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Author's title

Centrummaten eigen cijferreeks gemiddelde prijzen sieraden, klokken en horl...

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationSun, 04 Mar 2012 05:20:24 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2012/Mar/04/t1330857437o1rjb8zpeqv5pa6.htm/, Retrieved Sat, 04 May 2024 01:36:16 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=163447, Retrieved Sat, 04 May 2024 01:36:16 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDG2011W52a
Estimated Impact154
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [Centrummaten eige...] [2012-03-04 10:20:24] [e5023936a4a44f1411ffe7f6ed888868] [Current]
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Dataseries X:
128,27
128,38
128,47
128,52
128,71
128,92
128,92
128,82
128,97
129,04
128,95
129,39
129,39
129,48
130,16
129,89
129,85
129,9
129,9
129,57
129,54
129,57
128,97
129,01
129,01
128,72
128,32
128,39
128,33
128,44
128,44
128,6
128,3
128,56
128,01
128,01
128,01
128,26
128,38
128,36
128,48
128,46
128,46
129,56
129,66
129,47
129,41
129,48
129,48
130,17
129,77
129,87
129,97
130,05
130,05
129,89
130,33
130,6
131,46
131,73




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Herman Ole Andreas Wold' @ wold.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 2 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=163447&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=163447&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=163447&T=0

As an alternative you can also use a QR Code:  

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

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Herman Ole Andreas Wold' @ wold.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean129.1846666666670.1056741785634781222.48091655679
Geometric Mean129.182124822572
Harmonic Mean129.179591134769
Quadratic Mean129.187216692158
Winsorized Mean ( 1 / 20 )129.1801666666670.1039182891921591243.09366205784
Winsorized Mean ( 2 / 20 )129.15150.09480244847728421362.32240911949
Winsorized Mean ( 3 / 20 )129.15050.08919458351723821447.96348508135
Winsorized Mean ( 4 / 20 )129.14050.08681248868734451487.57974748426
Winsorized Mean ( 5 / 20 )129.1421666666670.08622598467483551497.71750538624
Winsorized Mean ( 6 / 20 )129.1331666666670.08377414203573211541.44421570546
Winsorized Mean ( 7 / 20 )129.1343333333330.08358302704823591544.98273027142
Winsorized Mean ( 8 / 20 )129.1276666666670.08100441735414841594.08179065254
Winsorized Mean ( 9 / 20 )129.1201666666670.07871693249481731640.30993808312
Winsorized Mean ( 10 / 20 )129.1201666666670.07871693249481731640.30993808312
Winsorized Mean ( 11 / 20 )129.1201666666670.07811858711909721652.87380927428
Winsorized Mean ( 12 / 20 )129.1301666666670.07656225695606871686.60344927869
Winsorized Mean ( 13 / 20 )129.1258333333330.07583743081995211702.66624194977
Winsorized Mean ( 14 / 20 )129.1258333333330.07435230370279921736.67562271473
Winsorized Mean ( 15 / 20 )129.1058333333330.07111711184368231815.39758837665
Winsorized Mean ( 16 / 20 )129.0791666666670.06619620368493591949.94817650005
Winsorized Mean ( 17 / 20 )129.05650.06206467603475782079.38731409353
Winsorized Mean ( 18 / 20 )129.06850.06019310967193252144.24044053307
Winsorized Mean ( 19 / 20 )129.0780.05780534254823372232.97699329946
Winsorized Mean ( 20 / 20 )129.0846666666670.05485392346059392353.24400741177
Trimmed Mean ( 1 / 20 )129.1610344827590.09782934189919231320.26886796245
Trimmed Mean ( 2 / 20 )129.1405357142860.09010578906797351433.21019714799
Trimmed Mean ( 3 / 20 )129.1344444444440.08686747686650911486.56838097057
Trimmed Mean ( 4 / 20 )129.1282692307690.08553033965233731509.73642517554
Trimmed Mean ( 5 / 20 )129.12460.08470366592071531524.42752738546
Trimmed Mean ( 6 / 20 )129.1202083333330.08375363312926931541.66695233439
Trimmed Mean ( 7 / 20 )129.1173913043480.08317343197054741552.38744206287
Trimmed Mean ( 8 / 20 )129.1140909090910.08234686484801881567.92964914192
Trimmed Mean ( 9 / 20 )129.1116666666670.0818208267892531577.98046943746
Trimmed Mean ( 10 / 20 )129.110250.08153690960666281583.4577324899
Trimmed Mean ( 11 / 20 )129.1086842105260.08095374849765991594.84503937774
Trimmed Mean ( 12 / 20 )129.1069444444440.08011481784789041611.52390921705
Trimmed Mean ( 13 / 20 )129.1035294117650.0791486364903291631.15291856657
Trimmed Mean ( 14 / 20 )129.10031250.07777589338435021659.90137666457
Trimmed Mean ( 15 / 20 )129.0966666666670.07602379139609851698.10876695229
Trimmed Mean ( 16 / 20 )129.0953571428570.07426443910849741738.31996434059
Trimmed Mean ( 17 / 20 )129.0976923076920.07295374233519481769.58286409129
Trimmed Mean ( 18 / 20 )129.103750.07190425523075651795.49526777905
Trimmed Mean ( 19 / 20 )129.1090909090910.07048351589826171831.76292021884
Trimmed Mean ( 20 / 20 )129.1140.06863097352009311881.27886547026
Median129.01
Midrange129.87
Midmean - Weighted Average at Xnp129.076129032258
Midmean - Weighted Average at X(n+1)p129.076129032258
Midmean - Empirical Distribution Function129.076129032258
