 / 20 )114.1606521739130.325395248648302350.83687499476
Trimmed Mean ( 8 / 20 )114.1504545454550.319213315938509357.599288143242
Trimmed Mean ( 9 / 20 )114.1485714285710.314268054619469363.220409299278
Trimmed Mean ( 10 / 20 )114.144250.308777757498238369.66474180269
Trimmed Mean ( 11 / 20 )114.1394736842110.302679815563278377.096416131352
Trimmed Mean ( 12 / 20 )114.1391666666670.29774213169138383.349061210376
Trimmed Mean ( 13 / 20 )114.1364705882350.292956191584493389.60252033218
Trimmed Mean ( 14 / 20 )114.13968750.289303419654853394.532797559641
Trimmed Mean ( 15 / 20 )114.1450.283877401901498402.092590799484
Trimmed Mean ( 16 / 20 )114.1439285714290.281257258241776405.834605958178
Trimmed Mean ( 17 / 20 )114.1469230769230.279709062712157408.091614801875
Trimmed Mean ( 18 / 20 )114.1504166666670.276893663971105412.253624837652
Trimmed Mean ( 19 / 20 )114.1568181818180.272835350158198418.409191168324
Trimmed Mean ( 20 / 20 )114.1640.265248046770922430.40467739465
Median114.5
Midrange113.125
Midmean - Weighted Average at Xnp114.060322580645
Midmean - Weighted Average at X(n+1)p114.145
Midmean - Empirical Distribution Function114.060322580645
Midmean - Empirical Distribution Function - Averaging114.145
Midmean - Empirical Distribution Function - Interpolation114.145
Midmean - Closest Observation114.060322580645
Midmean - True Basic - Statistics Graphics Toolkit114.145
Midmean - MS Excel (old versions)114.1396875
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 114.0885 & 0.418492439975185 & 272.617827951121 \tabularnewline
Geometric Mean & 114.042928168590 &  &  \tabularnewline
Harmonic Mean & 113.997066300250 &  &  \tabularnewline
Quadratic Mean & 114.133776121123 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 114.0785 & 0.415397082170429 & 274.625183701208 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 114.110833333333 & 0.403983364572384 & 282.464188727473 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 114.203833333333 & 0.378933314920065 & 301.382403807447 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 114.227166666667 & 0.357972010052696 & 319.095246161429 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 114.253833333333 & 0.34990314169601 & 326.529887041126 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 114.232833333333 & 0.344546134903895 & 331.545827281437 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 114.213 & 0.337691088402464 & 338.217394306478 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 114.161 & 0.325263100805737 & 350.980482314785 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 114.1745 & 0.319803296269886 & 357.014769177509 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 114.1745 & 0.313503297903882 & 364.189151321161 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 114.1415 & 0.299262259093114 & 381.409604892695 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 114.1575 & 0.289429950640364 & 394.421861826761 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 114.114166666667 & 0.275521620514612 & 414.174998149064 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 114.1025 & 0.272965781365742 & 418.010270111901 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 114.1525 & 0.251941907145817 & 453.090560809051 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 114.123166666667 & 0.239449520725179 & 476.606369146373 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 114.123166666667 & 0.235220595065036 & 485.175061457153 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 114.108166666667 & 0.228577582876355 & 499.209787901168 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 114.111333333333 & 0.225305626284399 & 506.47351872737 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 114.081333333333 & 0.21125432054107 & 540.01893566553 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 114.121724137931 & 0.397626970131992 & 287.007000807939 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 114.168035714286 & 0.375520800230001 & 304.025863931797 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 114.199814814815 & 0.355879093895314 & 320.894980272171 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 114.198269230769 & 0.344017467850928 & 331.954856665169 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 114.1896 & 0.337396993804882 & 338.442849511684 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 114.173541666667 & 0.331512824220476 & 344.401583664632 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 114.160652173913 & 0.325395248648302 & 350.83687499476 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 114.150454545455 & 0.319213315938509 & 357.599288143242 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 114.148571428571 & 0.314268054619469 & 363.220409299278 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 114.14425 & 0.308777757498238 & 369.66474180269 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 114.139473684211 & 0.302679815563278 & 377.096416131352 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 114.139166666667 & 0.29774213169138 & 383.349061210376 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 114.136470588235 & 0.292956191584493 & 389.60252033218 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 114.1396875 & 0.289303419654853 & 394.532797559641 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 114.145 & 0.283877401901498 & 402.092590799484 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 114.143928571429 & 0.281257258241776 & 405.834605958178 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 114.146923076923 & 0.279709062712157 & 408.091614801875 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 114.150416666667 & 0.276893663971105 & 412.253624837652 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 114.156818181818 & 0.272835350158198 & 418.409191168324 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 114.164 & 0.265248046770922 & 430.40467739465 \tabularnewline
