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R Software Module

rwasp_centraltendency.wasp

Title produced by software

Central Tendency

Date of computation

Fri, 30 Nov 2007 07:24:36 -0700

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Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2007/Nov/30/t1196432009t97moy9oz6w9l8s.htm/, Retrieved Sat, 27 Apr 2024 15:32:09 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=7697, Retrieved Sat, 27 Apr 2024 15:32:09 +0000

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Estimated Impact

158

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)

-       [Central Tendency] [] [2007-11-30 14:24:36] [2467046df5c61f7ccf2ce4e184abae94] [Current]

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Summary of compuational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	2 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 & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=7697&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]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=7697&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=7697&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 Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	2 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Central Tendency - Ungrouped Data
Measure	Value	S.E.	Value/S.E.
Arithmetic Mean	100.265555555556	0.312129836408762	321.230282593839
Geometric Mean	100.230913869108
Harmonic Mean	100.196138218436
Quadratic Mean	100.300043909927
Winsorized Mean ( 1 / 24 )	100.265555555556	0.312129836408762	321.230282593840
Winsorized Mean ( 2 / 24 )	100.265555555556	0.312129836408762	321.230282593839
Winsorized Mean ( 3 / 24 )	100.176805555556	0.297851449829356	336.331435059149
Winsorized Mean ( 4 / 24 )	100.176805555556	0.297851449829356	336.331435059149
Winsorized Mean ( 5 / 24 )	100.176805555556	0.297851449829356	336.331435059149
Winsorized Mean ( 6 / 24 )	100.176805555556	0.297851449829356	336.331435059149
Winsorized Mean ( 7 / 24 )	100.201111111111	0.290262519160776	345.208576707796
Winsorized Mean ( 8 / 24 )	100.195555555556	0.289648138551298	345.921627726292
Winsorized Mean ( 9 / 24 )	100.195555555556	0.289648138551298	345.921627726292
Winsorized Mean ( 10 / 24 )	100.195555555556	0.289648138551298	345.921627726292
Winsorized Mean ( 11 / 24 )	100.195555555556	0.289648138551298	345.921627726292
Winsorized Mean ( 12 / 24 )	100.198888888889	0.289140810465803	346.540112160125
Winsorized Mean ( 13 / 24 )	100.198888888889	0.289140810465803	346.540112160125
Winsorized Mean ( 14 / 24 )	100.198888888889	0.289140810465803	346.540112160125
Winsorized Mean ( 15 / 24 )	100.198888888889	0.289140810465803	346.540112160125
Winsorized Mean ( 16 / 24 )	100.261111111111	0.279869013875846	358.242985611792
Winsorized Mean ( 17 / 24 )	100.277638888889	0.277467905703424	361.402658929758
Winsorized Mean ( 18 / 24 )	100.277638888889	0.277467905703424	361.402658929758
Winsorized Mean ( 19 / 24 )	100.248611111111	0.274308656209571	365.459160116776
Winsorized Mean ( 20 / 24 )	100.248611111111	0.274308656209571	365.459160116776
Winsorized Mean ( 21 / 24 )	100.248611111111	0.274308656209571	365.459160116776
Winsorized Mean ( 22 / 24 )	100.285277777778	0.269029800100338	372.766428627517
Winsorized Mean ( 23 / 24 )	100.285277777778	0.269029800100338	372.766428627517
Winsorized Mean ( 24 / 24 )	100.285277777778	0.269029800100338	372.766428627517
Trimmed Mean ( 1 / 24 )	100.252571428571	0.310214958245782	323.171300299265
Trimmed Mean ( 2 / 24 )	100.238823529412	0.307768921318254	325.695080257172
Trimmed Mean ( 3 / 24 )	100.224242424242	0.304691372805807	328.936922307018
Trimmed Mean ( 4 / 24 )	100.24203125	0.306906785174402	326.620446638340
Trimmed Mean ( 5 / 24 )	100.260967741935	0.309059978509186	324.406182338991
Trimmed Mean ( 6 / 24 )	100.281166666667	0.311126084099608	322.316809138257
Trimmed Mean ( 7 / 24 )	100.302758620690	0.313073845111096	320.380511457598
Trimmed Mean ( 8 / 24 )	100.321428571429	0.316574341259047	316.896903812358
Trimmed Mean ( 9 / 24 )	100.342407407407	0.320226589848384	313.348143434673
Trimmed Mean ( 10 / 24 )	100.365	0.323909762027407	309.854816884178
Trimmed Mean ( 11 / 24 )	100.3894	0.327601850185401	306.437219274513
Trimmed Mean ( 12 / 24 )	100.415833333333	0.331272508044795	303.121541615386
Trimmed Mean ( 13 / 24 )	100.444130434783	0.334977333732720	299.853513416904
Trimmed Mean ( 14 / 24 )	100.475	0.33857953181749	296.754500960681
Trimmed Mean ( 15 / 24 )	100.508809523810	0.342004102776593	293.881882433044
Trimmed Mean ( 16 / 24 )	100.546	0.34514634577234	291.314108440019