Midmean - Empirical Distribution Function - Averaging129.076129032258
Midmean - Empirical Distribution Function - Interpolation129.076129032258
Midmean - Closest Observation129.076129032258
Midmean - True Basic - Statistics Graphics Toolkit129.076129032258
Midmean - MS Excel (old versions)129.1003125
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 129.184666666667 & 0.105674178563478 & 1222.48091655679 \tabularnewline
Geometric Mean & 129.182124822572 &  &  \tabularnewline
Harmonic Mean & 129.179591134769 &  &  \tabularnewline
Quadratic Mean & 129.187216692158 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 129.180166666667 & 0.103918289192159 & 1243.09366205784 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 129.1515 & 0.0948024484772842 & 1362.32240911949 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 129.1505 & 0.0891945835172382 & 1447.96348508135 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 129.1405 & 0.0868124886873445 & 1487.57974748426 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 129.142166666667 & 0.0862259846748355 & 1497.71750538624 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 129.133166666667 & 0.0837741420357321 & 1541.44421570546 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 129.134333333333 & 0.0835830270482359 & 1544.98273027142 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 129.127666666667 & 0.0810044173541484 & 1594.08179065254 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 129.120166666667 & 0.0787169324948173 & 1640.30993808312 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 129.120166666667 & 0.0787169324948173 & 1640.30993808312 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 129.120166666667 & 0.0781185871190972 & 1652.87380927428 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 129.130166666667 & 0.0765622569560687 & 1686.60344927869 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 129.125833333333 & 0.0758374308199521 & 1702.66624194977 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 129.125833333333 & 0.0743523037027992 & 1736.67562271473 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 129.105833333333 & 0.0711171118436823 & 1815.39758837665 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 129.079166666667 & 0.0661962036849359 & 1949.94817650005 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 129.0565 & 0.0620646760347578 & 2079.38731409353 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 129.0685 & 0.0601931096719325 & 2144.24044053307 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 129.078 & 0.0578053425482337 & 2232.97699329946 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 129.084666666667 & 0.0548539234605939 & 2353.24400741177 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 129.161034482759 & 0.0978293418991923 & 1320.26886796245 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 129.140535714286 & 0.0901057890679735 & 1433.21019714799 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 129.134444444444 & 0.0868674768665091 & 1486.56838097057 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 129.128269230769 & 0.0855303396523373 & 1509.73642517554 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 129.1246 & 0.0847036659207153 & 1524.42752738546 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 129.120208333333 & 0.0837536331292693 & 1541.66695233439 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 129.117391304348 & 0.0831734319705474 & 1552.38744206287 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 129.114090909091 & 0.0823468648480188 & 1567.92964914192 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 129.111666666667 & 0.081820826789253 & 1577.98046943746 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 129.11025 & 0.0815369096066628 & 1583.4577324899 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 129.108684210526 & 0.0809537484976599 & 1594.84503937774 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 129.106944444444 & 0.0801148178478904 & 1611.52390921705 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 129.103529411765 & 0.079148636490329 & 1631.15291856657 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 129.1003125 & 0.0777758933843502 & 1659.90137666457 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 129.096666666667 & 0.0760237913960985 & 1698.10876695229 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 129.095357142857 & 0.0742644391084974 & 1738.31996434059 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 129.097692307692 & 0.0729537423351948 & 1769.58286409129 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 129.10375 & 0.0719042552307565 & 1795.49526777905 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 129.109090909091 & 0.0704835158982617 & 1831.76292021884 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 129.114 & 0.0686309735200931 & 1881.27886547026 \tabularnewline
Median & 129.01 &  &  \tabularnewline
