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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, 21 Dec 2009 07:51:14 -0700
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2009/Dec/21/t12614071550qkqoe5uom967ln.htm/, Retrieved Sun, 28 Apr 2024 23:54:28 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=70219, Retrieved Sun, 28 Apr 2024 23:54:28 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact177
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Central Tendency] [central tendency] [2009-12-03 11:49:09] [757146c69eaf0537be37c7b0c18216d8]
- R  D  [Central Tendency] [] [2009-12-04 15:32:48] [757146c69eaf0537be37c7b0c18216d8]
-           [Central Tendency] [central tendency ...] [2009-12-21 14:51:14] [4563e36d4b7005634fe3557528d9fcab] [Current]
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Dataseries X:
108,5
112,3
116,6
115,5
120,1
132,9
128,1
129,3
132,5
131
124,9
120,8
122
122,1
127,4
135,2
137,3
135
136
138,4
134,7
138,4
133,9
133,6
141,2
151,8
155,4
156,6
161,6
160,7
156
159,5
168,7
169,9
169,9
185,9
190,8
195,8
211,9
227,1
251,3
256,7
251,9
251,2
270,3
267,2
243
229,9
187,2
178,2
175,2
192,4
187
184
194,1
212,7
217,5
200,5
205,9
196,5
206,3




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

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=70219&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=70219&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=70219&T=0

As an alternative you can also use a QR Code:  

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

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







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean170.35.7032365463677929.8602378869344
Geometric Mean164.902221190153
Harmonic Mean159.914992641311
Quadratic Mean175.936648900192
Winsorized Mean ( 1 / 20 )170.3114754098365.6776534916609429.9968068956623
Winsorized Mean ( 2 / 20 )170.0721311475415.5664996855690330.5527963270073
Winsorized Mean ( 3 / 20 )169.8901639344265.4977425595346130.9018041668374
Winsorized Mean ( 4 / 20 )170.0803278688525.4518908434322331.1965761518766
Winsorized Mean ( 5 / 20 )170.1295081967215.4411372486650631.2672701352022
Winsorized Mean ( 6 / 20 )169.4409836065575.2284778093107132.4073257621601
Winsorized Mean ( 7 / 20 )167.9491803278694.8912152897475534.3369020537506
Winsorized Mean ( 8 / 20 )167.9491803278694.7580186116723935.2981343780067
Winsorized Mean ( 9 / 20 )166.9016393442624.4204588267918737.756632486359
Winsorized Mean ( 10 / 20 )166.2295081967214.2566356710911939.0518524584248
Winsorized Mean ( 11 / 20 )166.3016393442624.1984062106122539.6106596174291
Winsorized Mean ( 12 / 20 )165.5344262295083.9550209392314341.8542477455698
Winsorized Mean ( 13 / 20 )165.7688524590163.8943559699487542.5664355642348
Winsorized Mean ( 14 / 20 )164.621311475413.6737624694196544.8100041430864
Winsorized Mean ( 15 / 20 )163.8098360655743.4921024910926246.9086564565064
Winsorized Mean ( 16 / 20 )163.7049180327873.4522198657174447.4201888641197
Winsorized Mean ( 17 / 20 )163.4540983606563.3473589407960548.8307651649046
Winsorized Mean ( 18 / 20 )163.0409836065573.2587321758179850.0320292709027
Winsorized Mean ( 19 / 20 )162.6049180327873.1754879374040251.2062779762022
Winsorized Mean ( 20 / 20 )161.6868852459022.9656489401342454.5199005377161
Trimmed Mean ( 1 / 20 )169.6525423728815.5446887280859130.5973068449322
Trimmed Mean ( 2 / 20 )168.9473684210535.3794414564947531.4061171196645
Trimmed Mean ( 3 / 20 )168.3236363636365.2478246021366132.0749356400183
Trimmed Mean ( 4 / 20 )167.7226415094345.115264757351732.7886530737987
Trimmed Mean ( 5 / 20 )167.0176470588244.9639829879804833.6458943278474
Trimmed Mean ( 6 / 20 )166.2428571428574.7730251107115534.8296632191977
Trimmed Mean ( 7 / 20 )165.5510638297874.5981503665233136.0038386380482
Trimmed Mean ( 8 / 20 )165.0866666666674.4762364693225236.8806848784851
Trimmed Mean ( 9 / 20 )164.5790697674424.351712736914537.8193781890423
Trimmed Mean ( 10 / 20 )164.1951219512204.2778498577107638.3826285196195
Trimmed Mean ( 11 / 20 )163.8769230769234.216834492622538.8625456758219
Trimmed Mean ( 12 / 20 )163.5135135135144.1414374239349339.4823093471139
Trimmed Mean ( 13 / 20 )163.224.094983198373139.8585273963629
Trimmed Mean ( 14 / 20 )162.8575757575764.0341042111034140.3701955218036
Trimmed Mean ( 15 / 20 )162.6096774193553.9985248754168240.6674167313774
Trimmed Mean ( 16 / 20 )162.4413793103453.9824260411755340.7895533101716
Trimmed Mean ( 17 / 20 )162.2629629629633.9494352012381741.0851057670456
Trimmed Mean ( 18 / 20 )162.0923.9106219454199441.4491613513906
Trimmed Mean ( 19 / 20 )161.9521739130433.8557942106228442.0022867057738
Trimmed Mean ( 20 / 20 )161.8523809523813.7716651561195942.9127120921041
Median160.7
Midrange189.4
Midmean - Weighted Average at Xnp161.48
Midmean - Weighted Average at X(n+1)p162.609677419355
Midmean - Empirical Distribution Function162.609677419355
Midmean - Empirical Distribution Function - Averaging162.609677419355
Midmean - Empirical Distribution Function - Interpolation162.609677419355
Midmean - Closest Observation161.68125
Midmean - True Basic - Statistics Graphics Toolkit162.609677419355
Midmean - MS Excel (old versions)162.609677419355
Number of observations61

