Free Statistics

of Irreproducible Research!

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationFri, 24 Dec 2010 14:59:34 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2010/Dec/24/t1293202668v4zh72bxs6szy0t.htm/, Retrieved Tue, 30 Apr 2024 03:26:12 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=115046, Retrieved Tue, 30 Apr 2024 03:26:12 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact124
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Bivariate Data Series] [Bivariate dataset] [2008-01-05 23:51:08] [74be16979710d4c4e7c6647856088456]
F RMPD  [Mean Plot] [Colombia Coffee] [2008-01-07 13:38:24] [74be16979710d4c4e7c6647856088456]
- RM D    [Central Tendency] [Paper uitvoer cen...] [2010-11-30 13:39:00] [247f085ab5b7724f755ad01dc754a3e8]
-    D      [Central Tendency] [paperCTuit] [2010-12-22 19:59:22] [7e261c986c934df955dd3ac53e9d45c6]
-    D        [Central Tendency] [paperCTwerk] [2010-12-22 20:11:32] [7e261c986c934df955dd3ac53e9d45c6]
-                 [Central Tendency] [] [2010-12-24 14:59:34] [fff0a1ca5ad3b1801f382406d5a383a7] [Current]
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Dataseries X:
6,7
6,7
6,5
6,3
6,3
6,3
6,5
6,6
6,5
6,3
6,3
6,5
7
7,1
7,3
7,3
7,4
7,4
7,3
7,4
7,5
7,7
7,7
7,7
7,7
7,7
7,8
8
8,1
8,1
8,2
8,2
8,2
8,1
8,1
8,2
8,3
8,3
8,4
8,5
8,5
8,4
8
7,9
8,1
8,5
8,8
8,8
8,6
8,3
8,3
8,3
8,4
8,4
8,5
8,6
8,6
8,6
8,6
8,6
8,5
8,4
8,4
8,4
8,5
8,5
8,6
8,6
8,4
8,2
8
8
8
8
7,9
7,9
7,8
7,8
8
7,8
7,4
7,2
7
7
7,2
7,2
7,2
7
6,9
6,8
6,8
6,8
6,9
7,2
7,2
7,2
7,1
7,2
7,3
7,5
7,6
7,7
7,7
7,7
7,8
8
8,1
8,1
8
8,1
8,2
8,3
8,4
8,4
8,4
8,5
8,5
8,6
8,6
8,5
8,5




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'RServer@AstonUniversity' @ vre.aston.ac.uk

\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 & 'RServer@AstonUniversity' @ vre.aston.ac.uk \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=115046&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]'RServer@AstonUniversity' @ vre.aston.ac.uk[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=115046&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=115046&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'RServer@AstonUniversity' @ vre.aston.ac.uk