Trimmed Mean ( 17 / 24 )	100.579736842105	0.349778935844442	287.552298137348
Trimmed Mean ( 18 / 24 )	100.615277777778	0.354733632711034	283.636138498711
Trimmed Mean ( 19 / 24 )	100.655	0.359475070350099	280.005508871506
Trimmed Mean ( 20 / 24 )	100.703125	0.364328657208995	276.407367379372
Trimmed Mean ( 21 / 24 )	100.757666666667	0.368581525576322	273.366025356588
Trimmed Mean ( 22 / 24 )	100.82	0.371799570514707	271.167607483860
Trimmed Mean ( 23 / 24 )	100.887307692308	0.374955405632480	269.064817247079
Trimmed Mean ( 24 / 24 )	100.965833333333	0.375877194651308	268.613884454993
Median	101.705
Midrange	100.72
Midmean - Weighted Average at Xnp	100.937872340426
Midmean - Weighted Average at X(n+1)p	100.937872340426
Midmean - Empirical Distribution Function	100.937872340426
Midmean - Empirical Distribution Function - Averaging	100.937872340426
Midmean - Empirical Distribution Function - Interpolation	100.937872340426
Midmean - Closest Observation	100.937872340426
Midmean - True Basic - Statistics Graphics Toolkit	100.937872340426
Midmean - MS Excel (old versions)	100.937872340426
Number of observations	72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 100.265555555556 & 0.312129836408762 & 321.230282593839 \tabularnewline
Geometric Mean & 100.230913869108 &  &  \tabularnewline
Harmonic Mean & 100.196138218436 &  &  \tabularnewline
Quadratic Mean & 100.300043909927 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 100.265555555556 & 0.312129836408762 & 321.230282593840 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 100.265555555556 & 0.312129836408762 & 321.230282593839 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 100.176805555556 & 0.297851449829356 & 336.331435059149 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 100.176805555556 & 0.297851449829356 & 336.331435059149 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 100.176805555556 & 0.297851449829356 & 336.331435059149 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 100.176805555556 & 0.297851449829356 & 336.331435059149 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 100.201111111111 & 0.290262519160776 & 345.208576707796 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 100.195555555556 & 0.289648138551298 & 345.921627726292 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 100.195555555556 & 0.289648138551298 & 345.921627726292 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 100.195555555556 & 0.289648138551298 & 345.921627726292 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 100.195555555556 & 0.289648138551298 & 345.921627726292 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 100.198888888889 & 0.289140810465803 & 346.540112160125 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 100.198888888889 & 0.289140810465803 & 346.540112160125 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 100.198888888889 & 0.289140810465803 & 346.540112160125 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 100.198888888889 & 0.289140810465803 & 346.540112160125 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 100.261111111111 & 0.279869013875846 & 358.242985611792 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 100.277638888889 & 0.277467905703424 & 361.402658929758 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 100.277638888889 & 0.277467905703424 & 361.402658929758 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 100.248611111111 & 0.274308656209571 & 365.459160116776 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 100.248611111111 & 0.274308656209571 & 365.459160116776 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 100.248611111111 & 0.274308656209571 & 365.459160116776 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 100.285277777778 & 0.269029800100338 & 372.766428627517 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 100.285277777778 & 0.269029800100338 & 372.766428627517 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 100.285277777778 & 0.269029800100338 & 372.766428627517 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 100.252571428571 & 0.310214958245782 & 323.171300299265 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 100.238823529412 & 0.307768921318254 & 325.695080257172 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 100.224242424242 & 0.304691372805807 & 328.936922307018 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 100.24203125 & 0.306906785174402 & 326.620446638340 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 100.260967741935 & 0.309059978509186 & 324.406182338991 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 100.281166666667 & 0.311126084099608 & 322.316809138257 