Midrange & 129.87 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 129.076129032258 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 129.076129032258 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 129.076129032258 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 129.076129032258 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 129.076129032258 &  &  \tabularnewline
Midmean - Closest Observation & 129.076129032258 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 129.076129032258 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 129.1003125 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=163447&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]129.184666666667[/C][C]0.105674178563478[/C][C]1222.48091655679[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]129.182124822572[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]129.179591134769[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]129.187216692158[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]129.180166666667[/C][C]0.103918289192159[/C][C]1243.09366205784[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]129.1515[/C][C]0.0948024484772842[/C][C]1362.32240911949[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]129.1505[/C][C]0.0891945835172382[/C][C]1447.96348508135[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]129.1405[/C][C]0.0868124886873445[/C][C]1487.57974748426[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]129.142166666667[/C][C]0.0862259846748355[/C][C]1497.71750538624[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]129.133166666667[/C][C]0.0837741420357321[/C][C]1541.44421570546[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]129.134333333333[/C][C]0.0835830270482359[/C][C]1544.98273027142[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]129.127666666667[/C][C]0.0810044173541484[/C][C]1594.08179065254[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]129.120166666667[/C][C]0.0787169324948173[/C][C]1640.30993808312[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]129.120166666667[/C][C]0.0787169324948173[/C][C]1640.30993808312[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]129.120166666667[/C][C]0.0781185871190972[/C][C]1652.87380927428[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]129.130166666667[/C][C]0.0765622569560687[/C][C]1686.60344927869[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]129.125833333333[/C][C]0.0758374308199521[/C][C]1702.66624194977[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]129.125833333333[/C][C]0.0743523037027992[/C][C]1736.67562271473[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]129.105833333333[/C][C]0.0711171118436823[/C][C]1815.39758837665[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]129.079166666667[/C][C]0.0661962036849359[/C][C]1949.94817650005[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]129.0565[/C][C]0.0620646760347578[/C][C]2079.38731409353[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]129.0685[/C][C]0.0601931096719325[/C][C]2144.24044053307[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]129.078[/C][C]0.0578053425482337[/C][C]2232.97699329946[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]129.084666666667[/C][C]0.0548539234605939[/C][C]2353.24400741177[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]129.161034482759[/C][C]0.0978293418991923[/C][C]1320.26886796245[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]129.140535714286[/C][C]0.0901057890679735[/C][C]1433.21019714799[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]129.134444444444[/C][C]0.0868674768665091[/C][C]1486.56838097057[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]129.128269230769[/C][C]0.0855303396523373[/C][C]1509.73642517554[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]129.1246[/C][C]0.0847036659207153[/C][C]1524.42752738546[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]129.120208333333[/C][C]0.0837536331292693[/C][C]1541.66695233439[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]129.117391304348[/C][C]0.0831734319705474[/C][C]1552.38744206287[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]129.114090909091[/C][C]0.0823468648480188[/C][C]1567.92964914192[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]129.111666666667[/C][C]0.081820826789253[/C][C]1577.98046943746[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]129.11025[/C][C]0.0815369096066628[/C][C]1583.4577324899[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]129.108684210526[/C][C]0.0809537484976599[/C][C]1594.84503937774[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]129.106944444444[/C][C]0.0801148178478904[/C][C]1611.52390921705[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]129.103529411765[/C][C]0.079148636490329[/C][C]1631.15291856657[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]129.1003125[/C][C]0.0777758933843502[/C][C]1659.90137666457[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]129.096666666667[/C][C]0.0760237913960985[/C][C]1698.10876695229[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]129.095357142857[/C][C]0.0742644391084974[/C][C]1738.31996434059[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]129.097692307692[/C][C]0.0729537423351948[/C][C]1769.58286409129[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]129.10375[/C][C]0.0719042552307565[/C][C]1795.49526777905[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]129.109090909091[/C][C]0.0704835158982617[/C][C]1831.76292021884[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]129.114[/C][C]0.0686309735200931[/C][C]1881.27886547026[/C][/ROW]