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean7.78925619834710.0621891902958961125.250966627574
Geometric Mean7.75818115708727
Harmonic Mean7.72583262373508
Quadratic Mean7.81899044444025
Winsorized Mean ( 1 / 40 )7.78925619834710.0621891902958961125.250966627574
Winsorized Mean ( 2 / 40 )7.785950413223140.0617837001105009126.019490566248
Winsorized Mean ( 3 / 40 )7.785950413223140.0617837001105009126.019490566248
Winsorized Mean ( 4 / 40 )7.785950413223140.0617837001105009126.019490566248
Winsorized Mean ( 5 / 40 )7.794214876033060.0602142355318931129.44139881847
Winsorized Mean ( 6 / 40 )7.794214876033060.0602142355318931129.44139881847
Winsorized Mean ( 7 / 40 )7.794214876033060.0602142355318931129.44139881847
Winsorized Mean ( 8 / 40 )7.794214876033060.0602142355318931129.44139881847
Winsorized Mean ( 9 / 40 )7.801652892561980.058915631313346132.420763703074
Winsorized Mean ( 10 / 40 )7.80991735537190.0575486972933541135.709715817908
Winsorized Mean ( 11 / 40 )7.80991735537190.0575486972933541135.709715817908
Winsorized Mean ( 12 / 40 )7.80991735537190.0549029316066554142.249550740296
Winsorized Mean ( 13 / 40 )7.80991735537190.0549029316066554142.249550740296
Winsorized Mean ( 14 / 40 )7.80991735537190.0549029316066554142.249550740296
Winsorized Mean ( 15 / 40 )7.822314049586780.0530539462874783147.440757888221
Winsorized Mean ( 16 / 40 )7.822314049586780.0530539462874783147.440757888221
Winsorized Mean ( 17 / 40 )7.836363636363640.0510765643617231153.42385953892
Winsorized Mean ( 18 / 40 )7.836363636363640.0510765643617231153.42385953892
Winsorized Mean ( 19 / 40 )7.836363636363640.0510765643617231153.42385953892
Winsorized Mean ( 20 / 40 )7.836363636363640.0510765643617231153.42385953892
Winsorized Mean ( 21 / 40 )7.853719008264460.0487734025527831161.024628121138
Winsorized Mean ( 22 / 40 )7.853719008264460.0487734025527831161.024628121138
Winsorized Mean ( 23 / 40 )7.853719008264460.0443508631995847177.081536675435
Winsorized Mean ( 24 / 40 )7.853719008264460.0443508631995847177.081536675435
Winsorized Mean ( 25 / 40 )7.853719008264460.0443508631995847177.081536675435
Winsorized Mean ( 26 / 40 )7.853719008264460.0443508631995847177.081536675435
Winsorized Mean ( 27 / 40 )7.853719008264460.0443508631995847177.081536675435
Winsorized Mean ( 28 / 40 )7.853719008264460.0443508631995847177.081536675435
Winsorized Mean ( 29 / 40 )7.853719008264460.0443508631995847177.081536675435
Winsorized Mean ( 30 / 40 )7.853719008264460.0443508631995847177.081536675435
Winsorized Mean ( 31 / 40 )7.87933884297520.0412764207960841190.892007858461
Winsorized Mean ( 32 / 40 )7.87933884297520.0412764207960841190.892007858461
Winsorized Mean ( 33 / 40 )7.87933884297520.0412764207960841190.892007858461
Winsorized Mean ( 34 / 40 )7.851239669421490.0384284190651245204.308162043201
Winsorized Mean ( 35 / 40 )7.88016528925620.0350446357391817224.860813161364
Winsorized Mean ( 36 / 40 )7.88016528925620.0350446357391817224.860813161364
Winsorized Mean ( 37 / 40 )7.88016528925620.0350446357391817224.860813161364
Winsorized Mean ( 38 / 40 )7.88016528925620.0350446357391817224.860813161364
Winsorized Mean ( 39 / 40 )7.912396694214880.0314386509134663251.677360965439
Winsorized Mean ( 40 / 40 )7.87933884297520.0281651308212153279.755094801126
Trimmed Mean ( 1 / 40 )7.793277310924370.061386569488755126.954110252927
Trimmed Mean ( 2 / 40 )7.79743589743590.0604953218416412128.893204632373
Trimmed Mean ( 3 / 40 )7.803478260869570.0597340972301691130.636916312655
Trimmed Mean ( 4 / 40 )7.809734513274340.0588818671228164132.633948189596
Trimmed Mean ( 5 / 40 )7.816216216216220.0579267879388989134.932670951145
Trimmed Mean ( 6 / 40 )7.821100917431190.057278186776646136.545888715529
Trimmed Mean ( 7 / 40 )7.826168224299070.0565469743165114138.401184482365
Trimmed Mean ( 8 / 40 )7.831428571428570.0557222686119018140.5439650344
Trimmed Mean ( 9 / 40 )7.83689320388350.0547911996512886143.031969618486
Trimmed Mean ( 10 / 40 )7.841584158415840.0539759265505965145.279287629555
Trimmed Mean ( 11 / 40 )7.845454545454550.053283695346715147.239310156784
Trimmed Mean ( 12 / 40 )7.849484536082470.0524961893425621149.524844267475
Trimmed Mean ( 13 / 40 )7.853684210526320.0519886826842824151.065266612356
Trimmed Mean ( 14 / 40 )7.858064516129030.0514020940266571152.874404534061
Trimmed Mean ( 15 / 40 )7.862637362637360.0507248641963399155.005587244228
Trimmed Mean ( 16 / 40 )7.866292134831460.0502024456281748156.691412866482
Trimmed Mean ( 17 / 40 )7.870114942528740.0495937773247987158.691581223707
Trimmed Mean ( 18 / 40 )7.872941176470590.0491492962325158160.184209743823
Trimmed Mean ( 19 / 40 )7.875903614457830.0486246444001173161.973495366864
Trimmed Mean ( 20 / 40 )7.879012345679010.0480070741116501164.121902687816
Trimmed Mean ( 21 / 40 )7.882278481012660.047281141151325166.710834152355
Trimmed Mean ( 22 / 40 )7.884415584415580.0467342560352314168.707416214603
Trimmed Mean ( 23 / 40 )7.886666666666670.0460838770474417171.137221344194
Trimmed Mean ( 24 / 40 )7.889041095890410.0458540486119615172.046773070164
Trimmed Mean ( 25 / 40 )7.891549295774650.0455569813176158173.223709463014
Trimmed Mean ( 26 / 40 )7.894202898550720.0451805159276019174.725824539068
Trimmed Mean ( 27 / 40 )7.897014925373130.0447097352013154176.628532685669
Trimmed Mean ( 28 / 40 )7.90.0441261304060914179.03224069948
Trimmed Mean ( 29 / 40 )7.90317460317460.043406428600753182.073827724161
Trimmed Mean ( 30 / 40 )7.906557377049180.0425208950537202185.945224508096
Trimmed Mean ( 31 / 40 )7.906557377049180.0414307894818673190.837719385231
Trimmed Mean ( 32 / 40 )7.912280701754390.0405993764720102194.886754165036
Trimmed Mean ( 33 / 40 )7.914545454545450.0395614155645275200.057185558395
Trimmed Mean ( 34 / 40 )7.916981132075470.0382619351648451206.915334991983
Trimmed Mean ( 35 / 40 )7.921568627450980.0370811220392238213.628072502004
Trimmed Mean ( 36 / 40 )7.924489795918370.0362496319761869218.608834460005
Trimmed Mean ( 37 / 40 )7.927659574468080.0351686997720891225.418045757828
Trimmed Mean ( 38 / 40 )7.931111111111110.0337582346440846234.938562242054
Trimmed Mean ( 39 / 40 )7.934883720930230.0318988783151632248.751183114749
Trimmed Mean ( 40 / 40 )7.936585365853660.030394980643267261.114999841651
Median8
Midrange7.55
Midmean - Weighted Average at Xnp7.88666666666667
Midmean - Weighted Average at X(n+1)p7.88666666666667
Midmean - Empirical Distribution Function7.88666666666667
Midmean - Empirical Distribution Function - Averaging7.88666666666667
Midmean - Empirical Distribution Function - Interpolation7.88666666666667
Midmean - Closest Observation7.88666666666667
Midmean - True Basic - Statistics Graphics Toolkit7.88666666666667
Midmean - MS Excel (old versions)7.88666666666667
Number of observations121

