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of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationMon, 22 Oct 2007 03:39:45 -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/22/95tehtjmtvr2a1l1193049361.htm/, Retrieved Sun, 05 May 2024 22:51:50 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=1393, Retrieved Sun, 05 May 2024 22:51:50 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsQ9
Estimated Impact194
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [Prediction of tim...] [2007-10-22 10:39:45] [1329bc68d11d0852ec1dfd239c736a2c] [Current]
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Dataseries X:
12710,3
12120,8
12469,5
12054,6
12112,9
9617,2
12645,8
13581,3
12162,3
10969,7
11880,0
11887,6
12926,9
12300,0
12092,8
12380,8
12196,9
9455,0
13168,0
13427,9
11980,5
11884,8
11691,7
12233,8
14341,4
13130,7
12421,1
14285,8
12864,6
11160,2
14316,2
14388,7
14013,9
13419,0
12769,6
13315,5
15332,9
14243,0
13824,4
14962,9
13202,9
12199,0
15508,9
14199,8
15169,6
14058,0
13786,2
14147,9
16541,7
13587,5
15582,4
15802,8
14130,5
12923,2
15612,2
16033,7
16036,6
14037,8
15330,6
15038,3
17401,8




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=1393&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=1393&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=1393&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 Mean13427.4163934426205.4670809550265.3506942865563
Geometric Mean13331.8651719287
Harmonic Mean13234.5656090411
Quadratic Mean13521.4094784628
Winsorized Mean ( 1 / 20 )13415.9754098361200.50885389409166.9096408925781
Winsorized Mean ( 2 / 20 )13443.7590163934184.36199077197272.920448299028
Winsorized Mean ( 3 / 20 )13452.9852459016182.29842247032773.7964984205577
Winsorized Mean ( 4 / 20 )13472.6967213115172.12529136876678.2726153383653
Winsorized Mean ( 5 / 20 )13472.5081967213166.11880558780481.1016437846966
Winsorized Mean ( 6 / 20 )13470.0491803279165.41683568486781.4309445864957
Winsorized Mean ( 7 / 20 )13461.9360655738163.58825993042582.2915780832877
Winsorized Mean ( 8 / 20 )13451.0377049180156.94396797221385.7059871667036
Winsorized Mean ( 9 / 20 )13461.6311475410155.19621316962386.739430509351
Winsorized Mean ( 10 / 20 )13441.5149.05008347033490.1810967631915
Winsorized Mean ( 11 / 20 )13421.4475409836143.99800957956893.2057851366856
Winsorized Mean ( 12 / 20 )13408.1688524590141.01110314654895.0859085083842
Winsorized Mean ( 13 / 20 )13294.6426229508118.849607714432111.861055990145
Winsorized Mean ( 14 / 20 )13291.7278688525115.942231708782114.640952420495
Winsorized Mean ( 15 / 20 )13286.0475409836114.930505531278115.600705657453
Winsorized Mean ( 16 / 20 )13287.2016393443112.311080877772118.307129942100
Winsorized Mean ( 17 / 20 )13293.7229508197107.689751921047123.444642722977
Winsorized Mean ( 18 / 20 )13304.8180327869102.191912395557130.194432425216
Winsorized Mean ( 19 / 20 )13301.204918032897.9617127011088135.779628094255
Winsorized Mean ( 20 / 20 )13311.368852459094.7769908365276140.449372099380
Trimmed Mean ( 1 / 20 )13427.3830508475189.54048145343570.8417692509988
Trimmed Mean ( 2 / 20 )13439.5912280702175.85489615164476.4243221097515
Trimmed Mean ( 3 / 20 )13437.28170.03397542052179.0270295496383
Trimmed Mean ( 4 / 20 )13431.2547169811163.79358132348382.0011053452405
Trimmed Mean ( 5 / 20 )13418.8627450980160.00096605004483.8673857812895
Trimmed Mean ( 6 / 20 )13405.5061224490157.16074014609085.298059235327
Trimmed Mean ( 7 / 20 )13391.5446808511153.63713222349187.1634642422952
Trimmed Mean ( 8 / 20 )13377.9133333333149.54347989731389.4583524639093
Trimmed Mean ( 9 / 20 )13364.9465116279146.00109388950091.5400436776389
Trimmed Mean ( 10 / 20 )13348.9634146341141.64968256299294.2392751829702
Trimmed Mean ( 11 / 20 )13334.4897435897137.46589152682397.0021697417785
Trimmed Mean ( 12 / 20 )13321.4567567568133.118147445370100.072431989212
Trimmed Mean ( 13 / 20 )13308.8628571429127.885728475304104.068397747079
Trimmed Mean ( 14 / 20 )13310.8848484848126.810279067967104.966923393888
Trimmed Mean ( 15 / 20 )13313.5774193548125.630563683329105.974032345455
Trimmed Mean ( 16 / 20 )13317.4379310345123.726312696781107.636262980469
Trimmed Mean ( 17 / 20 )13321.7074074074121.233982632339109.884267745353
Trimmed Mean ( 18 / 20 )13325.724118.495435535157112.457698811920
Trimmed Mean ( 19 / 20 )13328.8043478261115.648989250040115.252233800405
Trimmed Mean ( 20 / 20 )13333.0238095238112.041379878100119.000888993246
Median13315.5
Midrange13428.4
Midmean - Weighted Average at Xnp13280.1566666667
Midmean - Weighted Average at X(n+1)p13313.5774193548
Midmean - Empirical Distribution Function13313.5774193548
Midmean - Empirical Distribution Function - Averaging13313.5774193548
Midmean - Empirical Distribution Function - Interpolation13313.5774193548
Midmean - Closest Observation13278.68125
Midmean - True Basic - Statistics Graphics Toolkit13313.5774193548
Midmean - MS Excel (old versions)13313.5774193548
Number of observations61

