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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 computationSat, 06 Dec 2008 05:48:02 -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/2008/Dec/06/t1228567739usingpmv4cw3qmh.htm/, Retrieved Fri, 17 May 2024 03:03:18 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=29555, Retrieved Fri, 17 May 2024 03:03:18 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact165
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [Central Tendency ...] [2008-12-06 12:48:02] [6912578025c824de531bc660dd61b996] [Current]
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Dataseries X:
99.2
99.5
99.3
99.9
100
100.3
100.5
100.7
100.9
100.8
100.9
101
100.3
100.1
99.8
99.9
99.9
100.2
99.7
100.4
100.9
101.3
101.4
101.3
100.9
100.9
100.9
101.1
101.1
101.3
101.8
102.9
103.2
103.3
104.5
105
104.9
104.9
105.4
106
105.7
105.9
106.2
106.4
106.9
107.3
107.9
109.2
110.2
110.2
110.5
110.6
110.8
111.3
111.1
111.2
111.2
111.1
111.5
112.1
111.4




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'George Udny Yule' @ 72.249.76.132

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 1 seconds \tabularnewline
R Server & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=29555&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]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=29555&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=29555&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 time1 seconds
R Server'George Udny Yule' @ 72.249.76.132







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean104.1803278688520.553043341971565188.376425430702
Geometric Mean104.093578537841
Harmonic Mean104.008206291270
Quadratic Mean104.268365917701
Winsorized Mean ( 1 / 20 )104.1721311475410.550534420674328189.220014654024
Winsorized Mean ( 2 / 20 )104.1754098360660.548861990764064189.802558000135
Winsorized Mean ( 3 / 20 )104.1803278688520.546418141255955190.660448478873
Winsorized Mean ( 4 / 20 )104.1803278688520.54411315357325191.468129716565
Winsorized Mean ( 5 / 20 )104.1885245901640.543023806503741191.867323941066
Winsorized Mean ( 6 / 20 )104.1786885245900.540916621121963192.596574881548
Winsorized Mean ( 7 / 20 )104.1786885245900.540916621121963192.596574881548
Winsorized Mean ( 8 / 20 )104.1524590163930.530895761008416196.182502603825
Winsorized Mean ( 9 / 20 )104.1377049180330.522866019127858199.167092731968
Winsorized Mean ( 10 / 20 )104.1377049180330.517402951140911201.270025013196
Winsorized Mean ( 11 / 20 )104.1016393442620.5041277258318206.498539973172
Winsorized Mean ( 12 / 20 )104.1016393442620.5041277258318206.498539973172
Winsorized Mean ( 13 / 20 )103.9098360655740.45945266152888226.160048175153
Winsorized Mean ( 14 / 20 )103.6344262295080.40129493429963258.250023540364
Winsorized Mean ( 15 / 20 )103.5360655737710.369322469215092280.340553862894
Winsorized Mean ( 16 / 20 )103.4573770491800.348419217192815296.93361314203
Winsorized Mean ( 17 / 20 )103.3459016393440.322393488748434320.558278148060
Winsorized Mean ( 18 / 20 )103.2868852459020.313158381076490329.8231549507
Winsorized Mean ( 19 / 20 )103.2245901639340.303582037036947340.022061817089
Winsorized Mean ( 20 / 20 )103.1918032786890.29860600612847345.578458439621
Trimmed Mean ( 1 / 20 )104.1305084745760.549098694244992189.638965755974
Trimmed Mean ( 2 / 20 )104.0859649122810.546694547759024190.391444983206
Trimmed Mean ( 3 / 20 )104.0363636363640.544129141660135191.197926505001
Trimmed Mean ( 4 / 20 )103.9811320754720.541332660546419192.083610788445
Trimmed Mean ( 5 / 20 )103.9215686274510.537914008183393193.193646282624
Trimmed Mean ( 6 / 20 )103.8551020408160.533121194186875194.805802457765
Trimmed Mean ( 7 / 20 )103.7851063829790.526854933924505196.989910694944
Trimmed Mean ( 8 / 20 )103.7088888888890.517987775510197200.214935162784
Trimmed Mean ( 9 / 20 )103.6302325581400.508483238253681203.802652205497
Trimmed Mean ( 10 / 20 )103.5463414634150.497323293301931208.207302690225
Trimmed Mean ( 11 / 20 )103.4538461538460.483001833647623214.189344526012
Trimmed Mean ( 12 / 20 )103.3567567567570.466546647058995221.535740120081
Trimmed Mean ( 13 / 20 )103.2485714285710.442820817160219233.161060698767
Trimmed Mean ( 14 / 20 )103.1545454545450.423640671716943243.495377902404
Trimmed Mean ( 15 / 20 )103.0870967741940.414540604273033248.677923734333
Trimmed Mean ( 16 / 20 )103.0241379310340.409633236545936251.503366278926
Trimmed Mean ( 17 / 20 )102.9629629629630.40682034885627253.091968610793
Trimmed Mean ( 18 / 20 )102.9080.408326666612244252.023706543084
Trimmed Mean ( 19 / 20 )102.8521739130430.410093480388087250.801777720803
Trimmed Mean ( 20 / 20 )102.7952380952380.412049245235162249.473186236688
Median101.8
Midrange105.65
Midmean - Weighted Average at Xnp102.946666666667
Midmean - Weighted Average at X(n+1)p103.087096774194
Midmean - Empirical Distribution Function103.087096774194
Midmean - Empirical Distribution Function - Averaging103.087096774194
Midmean - Empirical Distribution Function - Interpolation103.087096774194
