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Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationThu, 18 Oct 2007 10:23:57 -0700
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2007/Oct/18/xvtof1emu5r4w5g1192728312.htm/, Retrieved Mon, 29 Apr 2024 00:30:49 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=990, Retrieved Mon, 29 Apr 2024 00:30:49 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsCentral tendency, eigen reeks, kim, wim, hoyi
Estimated Impact187
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [Workshop 2 Questi...] [2007-10-18 17:23:57] [181c187d2008ac66a37ecc12859b08c5] [Current]
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Dataseries X:
99
115,4
106,9
107,1
99,3
99,2
108,3
105,6
99,5
107,4
93,1
88,1
110,7
113,1
99,6
93,6
98,6
99,6
114,3
107,8
101,2
112,5
100,5
93,9
116,2
112
106,4
95,7
96
95,8
103
102,2
98,4
111,4
86,6
91,3
107,9
101,8
104,4
93,4
100,1
98,5
112,9
101,4
107,1
110,8
90,3
95,5
111,4
113
107,5
95,9
106,3
105,2
117,2
106,9
108,2
110
96,1
100,6




Summary of compuational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Herman Ole Andreas Wold' @ 193.190.124.10:1001

\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 & 3 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ 193.190.124.10:1001 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=990&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]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Herman Ole Andreas Wold' @ 193.190.124.10:1001[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=990&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=990&T=0

As an alternative you can also use a QR Code:  

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

Summary of compuational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Herman Ole Andreas Wold' @ 193.190.124.10:1001







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean103.1950.966364919785528106.786781977664
Geometric Mean102.925277549899
Harmonic Mean102.652957988974
Quadratic Mean103.461615265437
Winsorized Mean ( 1 / 20 )103.2033333333330.95540675712656108.020309217535
Winsorized Mean ( 2 / 20 )103.250.930896232998163110.914617913384
Winsorized Mean ( 3 / 20 )103.2450.907655528998768113.749100513814
Winsorized Mean ( 4 / 20 )103.2850.86633139429768119.221121016550
Winsorized Mean ( 5 / 20 )103.3016666666670.859803852505574120.145619684807
Winsorized Mean ( 6 / 20 )103.3116666666670.854017066960101120.971430974334
Winsorized Mean ( 7 / 20 )103.30.838538545718303123.190520611681
Winsorized Mean ( 8 / 20 )103.4466666666670.787632032395676131.338826268939
Winsorized Mean ( 9 / 20 )103.3866666666670.766253143205751134.924949520117
Winsorized Mean ( 10 / 20 )103.4033333333330.76342954516651135.445810275499
Winsorized Mean ( 11 / 20 )103.3116666666670.74114010381573139.395596237163
Winsorized Mean ( 12 / 20 )103.3116666666670.734339672889126140.686484035659
Winsorized Mean ( 13 / 20 )103.1816666666670.705300719878687146.294571604030
Winsorized Mean ( 14 / 20 )103.3216666666670.555837494372824185.884665415112
Winsorized Mean ( 15 / 20 )103.3216666666670.54831581721203188.434590838573
Winsorized Mean ( 16 / 20 )103.2683333333330.532415302760858193.961993199354
Winsorized Mean ( 17 / 20 )103.3533333333330.511641131882763202.003566353253
Winsorized Mean ( 18 / 20 )103.3233333333330.489900062832297210.906960770697
Winsorized Mean ( 19 / 20 )103.3233333333330.480832415375756214.884292384051
Winsorized Mean ( 20 / 20 )103.290.457169503359815225.933705640697
Trimmed Mean ( 1 / 20 )103.2396551724140.925902511449692111.501647199089
Trimmed Mean ( 2 / 20 )103.2785714285710.889504875722116.107931780297
Trimmed Mean ( 3 / 20 )103.2944444444440.860981257538601119.972930351290
Trimmed Mean ( 4 / 20 )103.3134615384620.836696210919875123.477864713738
Trimmed Mean ( 5 / 20 )103.3220.822258164931136125.656398934820
Trimmed Mean ( 6 / 20 )103.3270833333330.805663351544837128.25094145738
Trimmed Mean ( 7 / 20 )103.3304347826090.785772456431965131.501726659918
Trimmed Mean ( 8 / 20 )103.3363636363640.764252117596303135.212400799586
Trimmed Mean ( 9 / 20 )103.3166666666670.74998967601618137.757451829827
Trimmed Mean ( 10 / 20 )103.3050.736084147224264140.344008751660
Trimmed Mean ( 11 / 20 )103.2894736842110.717280995602624144.001408537852
Trimmed Mean ( 12 / 20 )103.2861111111110.697138741603199148.157181558416
Trimmed Mean ( 13 / 20 )103.2823529411760.670427944691898154.054367451287
Trimmed Mean ( 14 / 20 )103.2968750.640996646722018161.150414012691
Trimmed Mean ( 15 / 20 )103.2933333333330.641996407289932160.893942957355
Trimmed Mean ( 16 / 20 )103.2892857142860.641928709340874160.904605466769