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 100.302758620690 & 0.313073845111096 & 320.380511457598 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 100.321428571429 & 0.316574341259047 & 316.896903812358 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 100.342407407407 & 0.320226589848384 & 313.348143434673 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 100.365 & 0.323909762027407 & 309.854816884178 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 100.3894 & 0.327601850185401 & 306.437219274513 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 100.415833333333 & 0.331272508044795 & 303.121541615386 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 100.444130434783 & 0.334977333732720 & 299.853513416904 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 100.475 & 0.33857953181749 & 296.754500960681 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 100.508809523810 & 0.342004102776593 & 293.881882433044 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 100.546 & 0.34514634577234 & 291.314108440019 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 100.579736842105 & 0.349778935844442 & 287.552298137348 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 100.615277777778 & 0.354733632711034 & 283.636138498711 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 100.655 & 0.359475070350099 & 280.005508871506 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 100.703125 & 0.364328657208995 & 276.407367379372 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 100.757666666667 & 0.368581525576322 & 273.366025356588 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 100.82 & 0.371799570514707 & 271.167607483860 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 100.887307692308 & 0.374955405632480 & 269.064817247079 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 100.965833333333 & 0.375877194651308 & 268.613884454993 \tabularnewline
Median & 101.705 &  &  \tabularnewline
Midrange & 100.72 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 100.937872340426 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 100.937872340426 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 100.937872340426 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 100.937872340426 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 100.937872340426 &  &  \tabularnewline
Midmean - Closest Observation & 100.937872340426 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 100.937872340426 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 100.937872340426 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=7697&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]100.265555555556[/C][C]0.312129836408762[/C][C]321.230282593839[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]100.230913869108[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]100.196138218436[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]100.300043909927[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]100.265555555556[/C][C]0.312129836408762[/C][C]321.230282593840[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]100.265555555556[/C][C]0.312129836408762[/C][C]321.230282593839[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]100.176805555556[/C][C]0.297851449829356[/C][C]336.331435059149[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]100.176805555556[/C][C]0.297851449829356[/C][C]336.331435059149[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]100.176805555556[/C][C]0.297851449829356[/C][C]336.331435059149[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]100.176805555556[/C][C]0.297851449829356[/C][C]336.331435059149[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]100.201111111111[/C][C]0.290262519160776[/C][C]345.208576707796[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]100.195555555556[/C][C]0.289648138551298[/C][C]345.921627726292[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]100.195555555556[/C][C]0.289648138551298[/C][C]345.921627726292[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]100.195555555556[/C][C]0.289648138551298[/C][C]345.921627726292[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]100.195555555556[/C][C]0.289648138551298[/C][C]345.921627726292[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]100.198888888889[/C][C]0.289140810465803[/C][C]346.540112160125[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]100.198888888889[/C][C]0.289140810465803[/C][C]346.540112160125[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]100.198888888889[/C][C]0.289140810465803[/C][C]346.540112160125[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]100