[ROW][C]Median[/C][C]129.01[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]129.87[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]129.076129032258[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]129.076129032258[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]129.076129032258[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]129.076129032258[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]129.076129032258[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]129.076129032258[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]129.076129032258[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]129.1003125[/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=163447&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=163447&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 Mean129.1846666666670.1056741785634781222.48091655679
Geometric Mean129.182124822572
Harmonic Mean129.179591134769
Quadratic Mean129.187216692158
Winsorized Mean ( 1 / 20 )129.1801666666670.1039182891921591243.09366205784
Winsorized Mean ( 2 / 20 )129.15150.09480244847728421362.32240911949
Winsorized Mean ( 3 / 20 )129.15050.08919458351723821447.96348508135
Winsorized Mean ( 4 / 20 )129.14050.08681248868734451487.57974748426
Winsorized Mean ( 5 / 20 )129.1421666666670.08622598467483551497.71750538624
Winsorized Mean ( 6 / 20 )129.1331666666670.08377414203573211541.44421570546
Winsorized Mean ( 7 / 20 )129.1343333333330.08358302704823591544.98273027142
Winsorized Mean ( 8 / 20 )129.1276666666670.08100441735414841594.08179065254
Winsorized Mean ( 9 / 20 )129.1201666666670.07871693249481731640.30993808312
Winsorized Mean ( 10 / 20 )129.1201666666670.07871693249481731640.30993808312
Winsorized Mean ( 11 / 20 )129.1201666666670.07811858711909721652.87380927428
Winsorized Mean ( 12 / 20 )129.1301666666670.07656225695606871686.60344927869
Winsorized Mean ( 13 / 20 )129.1258333333330.07583743081995211702.66624194977
Winsorized Mean ( 14 / 20 )129.1258333333330.07435230370279921736.67562271473
Winsorized Mean ( 15 / 20 )129.1058333333330.07111711184368231815.39758837665
Winsorized Mean ( 16 / 20 )129.0791666666670.06619620368493591949.94817650005
Winsorized Mean ( 17 / 20 )129.05650.06206467603475782079.38731409353
Winsorized Mean ( 18 / 20 )129.06850.06019310967193252144.24044053307
Winsorized Mean ( 19 / 20 )129.0780.05780534254823372232.97699329946
Winsorized Mean ( 20 / 20 )129.0846666666670.05485392346059392353.24400741177
Trimmed Mean ( 1 / 20 )129.1610344827590.09782934189919231320.26886796245
Trimmed Mean ( 2 / 20 )129.1405357142860.09010578906797351433.21019714799
Trimmed Mean ( 3 / 20 )129.1344444444440.08686747686650911486.56838097057
Trimmed Mean ( 4 / 20 )129.1282692307690.08553033965233731509.73642517554
Trimmed Mean ( 5 / 20 )129.12460.08470366592071531524.42752738546
Trimmed Mean ( 6 / 20 )129.1202083333330.08375363312926931541.66695233439
Trimmed Mean ( 7 / 20 )129.1173913043480.08317343197054741552.38744206287
Trimmed Mean ( 8 / 20 )129.1140909090910.08234686484801881567.92964914192
Trimmed Mean ( 9 / 20 )129.1116666666670.0818208267892531577.98046943746
Trimmed Mean ( 10 / 20 )129.110250.08153690960666281583.4577324899
Trimmed Mean ( 11 / 20 )129.1086842105260.08095374849765991594.84503937774
Trimmed Mean ( 12 / 20 )129.1069444444440.08011481784789041611.52390921705
Trimmed Mean ( 13 / 20 )129.1035294117650.0791486364903291631.15291856657
Trimmed Mean ( 14 / 20 )129.10031250.07777589338435021659.90137666457
Trimmed Mean ( 15 / 20 )129.0966666666670.07602379139609851698.10876695229
Trimmed Mean ( 16 / 20 )129.0953571428570.07426443910849741738.31996434059
Trimmed Mean ( 17 / 20 )129.0976923076920.07295374233519481769.58286409129
Trimmed Mean ( 18 / 20 )129.103750.07190425523075651795.49526777905
Trimmed Mean ( 19 / 20 )129.1090909090910.07048351589826171831.76292021884
Trimmed Mean ( 20 / 20 )129.1140.06863097352009311881.27886547026
Median129.01
Midrange129.87
Midmean - Weighted Average at Xnp129.076129032258
Midmean - Weighted Average at X(n+1)p129.076129032258
Midmean - Empirical Distribution Function129.076129032258
Midmean - Empirical Distribution Function - Averaging129.076129032258
Midmean - Empirical Distribution Function - Interpolation129.076129032258
Midmean - Closest Observation129.076129032258
Midmean - True Basic - Statistics Graphics Toolkit129.076129032258
Midmean - MS Excel (old versions)129.1003125
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')