Midmean - Closest Observation103.00625
Midmean - True Basic - Statistics Graphics Toolkit103.087096774194
Midmean - MS Excel (old versions)103.087096774194
Number of observations61

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 104.180327868852 & 0.553043341971565 & 188.376425430702 \tabularnewline
Geometric Mean & 104.093578537841 &  &  \tabularnewline
Harmonic Mean & 104.008206291270 &  &  \tabularnewline
Quadratic Mean & 104.268365917701 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 104.172131147541 & 0.550534420674328 & 189.220014654024 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 104.175409836066 & 0.548861990764064 & 189.802558000135 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 104.180327868852 & 0.546418141255955 & 190.660448478873 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 104.180327868852 & 0.54411315357325 & 191.468129716565 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 104.188524590164 & 0.543023806503741 & 191.867323941066 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 104.178688524590 & 0.540916621121963 & 192.596574881548 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 104.178688524590 & 0.540916621121963 & 192.596574881548 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 104.152459016393 & 0.530895761008416 & 196.182502603825 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 104.137704918033 & 0.522866019127858 & 199.167092731968 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 104.137704918033 & 0.517402951140911 & 201.270025013196 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 104.101639344262 & 0.5041277258318 & 206.498539973172 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 104.101639344262 & 0.5041277258318 & 206.498539973172 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 103.909836065574 & 0.45945266152888 & 226.160048175153 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 103.634426229508 & 0.40129493429963 & 258.250023540364 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 103.536065573771 & 0.369322469215092 & 280.340553862894 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 103.457377049180 & 0.348419217192815 & 296.93361314203 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 103.345901639344 & 0.322393488748434 & 320.558278148060 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 103.286885245902 & 0.313158381076490 & 329.8231549507 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 103.224590163934 & 0.303582037036947 & 340.022061817089 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 103.191803278689 & 0.29860600612847 & 345.578458439621 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 104.130508474576 & 0.549098694244992 & 189.638965755974 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 104.085964912281 & 0.546694547759024 & 190.391444983206 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 104.036363636364 & 0.544129141660135 & 191.197926505001 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 103.981132075472 & 0.541332660546419 & 192.083610788445 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 103.921568627451 & 0.537914008183393 & 193.193646282624 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 103.855102040816 & 0.533121194186875 & 194.805802457765 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 103.785106382979 & 0.526854933924505 & 196.989910694944 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 103.708888888889 & 0.517987775510197 & 200.214935162784 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 103.630232558140 & 0.508483238253681 & 203.802652205497 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 103.546341463415 & 0.497323293301931 & 208.207302690225 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 103.453846153846 & 0.483001833647623 & 214.189344526012 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 103.356756756757 & 0.466546647058995 & 221.535740120081 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 103.248571428571 & 0.442820817160219 & 233.161060698767 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 103.154545454545 & 0.423640671716943 & 243.495377902404 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 103.087096774194 & 0.414540604273033 & 248.677923734333 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 103.024137931034 & 0.409633236545936 & 251.503366278926 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 102.962962962963 & 0.40682034885627 & 253.091968610793 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 102.908 & 0.408326666612244 & 252.023706543084 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 102.852173913043 & 0.410093480388087 & 250.801777720803 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 102.795238095238 & 0.412049245235162 & 249.473186236688 \tabularnewline
Median & 101.8 &  &  \tabularnewline