.198888888889[/C][C]0.289140810465803[/C][C]346.540112160125[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]100.261111111111[/C][C]0.279869013875846[/C][C]358.242985611792[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]100.277638888889[/C][C]0.277467905703424[/C][C]361.402658929758[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]100.277638888889[/C][C]0.277467905703424[/C][C]361.402658929758[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]100.248611111111[/C][C]0.274308656209571[/C][C]365.459160116776[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]100.248611111111[/C][C]0.274308656209571[/C][C]365.459160116776[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]100.248611111111[/C][C]0.274308656209571[/C][C]365.459160116776[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]100.285277777778[/C][C]0.269029800100338[/C][C]372.766428627517[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]100.285277777778[/C][C]0.269029800100338[/C][C]372.766428627517[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]100.285277777778[/C][C]0.269029800100338[/C][C]372.766428627517[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]100.252571428571[/C][C]0.310214958245782[/C][C]323.171300299265[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]100.238823529412[/C][C]0.307768921318254[/C][C]325.695080257172[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]100.224242424242[/C][C]0.304691372805807[/C][C]328.936922307018[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]100.24203125[/C][C]0.306906785174402[/C][C]326.620446638340[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]100.260967741935[/C][C]0.309059978509186[/C][C]324.406182338991[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]100.281166666667[/C][C]0.311126084099608[/C][C]322.316809138257[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]100.302758620690[/C][C]0.313073845111096[/C][C]320.380511457598[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]100.321428571429[/C][C]0.316574341259047[/C][C]316.896903812358[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]100.342407407407[/C][C]0.320226589848384[/C][C]313.348143434673[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]100.365[/C][C]0.323909762027407[/C][C]309.854816884178[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]100.3894[/C][C]0.327601850185401[/C][C]306.437219274513[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]100.415833333333[/C][C]0.331272508044795[/C][C]303.121541615386[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]100.444130434783[/C][C]0.334977333732720[/C][C]299.853513416904[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]100.475[/C][C]0.33857953181749[/C][C]296.754500960681[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]100.508809523810[/C][C]0.342004102776593[/C][C]293.881882433044[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]100.546[/C][C]0.34514634577234[/C][C]291.314108440019[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]100.579736842105[/C][C]0.349778935844442[/C][C]287.552298137348[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]100.615277777778[/C][C]0.354733632711034[/C][C]283.636138498711[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]100.655[/C][C]0.359475070350099[/C][C]280.005508871506[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]100.703125[/C][C]0.364328657208995[/C][C]276.407367379372[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]100.757666666667[/C][C]0.368581525576322[/C][C]273.366025356588[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]100.82[/C][C]0.371799570514707[/C][C]271.167607483860[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]100.887307692308[/C][C]0.374955405632480[/C][C]269.064817247079[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]100.965833333333[/C][C]0.375877194651308[/C][C]268.613884454993[/C][/ROW]
[ROW][C]Median[/C][C]101.705[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]100.72[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]100.937872340426[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]100.937872340426[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]100.937872340426[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]100.937872340426[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]100.937872340426[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]100.937872340426[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]100.937872340426[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]100.937872340426[/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=7697&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=7697&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