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 170.3 & 5.70323654636779 & 29.8602378869344 \tabularnewline
Geometric Mean & 164.902221190153 &  &  \tabularnewline
Harmonic Mean & 159.914992641311 &  &  \tabularnewline
Quadratic Mean & 175.936648900192 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 170.311475409836 & 5.67765349166094 & 29.9968068956623 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 170.072131147541 & 5.56649968556903 & 30.5527963270073 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 169.890163934426 & 5.49774255953461 & 30.9018041668374 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 170.080327868852 & 5.45189084343223 & 31.1965761518766 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 170.129508196721 & 5.44113724866506 & 31.2672701352022 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 169.440983606557 & 5.22847780931071 & 32.4073257621601 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 167.949180327869 & 4.89121528974755 & 34.3369020537506 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 167.949180327869 & 4.75801861167239 & 35.2981343780067 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 166.901639344262 & 4.42045882679187 & 37.756632486359 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 166.229508196721 & 4.25663567109119 & 39.0518524584248 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 166.301639344262 & 4.19840621061225 & 39.6106596174291 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 165.534426229508 & 3.95502093923143 & 41.8542477455698 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 165.768852459016 & 3.89435596994875 & 42.5664355642348 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 164.62131147541 & 3.67376246941965 & 44.8100041430864 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 163.809836065574 & 3.49210249109262 & 46.9086564565064 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 163.704918032787 & 3.45221986571744 & 47.4201888641197 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 163.454098360656 & 3.34735894079605 & 48.8307651649046 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 163.040983606557 & 3.25873217581798 & 50.0320292709027 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 162.604918032787 & 3.17548793740402 & 51.2062779762022 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 161.686885245902 & 2.96564894013424 & 54.5199005377161 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 169.652542372881 & 5.54468872808591 & 30.5973068449322 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 168.947368421053 & 5.37944145649475 & 31.4061171196645 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 168.323636363636 & 5.24782460213661 & 32.0749356400183 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 167.722641509434 & 5.1152647573517 & 32.7886530737987 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 167.017647058824 & 4.96398298798048 & 33.6458943278474 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 166.242857142857 & 4.77302511071155 & 34.8296632191977 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 165.551063829787 & 4.59815036652331 & 36.0038386380482 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 165.086666666667 & 4.47623646932252 & 36.8806848784851 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 164.579069767442 & 4.3517127369145 & 37.8193781890423 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 164.195121951220 & 4.27784985771076 & 38.3826285196195 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 163.876923076923 & 4.2168344926225 & 38.8625456758219 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 163.513513513514 & 4.14143742393493 & 39.4823093471139 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 163.22 & 4.0949831983731 & 39.8585273963629 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 162.857575757576 & 4.03410421110341 & 40.3701955218036 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 162.609677419355 & 3.99852487541682 & 40.6674167313774 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 162.441379310345 & 3.98242604117553 & 40.7895533101716 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 162.262962962963 & 3.94943520123817 & 41.0851057670456 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 162.092 & 3.91062194541994 & 41.4491613513906 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 161.952173913043 & 3.85579421062284 & 42.0022867057738 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 161.852380952381 & 3.77166515611959 & 42.9127120921041 \tabularnewline
Median & 160.7 &  &  \tabularnewline
Midrange & 189.4 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 161.48 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 162.609677419355 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 162.609677419355 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 162.609677419355 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 162.609677419355 &  &  \tabularnewline