Median & 114.5 &  &  \tabularnewline
Midrange & 113.125 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 114.060322580645 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 114.145 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 114.060322580645 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 114.145 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 114.145 &  &  \tabularnewline
Midmean - Closest Observation & 114.060322580645 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 114.145 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 114.1396875 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=3003&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]114.0885[/C][C]0.418492439975185[/C][C]272.617827951121[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]114.042928168590[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]113.997066300250[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]114.133776121123[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]114.0785[/C][C]0.415397082170429[/C][C]274.625183701208[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]114.110833333333[/C][C]0.403983364572384[/C][C]282.464188727473[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]114.203833333333[/C][C]0.378933314920065[/C][C]301.382403807447[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]114.227166666667[/C][C]0.357972010052696[/C][C]319.095246161429[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]114.253833333333[/C][C]0.34990314169601[/C][C]326.529887041126[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]114.232833333333[/C][C]0.344546134903895[/C][C]331.545827281437[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]114.213[/C][C]0.337691088402464[/C][C]338.217394306478[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]114.161[/C][C]0.325263100805737[/C][C]350.980482314785[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]114.1745[/C][C]0.319803296269886[/C][C]357.014769177509[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]114.1745[/C][C]0.313503297903882[/C][C]364.189151321161[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]114.1415[/C][C]0.299262259093114[/C][C]381.409604892695[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]114.1575[/C][C]0.289429950640364[/C][C]394.421861826761[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]114.114166666667[/C][C]0.275521620514612[/C][C]414.174998149064[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]114.1025[/C][C]0.272965781365742[/C][C]418.010270111901[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]114.1525[/C][C]0.251941907145817[/C][C]453.090560809051[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]114.123166666667[/C][C]0.239449520725179[/C][C]476.606369146373[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]114.123166666667[/C][C]0.235220595065036[/C][C]485.175061457153[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]114.108166666667[/C][C]0.228577582876355[/C][C]499.209787901168[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]114.111333333333[/C][C]0.225305626284399[/C][C]506.47351872737[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]114.081333333333[/C][C]0.21125432054107[/C][C]540.01893566553[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]114.121724137931[/C][C]0.397626970131992[/C][C]287.007000807939[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]114.168035714286[/C][C]0.375520800230001[/C][C]304.025863931797[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]114.199814814815[/C][C]0.355879093895314[/C][C]320.894980272171[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]114.198269230769[/C][C]0.344017467850928[/C][C]331.954856665169[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]114.1896[/C][C]0.337396993804882[/C][C]338.442849511684[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]114.173541666667[/C][C]0.331512824220476[/C][C]344.401583664632[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]114.160652173913[/C][C]0.325395248648302[/C][C]350.83687499476[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]114.150454545455[/C][C]0.319213315938509[/C][C]357.599288143242[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]114.148571428571[/C][C]0.314268054619469[/C][C]363.220409299278[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]114.14425[/C][C]0.308777757498238[/C][C]369.66474180269[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]114.139473684211[/C][C]0.302679815563278[/C][C]377.096416131352[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]114.139166666