Measure	Value	S.E.	Value/S.E.
Arithmetic Mean	100.265555555556	0.312129836408762	321.230282593839
Geometric Mean	100.230913869108
Harmonic Mean	100.196138218436
Quadratic Mean	100.300043909927
Winsorized Mean ( 1 / 24 )	100.265555555556	0.312129836408762	321.230282593840
Winsorized Mean ( 2 / 24 )	100.265555555556	0.312129836408762	321.230282593839
Winsorized Mean ( 3 / 24 )	100.176805555556	0.297851449829356	336.331435059149
Winsorized Mean ( 4 / 24 )	100.176805555556	0.297851449829356	336.331435059149
Winsorized Mean ( 5 / 24 )	100.176805555556	0.297851449829356	336.331435059149
Winsorized Mean ( 6 / 24 )	100.176805555556	0.297851449829356	336.331435059149
Winsorized Mean ( 7 / 24 )	100.201111111111	0.290262519160776	345.208576707796
Winsorized Mean ( 8 / 24 )	100.195555555556	0.289648138551298	345.921627726292
Winsorized Mean ( 9 / 24 )	100.195555555556	0.289648138551298	345.921627726292
Winsorized Mean ( 10 / 24 )	100.195555555556	0.289648138551298	345.921627726292
Winsorized Mean ( 11 / 24 )	100.195555555556	0.289648138551298	345.921627726292
Winsorized Mean ( 12 / 24 )	100.198888888889	0.289140810465803	346.540112160125
Winsorized Mean ( 13 / 24 )	100.198888888889	0.289140810465803	346.540112160125
Winsorized Mean ( 14 / 24 )	100.198888888889	0.289140810465803	346.540112160125
Winsorized Mean ( 15 / 24 )	100.198888888889	0.289140810465803	346.540112160125
Winsorized Mean ( 16 / 24 )	100.261111111111	0.279869013875846	358.242985611792
Winsorized Mean ( 17 / 24 )	100.277638888889	0.277467905703424	361.402658929758
Winsorized Mean ( 18 / 24 )	100.277638888889	0.277467905703424	361.402658929758
Winsorized Mean ( 19 / 24 )	100.248611111111	0.274308656209571	365.459160116776
Winsorized Mean ( 20 / 24 )	100.248611111111	0.274308656209571	365.459160116776
Winsorized Mean ( 21 / 24 )	100.248611111111	0.274308656209571	365.459160116776
Winsorized Mean ( 22 / 24 )	100.285277777778	0.269029800100338	372.766428627517
Winsorized Mean ( 23 / 24 )	100.285277777778	0.269029800100338	372.766428627517
Winsorized Mean ( 24 / 24 )	100.285277777778	0.269029800100338	372.766428627517
Trimmed Mean ( 1 / 24 )	100.252571428571	0.310214958245782	323.171300299265
Trimmed Mean ( 2 / 24 )	100.238823529412	0.307768921318254	325.695080257172
Trimmed Mean ( 3 / 24 )	100.224242424242	0.304691372805807	328.936922307018
Trimmed Mean ( 4 / 24 )	100.24203125	0.306906785174402	326.620446638340
Trimmed Mean ( 5 / 24 )	100.260967741935	0.309059978509186	324.406182338991
Trimmed Mean ( 6 / 24 )	100.281166666667	0.311126084099608	322.316809138257
Trimmed Mean ( 7 / 24 )	100.302758620690	0.313073845111096	320.380511457598
Trimmed Mean ( 8 / 24 )	100.321428571429	0.316574341259047	316.896903812358
Trimmed Mean ( 9 / 24 )	100.342407407407	0.320226589848384	313.348143434673
Trimmed Mean ( 10 / 24 )	100.365	0.323909762027407	309.854816884178
Trimmed Mean ( 11 / 24 )	100.3894	0.327601850185401	306.437219274513
Trimmed Mean ( 12 / 24 )	100.415833333333	0.331272508044795	303.121541615386
Trimmed Mean ( 13 / 24 )	100.444130434783	0.334977333732720	299.853513416904
Trimmed Mean ( 14 / 24 )	100.475	0.33857953181749	296.754500960681
Trimmed Mean ( 15 / 24 )	100.508809523810	0.342004102776593	293.881882433044
Trimmed Mean ( 16 / 24 )	100.546	0.34514634577234	291.314108440019
Trimmed Mean ( 17 / 24 )	100.579736842105	0.349778935844442	287.552298137348
Trimmed Mean ( 18 / 24 )	100.615277777778	0.354733632711034	283.636138498711
Trimmed Mean ( 19 / 24 )	100.655	0.359475070350099	280.005508871506
Trimmed Mean ( 20 / 24 )	100.703125	0.364328657208995	276.407367379372
Trimmed Mean ( 21 / 24 )	100.757666666667	0.368581525576322	273.366025356588
Trimmed Mean ( 22 / 24 )	100.82	0.371799570514707	271.167607483860
Trimmed Mean ( 23 / 24 )	100.887307692308	0.374955405632480	269.064817247079
Trimmed Mean ( 24 / 24 )	100.965833333333	0.375877194651308	268.613884454993
Median	101.705
Midrange	100.72
Midmean - Weighted Average at Xnp	100.937872340426
Midmean - Weighted Average at X(n+1)p	100.937872340426
Midmean - Empirical Distribution Function	100.937872340426
Midmean - Empirical Distribution Function - Averaging	100.937872340426
Midmean - Empirical Distribution Function - Interpolation	100.937872340426
Midmean - Closest Observation	100.937872340426
Midmean - True Basic - Statistics Graphics Toolkit	100.937872340426
Midmean - MS Excel (old versions)	100.937872340426
Number of observations	72

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

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')

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code