Midmean - Closest Observation & 161.68125 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 162.609677419355 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 162.609677419355 &  &  \tabularnewline
Number of observations & 61 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=70219&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]170.3[/C][C]5.70323654636779[/C][C]29.8602378869344[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]164.902221190153[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]159.914992641311[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]175.936648900192[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]170.311475409836[/C][C]5.67765349166094[/C][C]29.9968068956623[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]170.072131147541[/C][C]5.56649968556903[/C][C]30.5527963270073[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]169.890163934426[/C][C]5.49774255953461[/C][C]30.9018041668374[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]170.080327868852[/C][C]5.45189084343223[/C][C]31.1965761518766[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]170.129508196721[/C][C]5.44113724866506[/C][C]31.2672701352022[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]169.440983606557[/C][C]5.22847780931071[/C][C]32.4073257621601[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]167.949180327869[/C][C]4.89121528974755[/C][C]34.3369020537506[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]167.949180327869[/C][C]4.75801861167239[/C][C]35.2981343780067[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]166.901639344262[/C][C]4.42045882679187[/C][C]37.756632486359[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]166.229508196721[/C][C]4.25663567109119[/C][C]39.0518524584248[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]166.301639344262[/C][C]4.19840621061225[/C][C]39.6106596174291[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]165.534426229508[/C][C]3.95502093923143[/C][C]41.8542477455698[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]165.768852459016[/C][C]3.89435596994875[/C][C]42.5664355642348[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]164.62131147541[/C][C]3.67376246941965[/C][C]44.8100041430864[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]163.809836065574[/C][C]3.49210249109262[/C][C]46.9086564565064[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]163.704918032787[/C][C]3.45221986571744[/C][C]47.4201888641197[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]163.454098360656[/C][C]3.34735894079605[/C][C]48.8307651649046[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]163.040983606557[/C][C]3.25873217581798[/C][C]50.0320292709027[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]162.604918032787[/C][C]3.17548793740402[/C][C]51.2062779762022[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]161.686885245902[/C][C]2.96564894013424[/C][C]54.5199005377161[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]169.652542372881[/C][C]5.54468872808591[/C][C]30.5973068449322[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]168.947368421053[/C][C]5.37944145649475[/C][C]31.4061171196645[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]168.323636363636[/C][C]5.24782460213661[/C][C]32.0749356400183[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]167.722641509434[/C][C]5.1152647573517[/C][C]32.7886530737987[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]167.017647058824[/C][C]4.96398298798048[/C][C]33.6458943278474[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]166.242857142857[/C][C]4.77302511071155[/C][C]34.8296632191977[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]165.551063829787[/C][C]4.59815036652331[/C][C]36.0038386380482[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]165.086666666667[/C][C]4.47623646932252[/C][C]36.8806848784851[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]164.579069767442[/C][C]4.3517127369145[/C][C]37.8193781890423[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]164.195121951220[/C][C]4.27784985771076[/C][C]38.3826285196195[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]163.876923076923[/C][C]4.2168344926225[/C][C]38.8625456758219[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]163.513513513514[/C][C]4.14143742393493[/C][C]39.4823093471139[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]163.22[/C][C]4.0949831983731[/C][C]39.8585273963629[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]162.857575757576[/C][C]4.03410421110341[/C][C]40.3701955218036[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]162.609677419355[/C][C]3.99852487541682[/C][C]40.6674167313774[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]162.441379310345[/C][C]3.98242604117553[/C][C]40.7895533101716[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]162.262962962963[/C][C]3.94943520123817[/C][C]41.0851057670456[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]162.092[/C][C]3.91062194541994[/C][C]41.4491613513906[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]161.952173913043[/C][C]3.85579421062284[/C][C]42.0022867057738[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]161.852380952381[/C][C]3.77166515611959[/C][C]42.9127120921041[/C][/ROW]