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 13427.4163934426 & 205.46708095502 & 65.3506942865563 \tabularnewline
Geometric Mean & 13331.8651719287 &  &  \tabularnewline
Harmonic Mean & 13234.5656090411 &  &  \tabularnewline
Quadratic Mean & 13521.4094784628 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 13415.9754098361 & 200.508853894091 & 66.9096408925781 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 13443.7590163934 & 184.361990771972 & 72.920448299028 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 13452.9852459016 & 182.298422470327 & 73.7964984205577 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 13472.6967213115 & 172.125291368766 & 78.2726153383653 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 13472.5081967213 & 166.118805587804 & 81.1016437846966 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 13470.0491803279 & 165.416835684867 & 81.4309445864957 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 13461.9360655738 & 163.588259930425 & 82.2915780832877 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 13451.0377049180 & 156.943967972213 & 85.7059871667036 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 13461.6311475410 & 155.196213169623 & 86.739430509351 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 13441.5 & 149.050083470334 & 90.1810967631915 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 13421.4475409836 & 143.998009579568 & 93.2057851366856 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 13408.1688524590 & 141.011103146548 & 95.0859085083842 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 13294.6426229508 & 118.849607714432 & 111.861055990145 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 13291.7278688525 & 115.942231708782 & 114.640952420495 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 13286.0475409836 & 114.930505531278 & 115.600705657453 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 13287.2016393443 & 112.311080877772 & 118.307129942100 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 13293.7229508197 & 107.689751921047 & 123.444642722977 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 13304.8180327869 & 102.191912395557 & 130.194432425216 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 13301.2049180328 & 97.9617127011088 & 135.779628094255 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 13311.3688524590 & 94.7769908365276 & 140.449372099380 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 13427.3830508475 & 189.540481453435 & 70.8417692509988 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 13439.5912280702 & 175.854896151644 & 76.4243221097515 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 13437.28 & 170.033975420521 & 79.0270295496383 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 13431.2547169811 & 163.793581323483 & 82.0011053452405 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 13418.8627450980 & 160.000966050044 & 83.8673857812895 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 13405.5061224490 & 157.160740146090 & 85.298059235327 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 13391.5446808511 & 153.637132223491 & 87.1634642422952 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 13377.9133333333 & 149.543479897313 & 89.4583524639093 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 13364.9465116279 & 146.001093889500 & 91.5400436776389 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 13348.9634146341 & 141.649682562992 & 94.2392751829702 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 13334.4897435897 & 137.465891526823 & 97.0021697417785 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 13321.4567567568 & 133.118147445370 & 100.072431989212 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 13308.8628571429 & 127.885728475304 & 104.068397747079 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 13310.8848484848 & 126.810279067967 & 104.966923393888 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 13313.5774193548 & 125.630563683329 & 105.974032345455 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 13317.4379310345 & 123.726312696781 & 107.636262980469 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 13321.7074074074 & 121.233982632339 & 109.884267745353 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 13325.724 & 118.495435535157 & 112.457698811920 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 13328.8043478261 & 115.648989250040 & 115.252233800405 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 13333.0238095238 & 112.041379878100 & 119.000888993246 \tabularnewline
Median & 13315.5 &  &  \tabularnewline
Midrange & 13428.4 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 13280.1566666667 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 13313.5774193548 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 13313.5774193548 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 13313.5774193548 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 13313.5774193548 &  &  \tabularnewline