Trimmed Mean ( 17 / 20 )103.2923076923080.642445402096206160.779900292351
Trimmed Mean ( 18 / 20 )103.2833333333330.64484203960245160.168424188051
Trimmed Mean ( 19 / 20 )103.2772727272730.649806225468194158.935492889223
Trimmed Mean ( 20 / 20 )103.270.653456397288981158.036558259189
Median102.6
Midrange101.9
Midmean - Weighted Average at Xnp103.135483870968
Midmean - Weighted Average at X(n+1)p103.293333333333
Midmean - Empirical Distribution Function103.135483870968
Midmean - Empirical Distribution Function - Averaging103.293333333333
Midmean - Empirical Distribution Function - Interpolation103.293333333333
Midmean - Closest Observation103.135483870968
Midmean - True Basic - Statistics Graphics Toolkit103.293333333333
Midmean - MS Excel (old versions)103.296875
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 103.195 & 0.966364919785528 & 106.786781977664 \tabularnewline
Geometric Mean & 102.925277549899 &  &  \tabularnewline
Harmonic Mean & 102.652957988974 &  &  \tabularnewline
Quadratic Mean & 103.461615265437 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 103.203333333333 & 0.95540675712656 & 108.020309217535 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 103.25 & 0.930896232998163 & 110.914617913384 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 103.245 & 0.907655528998768 & 113.749100513814 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 103.285 & 0.86633139429768 & 119.221121016550 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 103.301666666667 & 0.859803852505574 & 120.145619684807 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 103.311666666667 & 0.854017066960101 & 120.971430974334 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 103.3 & 0.838538545718303 & 123.190520611681 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 103.446666666667 & 0.787632032395676 & 131.338826268939 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 103.386666666667 & 0.766253143205751 & 134.924949520117 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 103.403333333333 & 0.76342954516651 & 135.445810275499 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 103.311666666667 & 0.74114010381573 & 139.395596237163 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 103.311666666667 & 0.734339672889126 & 140.686484035659 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 103.181666666667 & 0.705300719878687 & 146.294571604030 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 103.321666666667 & 0.555837494372824 & 185.884665415112 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 103.321666666667 & 0.54831581721203 & 188.434590838573 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 103.268333333333 & 0.532415302760858 & 193.961993199354 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 103.353333333333 & 0.511641131882763 & 202.003566353253 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 103.323333333333 & 0.489900062832297 & 210.906960770697 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 103.323333333333 & 0.480832415375756 & 214.884292384051 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 103.29 & 0.457169503359815 & 225.933705640697 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 103.239655172414 & 0.925902511449692 & 111.501647199089 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 103.278571428571 & 0.889504875722 & 116.107931780297 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 103.294444444444 & 0.860981257538601 & 119.972930351290 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 103.313461538462 & 0.836696210919875 & 123.477864713738 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 103.322 & 0.822258164931136 & 125.656398934820 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 103.327083333333 & 0.805663351544837 & 128.25094145738 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 103.330434782609 & 0.785772456431965 & 131.501726659918 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 103.336363636364 & 0.764252117596303 & 135.212400799586 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 103.316666666667 & 0.74998967601618 & 137.757451829827 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 103.305 & 0.736084147224264 & 140.344008751660 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 103.289473684211 & 0.717280995602624 & 144.001408537852 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 103.286111111111 & 0.697138741603199 & 148.157181558416 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 103.282352941176 & 0.670427944691898 & 154.054367451287 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 