Midrange & 105.65 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 102.946666666667 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 103.087096774194 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 103.087096774194 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 103.087096774194 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 103.087096774194 &  &  \tabularnewline
Midmean - Closest Observation & 103.00625 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 103.087096774194 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 103.087096774194 &  &  \tabularnewline
Number of observations & 61 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=29555&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]104.180327868852[/C][C]0.553043341971565[/C][C]188.376425430702[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]104.093578537841[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]104.008206291270[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]104.268365917701[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]104.172131147541[/C][C]0.550534420674328[/C][C]189.220014654024[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]104.175409836066[/C][C]0.548861990764064[/C][C]189.802558000135[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]104.180327868852[/C][C]0.546418141255955[/C][C]190.660448478873[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]104.180327868852[/C][C]0.54411315357325[/C][C]191.468129716565[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]104.188524590164[/C][C]0.543023806503741[/C][C]191.867323941066[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]104.178688524590[/C][C]0.540916621121963[/C][C]192.596574881548[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]104.178688524590[/C][C]0.540916621121963[/C][C]192.596574881548[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]104.152459016393[/C][C]0.530895761008416[/C][C]196.182502603825[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]104.137704918033[/C][C]0.522866019127858[/C][C]199.167092731968[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]104.137704918033[/C][C]0.517402951140911[/C][C]201.270025013196[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]104.101639344262[/C][C]0.5041277258318[/C][C]206.498539973172[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]104.101639344262[/C][C]0.5041277258318[/C][C]206.498539973172[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]103.909836065574[/C][C]0.45945266152888[/C][C]226.160048175153[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]103.634426229508[/C][C]0.40129493429963[/C][C]258.250023540364[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]103.536065573771[/C][C]0.369322469215092[/C][C]280.340553862894[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]103.457377049180[/C][C]0.348419217192815[/C][C]296.93361314203[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]103.345901639344[/C][C]0.322393488748434[/C][C]320.558278148060[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]103.286885245902[/C][C]0.313158381076490[/C][C]329.8231549507[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]103.224590163934[/C][C]0.303582037036947[/C][C]340.022061817089[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]103.191803278689[/C][C]0.29860600612847[/C][C]345.578458439621[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]104.130508474576[/C][C]0.549098694244992[/C][C]189.638965755974[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]104.085964912281[/C][C]0.546694547759024[/C][C]190.391444983206[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]104.036363636364[/C][C]0.544129141660135[/C][C]191.197926505001[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]103.981132075472[/C][C]0.541332660546419[/C][C]192.083610788445[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]103.921568627451[/C][C]0.537914008183393[/C][C]193.193646282624[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]103.855102040816[/C][C]0.533121194186875[/C][C]194.805802457765[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]103.785106382979[/C][C]0.526854933924505[/C][C]196.989910694944[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]103.708888888889[/C][C]0.517987775510197[/C][C]200.214935162784[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]103.630232558140[/C][C]0.508483238253681[/C][C]203.802652205497[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]103.546341463415[/C][C]0.497323293301931[/C][C]208.207302690225[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]103.453846153846[/C][C]0.483001833647623[/C][C]214.189344526012[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]103.356756756757[/C][C]0.466546647058995[/C][C]221.535740120081[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]103.248571428571[/C][C]0.442820817160219[/C][C]233.161060698767[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]103.154545454545[/C][C]0.423640671716943[/C][C]243.495377902404[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]103.087096774194[/C][C]0.414540604273033[/C][C]248.677923734333[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]103.024137931034[/C][C]0.409633236545936[/C][C]251.503366278926[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]102.962962962963[/C][C]0.40682034885627[/C][C]253.091968610793[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]102.908[/C][C]0.408326666612244[/C][C]252.023706543084[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]102.852173913043[/C][C]0.410093480388087[/C][C]250.801777720803[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]102.795238095238[/C][C]0.412049245235162[/C][C]249.473186236688[/C][/ROW]