Midmean - Closest Observation & 13278.68125 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 13313.5774193548 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 13313.5774193548 &  &  \tabularnewline
Number of observations & 61 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=1393&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]13427.4163934426[/C][C]205.46708095502[/C][C]65.3506942865563[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]13331.8651719287[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]13234.5656090411[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]13521.4094784628[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]13415.9754098361[/C][C]200.508853894091[/C][C]66.9096408925781[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]13443.7590163934[/C][C]184.361990771972[/C][C]72.920448299028[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]13452.9852459016[/C][C]182.298422470327[/C][C]73.7964984205577[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]13472.6967213115[/C][C]172.125291368766[/C][C]78.2726153383653[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]13472.5081967213[/C][C]166.118805587804[/C][C]81.1016437846966[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]13470.0491803279[/C][C]165.416835684867[/C][C]81.4309445864957[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]13461.9360655738[/C][C]163.588259930425[/C][C]82.2915780832877[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]13451.0377049180[/C][C]156.943967972213[/C][C]85.7059871667036[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]13461.6311475410[/C][C]155.196213169623[/C][C]86.739430509351[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]13441.5[/C][C]149.050083470334[/C][C]90.1810967631915[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]13421.4475409836[/C][C]143.998009579568[/C][C]93.2057851366856[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]13408.1688524590[/C][C]141.011103146548[/C][C]95.0859085083842[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]13294.6426229508[/C][C]118.849607714432[/C][C]111.861055990145[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]13291.7278688525[/C][C]115.942231708782[/C][C]114.640952420495[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]13286.0475409836[/C][C]114.930505531278[/C][C]115.600705657453[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]13287.2016393443[/C][C]112.311080877772[/C][C]118.307129942100[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]13293.7229508197[/C][C]107.689751921047[/C][C]123.444642722977[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]13304.8180327869[/C][C]102.191912395557[/C][C]130.194432425216[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]13301.2049180328[/C][C]97.9617127011088[/C][C]135.779628094255[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]13311.3688524590[/C][C]94.7769908365276[/C][C]140.449372099380[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]13427.3830508475[/C][C]189.540481453435[/C][C]70.8417692509988[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]13439.5912280702[/C][C]175.854896151644[/C][C]76.4243221097515[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]13437.28[/C][C]170.033975420521[/C][C]79.0270295496383[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]13431.2547169811[/C][C]163.793581323483[/C][C]82.0011053452405[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]13418.8627450980[/C][C]160.000966050044[/C][C]83.8673857812895[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]13405.5061224490[/C][C]157.160740146090[/C][C]85.298059235327[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]13391.5446808511[/C][C]153.637132223491[/C][C]87.1634642422952[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]13377.9133333333[/C][C]149.543479897313[/C][C]89.4583524639093[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]13364.9465116279[/C][C]146.001093889500[/C][C]91.5400436776389[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]13348.9634146341[/C][C]141.649682562992[/C][C]94.2392751829702[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]13334.4897435897[/C][C]137.465891526823[/C][C]97.0021697417785[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]13321.4567567568[/C][C]133.118147445370[/C][C]100.072431989212[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]13308.8628571429[/C][C]127.885728475304[/C][C]104.068397747079[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]13310.8848484848[/C][C]126.810279067967[/C][C]104.966923393888[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]13313.5774193548[/C][C]125.630563683329[/C][C]105.974032345455[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]13317.4379310345[/C][C]123.726312696781[/C][C]107.636262980469[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]13321.7074074074[/C][C]121.233982632339[/C][C]109.884267745353[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]13325.724[/C][C]118.495435535157[/C][C]112.457698811920[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]13328.8043478261[/C][C]115.648989250040[/C][C]115.252233800405[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]13333.0238095238[/C][C]112.041379878100[/C][C]119.000888993246[/C][/ROW]