103.296875 & 0.640996646722018 & 161.150414012691 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 103.293333333333 & 0.641996407289932 & 160.893942957355 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 103.289285714286 & 0.641928709340874 & 160.904605466769 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 103.292307692308 & 0.642445402096206 & 160.779900292351 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 103.283333333333 & 0.64484203960245 & 160.168424188051 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 103.277272727273 & 0.649806225468194 & 158.935492889223 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 103.27 & 0.653456397288981 & 158.036558259189 \tabularnewline
Median & 102.6 &  &  \tabularnewline
Midrange & 101.9 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 103.135483870968 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 103.293333333333 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 103.135483870968 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 103.293333333333 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 103.293333333333 &  &  \tabularnewline
Midmean - Closest Observation & 103.135483870968 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 103.293333333333 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 103.296875 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=990&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]103.195[/C][C]0.966364919785528[/C][C]106.786781977664[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]102.925277549899[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]102.652957988974[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]103.461615265437[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]103.203333333333[/C][C]0.95540675712656[/C][C]108.020309217535[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]103.25[/C][C]0.930896232998163[/C][C]110.914617913384[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]103.245[/C][C]0.907655528998768[/C][C]113.749100513814[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]103.285[/C][C]0.86633139429768[/C][C]119.221121016550[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]103.301666666667[/C][C]0.859803852505574[/C][C]120.145619684807[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]103.311666666667[/C][C]0.854017066960101[/C][C]120.971430974334[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]103.3[/C][C]0.838538545718303[/C][C]123.190520611681[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]103.446666666667[/C][C]0.787632032395676[/C][C]131.338826268939[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]103.386666666667[/C][C]0.766253143205751[/C][C]134.924949520117[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]103.403333333333[/C][C]0.76342954516651[/C][C]135.445810275499[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]103.311666666667[/C][C]0.74114010381573[/C][C]139.395596237163[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]103.311666666667[/C][C]0.734339672889126[/C][C]140.686484035659[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]103.181666666667[/C][C]0.705300719878687[/C][C]146.294571604030[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]103.321666666667[/C][C]0.555837494372824[/C][C]185.884665415112[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]103.321666666667[/C][C]0.54831581721203[/C][C]188.434590838573[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]103.268333333333[/C][C]0.532415302760858[/C][C]193.961993199354[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]103.353333333333[/C][C]0.511641131882763[/C][C]202.003566353253[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]103.323333333333[/C][C]0.489900062832297[/C][C]210.906960770697[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]103.323333333333[/C][C]0.480832415375756[/C][C]214.884292384051[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]103.29[/C][C]0.457169503359815[/C][C]225.933705640697[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]103.239655172414[/C][C]0.925902511449692[/C][C]111.501647199089[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]103.278571428571[/C][C]0.889504875722[/C][C]116.107931780297[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]103.294444444444[/C][C]0.860981257538601[/C][C]119.972930351290[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]103.313461538462[/C][C]0.836696210919875[/C][C]123.477864713738[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]103.322[/C][C]0.822258164931136[/C][C]125.656398934820[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