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Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationMon, 22 Oct 2007 02:32:49 -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/22/urpckll2hbj7gvc1193045629.htm/, Retrieved Mon, 06 May 2024 03:09:44 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=1613, Retrieved Mon, 06 May 2024 03:09:44 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsWorkshop 2, Vraag 8, Wim
Estimated Impact222
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [Workshop 2 - Vraag 8] [2007-10-22 09:32:49] [014bfc073eb4f6c1ae65a07cc44c50c0] [Current]
- RM D    [Central Tendency] [Central tendency ...] [2010-12-14 15:57:18] [717f3d787904f94c39256c5c1fc72d4c]
-    D      [Central Tendency] [Central tendency ...] [2010-12-14 16:16:32] [717f3d787904f94c39256c5c1fc72d4c]
- RMP       [Histogram] [Histogram eur/usd] [2010-12-14 16:34:27] [717f3d787904f94c39256c5c1fc72d4c]
- RMPD      [Histogram] [Histogram eur/gbp] [2010-12-14 16:37:40] [717f3d787904f94c39256c5c1fc72d4c]
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Dataseries X:
99,0
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
112,0
106,4
95,7
96,0
95,8
103,0
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
113,0
107,5
95,9
106,3
105,2
117,2
106,9
108,2
110,0
96,1
100,6




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

\begin{tabular}{lllllllll}
\hline
Summary of compuational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=1613&T=0

[TABLE]
[ROW][C]Summary of compuational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=1613&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=1613&T=0

As an alternative you can also use a QR Code:  

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

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







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic 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=1613&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=1613&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=1613&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')