[ROW][C]Median[/C][C]13315.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]13428.4[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]13280.1566666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]13313.5774193548[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]13313.5774193548[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]13313.5774193548[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]13313.5774193548[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]13278.68125[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]13313.5774193548[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]13313.5774193548[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]61[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=1393&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=1393&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 Mean13427.4163934426205.4670809550265.3506942865563
Geometric Mean13331.8651719287
Harmonic Mean13234.5656090411
Quadratic Mean13521.4094784628
Winsorized Mean ( 1 / 20 )13415.9754098361200.50885389409166.9096408925781
Winsorized Mean ( 2 / 20 )13443.7590163934184.36199077197272.920448299028
Winsorized Mean ( 3 / 20 )13452.9852459016182.29842247032773.7964984205577
Winsorized Mean ( 4 / 20 )13472.6967213115172.12529136876678.2726153383653
Winsorized Mean ( 5 / 20 )13472.5081967213166.11880558780481.1016437846966
Winsorized Mean ( 6 / 20 )13470.0491803279165.41683568486781.4309445864957
Winsorized Mean ( 7 / 20 )13461.9360655738163.58825993042582.2915780832877
Winsorized Mean ( 8 / 20 )13451.0377049180156.94396797221385.7059871667036
Winsorized Mean ( 9 / 20 )13461.6311475410155.19621316962386.739430509351
Winsorized Mean ( 10 / 20 )13441.5149.05008347033490.1810967631915
Winsorized Mean ( 11 / 20 )13421.4475409836143.99800957956893.2057851366856
Winsorized Mean ( 12 / 20 )13408.1688524590141.01110314654895.0859085083842
Winsorized Mean ( 13 / 20 )13294.6426229508118.849607714432111.861055990145
Winsorized Mean ( 14 / 20 )13291.7278688525115.942231708782114.640952420495
Winsorized Mean ( 15 / 20 )13286.0475409836114.930505531278115.600705657453
Winsorized Mean ( 16 / 20 )13287.2016393443112.311080877772118.307129942100
Winsorized Mean ( 17 / 20 )13293.7229508197107.689751921047123.444642722977
Winsorized Mean ( 18 / 20 )13304.8180327869102.191912395557130.194432425216
Winsorized Mean ( 19 / 20 )13301.204918032897.9617127011088135.779628094255
Winsorized Mean ( 20 / 20 )13311.368852459094.7769908365276140.449372099380
Trimmed Mean ( 1 / 20 )13427.3830508475189.54048145343570.8417692509988
Trimmed Mean ( 2 / 20 )13439.5912280702175.85489615164476.4243221097515
Trimmed Mean ( 3 / 20 )13437.28170.03397542052179.0270295496383
Trimmed Mean ( 4 / 20 )13431.2547169811163.79358132348382.0011053452405
Trimmed Mean ( 5 / 20 )13418.8627450980160.00096605004483.8673857812895
Trimmed Mean ( 6 / 20 )13405.5061224490157.16074014609085.298059235327
Trimmed Mean ( 7 / 20 )13391.5446808511153.63713222349187.1634642422952
Trimmed Mean ( 8 / 20 )13377.9133333333149.54347989731389.4583524639093
Trimmed Mean ( 9 / 20 )13364.9465116279146.00109388950091.5400436776389
Trimmed Mean ( 10 / 20 )13348.9634146341141.64968256299294.2392751829702
Trimmed Mean ( 11 / 20 )13334.4897435897137.46589152682397.0021697417785
Trimmed Mean ( 12 / 20 )13321.4567567568133.118147445370100.072431989212
Trimmed Mean ( 13 / 20 )13308.8628571429127.885728475304104.068397747079
Trimmed Mean ( 14 / 20 )13310.8848484848126.810279067967104.966923393888
Trimmed Mean ( 15 / 20 )13313.5774193548125.630563683329105.974032345455
Trimmed Mean ( 16 / 20 )13317.4379310345123.726312696781107.636262980469
Trimmed Mean ( 17 / 20 )13321.7074074074121.233982632339109.884267745353
Trimmed Mean ( 18 / 20 )13325.724118.495435535157112.457698811920
Trimmed Mean ( 19 / 20 )13328.8043478261115.648989250040115.252233800405
Trimmed Mean ( 20 / 20 )13333.0238095238112.041379878100119.000888993246
Median13315.5
Midrange13428.4
Midmean - Weighted Average at Xnp13280.1566666667
Midmean - Weighted Average at X(n+1)p13313.5774193548
Midmean - Empirical Distribution Function13313.5774193548
Midmean - Empirical Distribution Function - Averaging13313.5774193548
Midmean - Empirical Distribution Function - Interpolation13313.5774193548
Midmean - Closest Observation13278.68125
Midmean - True Basic - Statistics Graphics Toolkit13313.5774193548
Midmean - MS Excel (old versions)13313.5774193548
Number of observations61



Parameters (Session):
par1 = 0.01 ; par2 = 0.99 ; par3 = 0.01 ;
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')