]103.327083333333[/C][C]0.805663351544837[/C][C]128.25094145738[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]103.330434782609[/C][C]0.785772456431965[/C][C]131.501726659918[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]103.336363636364[/C][C]0.764252117596303[/C][C]135.212400799586[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]103.316666666667[/C][C]0.74998967601618[/C][C]137.757451829827[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]103.305[/C][C]0.736084147224264[/C][C]140.344008751660[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]103.289473684211[/C][C]0.717280995602624[/C][C]144.001408537852[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]103.286111111111[/C][C]0.697138741603199[/C][C]148.157181558416[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]103.282352941176[/C][C]0.670427944691898[/C][C]154.054367451287[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]103.296875[/C][C]0.640996646722018[/C][C]161.150414012691[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]103.293333333333[/C][C]0.641996407289932[/C][C]160.893942957355[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]103.289285714286[/C][C]0.641928709340874[/C][C]160.904605466769[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]103.292307692308[/C][C]0.642445402096206[/C][C]160.779900292351[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]103.283333333333[/C][C]0.64484203960245[/C][C]160.168424188051[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]103.277272727273[/C][C]0.649806225468194[/C][C]158.935492889223[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]103.27[/C][C]0.653456397288981[/C][C]158.036558259189[/C][/ROW]
[ROW][C]Median[/C][C]102.6[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]101.9[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]103.135483870968[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]103.293333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]103.135483870968[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]103.293333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]103.293333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]103.135483870968[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]103.293333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]103.296875[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]60[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=990&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=990&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 Mean103.1950.966364919785528106.786781977664
Geometric Mean102.925277549899
Harmonic Mean102.652957988974
Quadratic Mean103.461615265437
Winsorized Mean ( 1 / 20 )103.2033333333330.95540675712656108.020309217535
Winsorized Mean ( 2 / 20 )103.250.930896232998163110.914617913384
Winsorized Mean ( 3 / 20 )103.2450.907655528998768113.749100513814
Winsorized Mean ( 4 / 20 )103.2850.86633139429768119.221121016550
Winsorized Mean ( 5 / 20 )103.3016666666670.859803852505574120.145619684807
Winsorized Mean ( 6 / 20 )103.3116666666670.854017066960101120.971430974334
Winsorized Mean ( 7 / 20 )103.30.838538545718303123.190520611681
Winsorized Mean ( 8 / 20 )103.4466666666670.787632032395676131.338826268939
Winsorized Mean ( 9 / 20 )103.3866666666670.766253143205751134.924949520117
Winsorized Mean ( 10 / 20 )103.4033333333330.76342954516651135.445810275499
Winsorized Mean ( 11 / 20 )103.3116666666670.74114010381573139.395596237163
Winsorized Mean ( 12 / 20 )103.3116666666670.734339672889126140.686484035659
Winsorized Mean ( 13 / 20 )103.1816666666670.705300719878687146.294571604030
Winsorized Mean ( 14 / 20 )103.3216666666670.555837494372824185.884665415112
Winsorized Mean ( 15 / 20 )103.3216666666670.54831581721203188.434590838573
Winsorized Mean ( 16 / 20 )103.2683333333330.532415302760858193.961993199354
Winsorized Mean ( 17 / 20 )103.3533333333330.511641131882763202.003566353253
Winsorized Mean ( 18 / 20 )103.3233333333330.489900062832297210.906960770697
Winsorized Mean ( 19 / 20 )103.3233333333330.480832415375756214.884292384051
Winsorized Mean ( 20 / 20 )103.290.457169503359815225.933705640697
Trimmed Mean ( 1 / 20 )103.2396551724140.925902511449692111.501647199089
Trimmed Mean ( 2 / 20 )103.2785714285710.889504875722116.107931780297
Trimmed Mean ( 3 / 20 )103.2944444444440.860981257538601119.972930351290
Trimmed Mean ( 4 / 20 )103.3134615384620.836696210919875123.477864713738
Trimmed Mean ( 5 / 20 )103.3220.822258164931136125.656398934820
Trimmed Mean ( 6 / 20 )103.3270833333330.805663351544837128.25094145738
Trimmed Mean ( 7 / 20 )103.3304347826090.785772456431965131.501726659918