[ROW][C]Median[/C][C]101.8[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]105.65[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]102.946666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]103.087096774194[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]103.087096774194[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]103.087096774194[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]103.087096774194[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]103.00625[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]103.087096774194[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]103.087096774194[/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=29555&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=29555&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 Mean104.1803278688520.553043341971565188.376425430702
Geometric Mean104.093578537841
Harmonic Mean104.008206291270
Quadratic Mean104.268365917701
Winsorized Mean ( 1 / 20 )104.1721311475410.550534420674328189.220014654024
Winsorized Mean ( 2 / 20 )104.1754098360660.548861990764064189.802558000135
Winsorized Mean ( 3 / 20 )104.1803278688520.546418141255955190.660448478873
Winsorized Mean ( 4 / 20 )104.1803278688520.54411315357325191.468129716565
Winsorized Mean ( 5 / 20 )104.1885245901640.543023806503741191.867323941066
Winsorized Mean ( 6 / 20 )104.1786885245900.540916621121963192.596574881548
Winsorized Mean ( 7 / 20 )104.1786885245900.540916621121963192.596574881548
Winsorized Mean ( 8 / 20 )104.1524590163930.530895761008416196.182502603825
Winsorized Mean ( 9 / 20 )104.1377049180330.522866019127858199.167092731968
Winsorized Mean ( 10 / 20 )104.1377049180330.517402951140911201.270025013196
Winsorized Mean ( 11 / 20 )104.1016393442620.5041277258318206.498539973172
Winsorized Mean ( 12 / 20 )104.1016393442620.5041277258318206.498539973172
Winsorized Mean ( 13 / 20 )103.9098360655740.45945266152888226.160048175153
Winsorized Mean ( 14 / 20 )103.6344262295080.40129493429963258.250023540364
Winsorized Mean ( 15 / 20 )103.5360655737710.369322469215092280.340553862894
Winsorized Mean ( 16 / 20 )103.4573770491800.348419217192815296.93361314203
Winsorized Mean ( 17 / 20 )103.3459016393440.322393488748434320.558278148060
Winsorized Mean ( 18 / 20 )103.2868852459020.313158381076490329.8231549507
Winsorized Mean ( 19 / 20 )103.2245901639340.303582037036947340.022061817089
Winsorized Mean ( 20 / 20 )103.1918032786890.29860600612847345.578458439621
Trimmed Mean ( 1 / 20 )104.1305084745760.549098694244992189.638965755974
Trimmed Mean ( 2 / 20 )104.0859649122810.546694547759024190.391444983206
Trimmed Mean ( 3 / 20 )104.0363636363640.544129141660135191.197926505001
Trimmed Mean ( 4 / 20 )103.9811320754720.541332660546419192.083610788445
Trimmed Mean ( 5 / 20 )103.9215686274510.537914008183393193.193646282624
Trimmed Mean ( 6 / 20 )103.8551020408160.533121194186875194.805802457765
Trimmed Mean ( 7 / 20 )103.7851063829790.526854933924505196.989910694944
Trimmed Mean ( 8 / 20 )103.7088888888890.517987775510197200.214935162784
Trimmed Mean ( 9 / 20 )103.6302325581400.508483238253681203.802652205497
Trimmed Mean ( 10 / 20 )103.5463414634150.497323293301931208.207302690225
Trimmed Mean ( 11 / 20 )103.4538461538460.483001833647623214.189344526012
Trimmed Mean ( 12 / 20 )103.3567567567570.466546647058995221.535740120081
Trimmed Mean ( 13 / 20 )103.2485714285710.442820817160219233.161060698767
Trimmed Mean ( 14 / 20 )103.1545454545450.423640671716943243.495377902404
Trimmed Mean ( 15 / 20 )103.0870967741940.414540604273033248.677923734333
Trimmed Mean ( 16 / 20 )103.0241379310340.409633236545936251.503366278926
Trimmed Mean ( 17 / 20 )102.9629629629630.40682034885627253.091968610793
Trimmed Mean ( 18 / 20 )102.9080.408326666612244252.023706543084
Trimmed Mean ( 19 / 20 )102.8521739130430.410093480388087250.801777720803
Trimmed Mean ( 20 / 20 )102.7952380952380.412049245235162249.473186236688
Median101.8
Midrange105.65
Midmean - Weighted Average at Xnp102.946666666667
Midmean - Weighted Average at X(n+1)p103.087096774194
Midmean - Empirical Distribution Function103.087096774194
Midmean - Empirical Distribution Function - Averaging103.087096774194
Midmean - Empirical Distribution Function - Interpolation103.087096774194
Midmean - Closest Observation103.00625
Midmean - True Basic - Statistics Graphics Toolkit103.087096774194
Midmean - MS Excel (old versions)103.087096774194
Number of observations61



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')