[ROW][C]Median[/C][C]160.7[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]189.4[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]161.48[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]162.609677419355[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]162.609677419355[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]162.609677419355[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]162.609677419355[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]161.68125[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]162.609677419355[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]162.609677419355[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]61[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=70219&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=70219&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 Mean170.35.7032365463677929.8602378869344
Geometric Mean164.902221190153
Harmonic Mean159.914992641311
Quadratic Mean175.936648900192
Winsorized Mean ( 1 / 20 )170.3114754098365.6776534916609429.9968068956623
Winsorized Mean ( 2 / 20 )170.0721311475415.5664996855690330.5527963270073
Winsorized Mean ( 3 / 20 )169.8901639344265.4977425595346130.9018041668374
Winsorized Mean ( 4 / 20 )170.0803278688525.4518908434322331.1965761518766
Winsorized Mean ( 5 / 20 )170.1295081967215.4411372486650631.2672701352022
Winsorized Mean ( 6 / 20 )169.4409836065575.2284778093107132.4073257621601
Winsorized Mean ( 7 / 20 )167.9491803278694.8912152897475534.3369020537506
Winsorized Mean ( 8 / 20 )167.9491803278694.7580186116723935.2981343780067
Winsorized Mean ( 9 / 20 )166.9016393442624.4204588267918737.756632486359
Winsorized Mean ( 10 / 20 )166.2295081967214.2566356710911939.0518524584248
Winsorized Mean ( 11 / 20 )166.3016393442624.1984062106122539.6106596174291
Winsorized Mean ( 12 / 20 )165.5344262295083.9550209392314341.8542477455698
Winsorized Mean ( 13 / 20 )165.7688524590163.8943559699487542.5664355642348
Winsorized Mean ( 14 / 20 )164.621311475413.6737624694196544.8100041430864
Winsorized Mean ( 15 / 20 )163.8098360655743.4921024910926246.9086564565064
Winsorized Mean ( 16 / 20 )163.7049180327873.4522198657174447.4201888641197
Winsorized Mean ( 17 / 20 )163.4540983606563.3473589407960548.8307651649046
Winsorized Mean ( 18 / 20 )163.0409836065573.2587321758179850.0320292709027
Winsorized Mean ( 19 / 20 )162.6049180327873.1754879374040251.2062779762022
Winsorized Mean ( 20 / 20 )161.6868852459022.9656489401342454.5199005377161
Trimmed Mean ( 1 / 20 )169.6525423728815.5446887280859130.5973068449322
Trimmed Mean ( 2 / 20 )168.9473684210535.3794414564947531.4061171196645
Trimmed Mean ( 3 / 20 )168.3236363636365.2478246021366132.0749356400183
Trimmed Mean ( 4 / 20 )167.7226415094345.115264757351732.7886530737987
Trimmed Mean ( 5 / 20 )167.0176470588244.9639829879804833.6458943278474
Trimmed Mean ( 6 / 20 )166.2428571428574.7730251107115534.8296632191977
Trimmed Mean ( 7 / 20 )165.5510638297874.5981503665233136.0038386380482
Trimmed Mean ( 8 / 20 )165.0866666666674.4762364693225236.8806848784851
Trimmed Mean ( 9 / 20 )164.5790697674424.351712736914537.8193781890423
Trimmed Mean ( 10 / 20 )164.1951219512204.2778498577107638.3826285196195
Trimmed Mean ( 11 / 20 )163.8769230769234.216834492622538.8625456758219
Trimmed Mean ( 12 / 20 )163.5135135135144.1414374239349339.4823093471139
Trimmed Mean ( 13 / 20 )163.224.094983198373139.8585273963629
Trimmed Mean ( 14 / 20 )162.8575757575764.0341042111034140.3701955218036
Trimmed Mean ( 15 / 20 )162.6096774193553.9985248754168240.6674167313774
Trimmed Mean ( 16 / 20 )162.4413793103453.9824260411755340.7895533101716
Trimmed Mean ( 17 / 20 )162.2629629629633.9494352012381741.0851057670456
Trimmed Mean ( 18 / 20 )162.0923.9106219454199441.4491613513906
Trimmed Mean ( 19 / 20 )161.9521739130433.8557942106228442.0022867057738
Trimmed Mean ( 20 / 20 )161.8523809523813.7716651561195942.9127120921041
Median160.7
Midrange189.4
Midmean - Weighted Average at Xnp161.48
Midmean - Weighted Average at X(n+1)p162.609677419355
Midmean - Empirical Distribution Function162.609677419355
Midmean - Empirical Distribution Function - Averaging162.609677419355
Midmean - Empirical Distribution Function - Interpolation162.609677419355
Midmean - Closest Observation161.68125
Midmean - True Basic - Statistics Graphics Toolkit162.609677419355
Midmean - MS Excel (old versions)162.609677419355
Number of observations61



Parameters (Session):
Parameters (R input):
par1 = ; par2 = ; par3 = ; par4 = ; par5 = ; par6 = ; par7 = ; par8 = ; par9 = ; par10 = ; par11 = ; par12 = ; par13 = ; par14 = ; par15 = ; par16 = ; par17 = ; par18 = ; par19 = ; par20 = ;
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')