667[/C][C]0.29774213169138[/C][C]383.349061210376[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]114.136470588235[/C][C]0.292956191584493[/C][C]389.60252033218[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]114.1396875[/C][C]0.289303419654853[/C][C]394.532797559641[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]114.145[/C][C]0.283877401901498[/C][C]402.092590799484[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]114.143928571429[/C][C]0.281257258241776[/C][C]405.834605958178[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]114.146923076923[/C][C]0.279709062712157[/C][C]408.091614801875[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]114.150416666667[/C][C]0.276893663971105[/C][C]412.253624837652[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]114.156818181818[/C][C]0.272835350158198[/C][C]418.409191168324[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]114.164[/C][C]0.265248046770922[/C][C]430.40467739465[/C][/ROW]
[ROW][C]Median[/C][C]114.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]113.125[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]114.060322580645[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]114.145[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]114.060322580645[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]114.145[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]114.145[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]114.060322580645[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]114.145[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]114.1396875[/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=3003&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=3003&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 Mean114.08850.418492439975185272.617827951121
Geometric Mean114.042928168590
Harmonic Mean113.997066300250
Quadratic Mean114.133776121123
Winsorized Mean ( 1 / 20 )114.07850.415397082170429274.625183701208
Winsorized Mean ( 2 / 20 )114.1108333333330.403983364572384282.464188727473
Winsorized Mean ( 3 / 20 )114.2038333333330.378933314920065301.382403807447
Winsorized Mean ( 4 / 20 )114.2271666666670.357972010052696319.095246161429
Winsorized Mean ( 5 / 20 )114.2538333333330.34990314169601326.529887041126
Winsorized Mean ( 6 / 20 )114.2328333333330.344546134903895331.545827281437
Winsorized Mean ( 7 / 20 )114.2130.337691088402464338.217394306478
Winsorized Mean ( 8 / 20 )114.1610.325263100805737350.980482314785
Winsorized Mean ( 9 / 20 )114.17450.319803296269886357.014769177509
Winsorized Mean ( 10 / 20 )114.17450.313503297903882364.189151321161
Winsorized Mean ( 11 / 20 )114.14150.299262259093114381.409604892695
Winsorized Mean ( 12 / 20 )114.15750.289429950640364394.421861826761
Winsorized Mean ( 13 / 20 )114.1141666666670.275521620514612414.174998149064
Winsorized Mean ( 14 / 20 )114.10250.272965781365742418.010270111901
Winsorized Mean ( 15 / 20 )114.15250.251941907145817453.090560809051
Winsorized Mean ( 16 / 20 )114.1231666666670.239449520725179476.606369146373
Winsorized Mean ( 17 / 20 )114.1231666666670.235220595065036485.175061457153
Winsorized Mean ( 18 / 20 )114.1081666666670.228577582876355499.209787901168
Winsorized Mean ( 19 / 20 )114.1113333333330.225305626284399506.47351872737
Winsorized Mean ( 20 / 20 )114.0813333333330.21125432054107540.01893566553
Trimmed Mean ( 1 / 20 )114.1217241379310.397626970131992287.007000807939
Trimmed Mean ( 2 / 20 )114.1680357142860.375520800230001304.025863931797
Trimmed Mean ( 3 / 20 )114.1998148148150.355879093895314320.894980272171
Trimmed Mean ( 4 / 20 )114.1982692307690.344017467850928331.954856665169
Trimmed Mean ( 5 / 20 )114.18960.337396993804882338.442849511684
Trimmed Mean ( 6 / 20 )114.1735416666670.331512824220476344.401583664632
Trimmed Mean ( 7 / 20 )114.1606521739130.325395248648302350.83687499476
Trimmed Mean ( 8 / 20 )114.1504545454550.319213315938509357.599288143242
Trimmed Mean ( 9 / 20 )114.1485714285710.314268054619469363.220409299278
Trimmed Mean ( 10 / 20 )114.144250.308777757498238369.66474180269
Trimmed Mean ( 11 / 20 )114.1394736842110.302679815563278377.096416131352
Trimmed Mean ( 12 / 20 )114.1391666666670.29774213169138383.349061210376
Trimmed Mean ( 13 / 20 )114.1364705882350.292956191584493389.60252033218
Trimmed Mean ( 14 / 20 )114.13968750.289303419654853394.532797559641
Trimmed Mean ( 15 / 20 )114.1450.283877401901498402.092590799484
Trimmed Mean ( 16 / 20 )114.1439285714290.281257258241776405.834605958178
Trimmed Mean ( 17 / 20 )114.1469230769230.279709062712157408.091614801875
Trimmed Mean ( 18 / 20 )114.1504166666670.276893663971105412.253624837652
Trimmed Mean ( 19 / 20 )114.1568181818180.272835350158198418.409191168324
Trimmed Mean ( 20 / 20 )114.1640.265248046770922430.40467739465
Median114.5
Midrange113.125
Midmean - Weighted Average at Xnp114.060322580645
Midmean - Weighted Average at X(n+1)p114.145
Midmean - Empirical Distribution Function114.060322580645
Midmean - Empirical Distribution Function - Averaging114.145
Midmean - Empirical Distribution Function - Interpolation114.145
Midmean - Closest Observation114.060322580645
Midmean - True Basic - Statistics Graphics Toolkit114.145
Midmean - MS Excel (old versions)114.1396875
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')