Trimmed Mean ( 8 / 20 )103.3363636363640.764252117596303135.212400799586
Trimmed Mean ( 9 / 20 )103.3166666666670.74998967601618137.757451829827
Trimmed Mean ( 10 / 20 )103.3050.736084147224264140.344008751660
Trimmed Mean ( 11 / 20 )103.2894736842110.717280995602624144.001408537852
Trimmed Mean ( 12 / 20 )103.2861111111110.697138741603199148.157181558416
Trimmed Mean ( 13 / 20 )103.2823529411760.670427944691898154.054367451287
Trimmed Mean ( 14 / 20 )103.2968750.640996646722018161.150414012691
Trimmed Mean ( 15 / 20 )103.2933333333330.641996407289932160.893942957355
Trimmed Mean ( 16 / 20 )103.2892857142860.641928709340874160.904605466769
Trimmed Mean ( 17 / 20 )103.2923076923080.642445402096206160.779900292351
Trimmed Mean ( 18 / 20 )103.2833333333330.64484203960245160.168424188051
Trimmed Mean ( 19 / 20 )103.2772727272730.649806225468194158.935492889223
Trimmed Mean ( 20 / 20 )103.270.653456397288981158.036558259189
Median102.6
Midrange101.9
Midmean - Weighted Average at Xnp103.135483870968
Midmean - Weighted Average at X(n+1)p103.293333333333
Midmean - Empirical Distribution Function103.135483870968
Midmean - Empirical Distribution Function - Averaging103.293333333333
Midmean - Empirical Distribution Function - Interpolation103.293333333333
Midmean - Closest Observation103.135483870968
Midmean - True Basic - Statistics Graphics Toolkit103.293333333333
Midmean - MS Excel (old versions)103.296875
Number of observations60



Parameters (Session):
Parameters (R input):
R code (references can be found in the software module):
geomean <- function(x) {
return(exp(mean(log(x))))
}
harmean <- function(x) {
return(1/mean(1/x))
}
quamean <- function(x) {
return(sqrt(mean(x*x)))
}
winmean <- function(x) {
x <-sort(x[!is.na(x)])
n<-length(x)
denom <- 3
nodenom <- n/denom
if (nodenom>40) denom <- n/40
sqrtn = sqrt(n)
roundnodenom = floor(nodenom)
win <- array(NA,dim=c(roundnodenom,2))
for (j in 1:roundnodenom) {
win[j,1] <- (j*x[j+1]+sum(x[(j+1):(n-j)])+j*x[n-j])/n
win[j,2] <- sd(c(rep(x[j+1],j),x[(j+1):(n-j)],rep(x[n-j],j)))/sqrtn
}
return(win)
}
trimean <- function(x) {
x <-sort(x[!is.na(x)])
n<-length(x)
denom <- 3
nodenom <- n/denom
if (nodenom>40) denom <- n/40
sqrtn = sqrt(n)
roundnodenom = floor(nodenom)
tri <- array(NA,dim=c(roundnodenom,2))
for (j in 1:roundnodenom) {
tri[j,1] <- mean(x,trim=j/n)
tri[j,2] <- sd(x[(j+1):(n-j)]) / sqrt(n-j*2)
}
return(tri)
}
midrange <- function(x) {
return((max(x)+min(x))/2)
}
q1 <- function(data,n,p,i,f) {
np <- n*p;
i <<- floor(np)
f <<- np - i
qvalue <- (1-f)*data[i] + f*data[i+1]
}
q2 <- function(data,n,p,i,f) {
np <- (n+1)*p
i <<- floor(np)
f <<- np - i
qvalue <- (1-f)*data[i] + f*data[i+1]
}
q3 <- function(data,n,p,i,f) {
np <- n*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i]
} else {
qvalue <- data[i+1]
}
}
q4 <- function(data,n,p,i,f) {
np <- n*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- (data[i]+data[i+1])/2
} else {
qvalue <- data[i+1]
}
}
q5 <- function(data,n,p,i,f) {
np <- (n-1)*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i+1]
} else {
qvalue <- data[i+1] + f*(data[i+2]-data[i+1])
}
}
q6 <- function(data,n,p,i,f) {
np <- n*p+0.5
i <<- floor(np)
f <<- np - i
qvalue <- data[i]
}
q7 <- function(data,n,p,i,f) {
np <- (n+1)*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i]
} else {
qvalue <- f*data[i] + (1-f)*data[i+1]
}
}
q8 <- function(data,n,p,i,f) {
np <- (n+1)*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i]
} else {
if (f == 0.5) {
qvalue <- (data[i]+data[i+1])/2
} else {
if (f < 0.5) {
qvalue <- data[i]
} else {
qvalue <- data[i+1]
}
}
}
}
midmean <- function(x,def) {
x <-sort(x[!is.na(x)])
n<-length(x)
if (def==1) {
qvalue1 <- q1(x,n,0.25,i,f)
qvalue3 <- q1(x,n,0.75,i,f)
}
if (def==2) {
qvalue1 <- q2(x,n,0.25,i,f)
qvalue3 <- q2(x,n,0.75,i,f)
}
if (def==3) {
qvalue1 <- q3(x,n,0.25,i,f)
qvalue3 <- q3(x,n,0.75,i,f)
}
if (def==4) {
qvalue1 <- q4(x,n,0.25,i,f)
qvalue3 <- q4(x,n,0.75,i,f)
}
if (def==5) {
qvalue1 <- q5(x,n,0.25,i,f)
qvalue3 <- q5(x,n,0.75,i,f)
}
if (def==6) {
qvalue1 <- q6(x,n,0.25,i,f)
qvalue3 <- q6(x,n,0.75,i,f)
}
if (def==7) {
qvalue1 <- q7(x,n,0.25,i,f)
qvalue3 <- q7(x,n,0.75,i,f)
}
if (def==8) {
qvalue1 <- q8(x,n,0.25,i,f)
qvalue3 <- q8(x,n,0.75,i,f)
}
midm <- 0
myn <- 0
roundno4 <- round(n/4)
round3no4 <- round(3*n/4)
for (i in 1:n) {
if ((x[i]>=qvalue1) & (x[i]<=qvalue3)){
midm = midm + x[i]
myn = myn + 1
}
}
midm = midm / myn
return(midm)
}
(arm <- mean(x))
sqrtn <- sqrt(length(x))
(armse <- sd(x) / sqrtn)
(armose <- arm / armse)
(geo <- geomean(x))
(har <- harmean(x))
(qua <- quamean(x))
(win <- winmean(x))
(tri <- trimean(x))
(midr <- midrange(x))
midm <- array(NA,dim=8)
for (j in 1:8) midm[j] <- midmean(x,j)
midm
bitmap(file='test1.png')
lb <- win[,1] - 2*win[,2]
ub <- win[,1] + 2*win[,2]
if ((ylimmin == '') | (ylimmax == '')) plot(win[,1],type='b',main=main, xlab='j', pch=19, ylab='Winsorized Mean(j/n)', ylim=c(min(lb),max(ub))) else plot(win[,1],type='l',main=main, xlab='j', pch=19, ylab='Winsorized Mean(j/n)', ylim=c(ylimmin,ylimmax))
lines(ub,lty=3)
lines(lb,lty=3)
grid()
dev.off()
bitmap(file='test2.png')
lb <- tri[,1] - 2*tri[,2]
ub <- tri[,1] + 2*tri[,2]
if ((ylimmin == '') | (ylimmax == '')) plot(tri[,1],type='b',main=main, xlab='j', pch=19, ylab='Trimmed Mean(j/n)', ylim=c(min(lb),max(ub))) else plot(tri[,1],type='l',main=main, xlab='j', pch=19, ylab='Trimmed Mean(j/n)', ylim=c(ylimmin,ylimmax))
lines(ub,lty=3)
lines(lb,lty=3)
grid()
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Central Tendency - Ungrouped Data',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Measure',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.element(a,'S.E.',header=TRUE)
a<-table.element(a,'Value/S.E.',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('arithmetic_mean.htm', 'Arithmetic Mean', 'click to view the definition of the Arithmetic Mean'),header=TRUE)
a<-table.element(a,arm)
a<-table.element(a,hyperlink('arithmetic_mean_standard_error.htm', armse, 'click to view the definition of the Standard Error of the Arithmetic Mean'))
a<-table.element(a,armose)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('geometric_mean.htm', 'Geometric Mean', 'click to view the definition of the Geometric Mean'),header=TRUE)
a<-table.element(a,geo)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('harmonic_mean.htm', 'Harmonic Mean', 'click to view the definition of the Harmonic Mean'),header=TRUE)
a<-table.element(a,har)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('quadratic_mean.htm', 'Quadratic Mean', 'click to view the definition of the Quadratic Mean'),header=TRUE)
a<-table.element(a,qua)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
for (j in 1:length(win[,1])) {
a<-table.row.start(a)
mylabel <- paste('Winsorized Mean (',j)
mylabel <- paste(mylabel,'/')
mylabel <- paste(mylabel,length(win[,1]))
mylabel <- paste(mylabel,')')
a<-table.element(a,hyperlink('winsorized_mean.htm', mylabel, 'click to view the definition of the Winsorized Mean'),header=TRUE)
a<-table.element(a,win[j,1])
a<-table.element(a,win[j,2])
a<-table.element(a,win[j,1]/win[j,2])
a<-table.row.end(a)
}
for (j in 1:length(tri[,1])) {
a<-table.row.start(a)
mylabel <- paste('Trimmed Mean (',j)
mylabel <- paste(mylabel,'/')
mylabel <- paste(mylabel,length(tri[,1]))
mylabel <- paste(mylabel,')')
a<-table.element(a,hyperlink('arithmetic_mean.htm', mylabel, 'click to view the definition of the Trimmed Mean'),header=TRUE)
a<-table.element(a,tri[j,1])
a<-table.element(a,tri[j,2])
a<-table.element(a,tri[j,1]/tri[j,2])
a<-table.row.end(a)
}
a<-table.row.start(a)
a<-table.element(a,hyperlink('median_1.htm', 'Median', 'click to view the definition of the Median'),header=TRUE)
a<-table.element(a,median(x))
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('midrange.htm', 'Midrange', 'click to view the definition of the Midrange'),header=TRUE)
a<-table.element(a,midr)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_1.htm','Weighted Average at Xnp',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[1])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_2.htm','Weighted Average at X(n+1)p',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[2])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_3.htm','Empirical Distribution Function',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[3])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_4.htm','Empirical Distribution Function - Averaging',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[4])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_5.htm','Empirical Distribution Function - Interpolation',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[5])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_6.htm','Closest Observation',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[6])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_7.htm','True Basic - Statistics Graphics Toolkit',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[7])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_8.htm','MS Excel (old versions)',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[8])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Number of observations',header=TRUE)
a<-table.element(a,length(x))
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')