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 7.7892561983471 & 0.0621891902958961 & 125.250966627574 \tabularnewline
Geometric Mean & 7.75818115708727 &  &  \tabularnewline
Harmonic Mean & 7.72583262373508 &  &  \tabularnewline
Quadratic Mean & 7.81899044444025 &  &  \tabularnewline
Winsorized Mean ( 1 / 40 ) & 7.7892561983471 & 0.0621891902958961 & 125.250966627574 \tabularnewline
Winsorized Mean ( 2 / 40 ) & 7.78595041322314 & 0.0617837001105009 & 126.019490566248 \tabularnewline
Winsorized Mean ( 3 / 40 ) & 7.78595041322314 & 0.0617837001105009 & 126.019490566248 \tabularnewline
Winsorized Mean ( 4 / 40 ) & 7.78595041322314 & 0.0617837001105009 & 126.019490566248 \tabularnewline
Winsorized Mean ( 5 / 40 ) & 7.79421487603306 & 0.0602142355318931 & 129.44139881847 \tabularnewline
Winsorized Mean ( 6 / 40 ) & 7.79421487603306 & 0.0602142355318931 & 129.44139881847 \tabularnewline
Winsorized Mean ( 7 / 40 ) & 7.79421487603306 & 0.0602142355318931 & 129.44139881847 \tabularnewline
Winsorized Mean ( 8 / 40 ) & 7.79421487603306 & 0.0602142355318931 & 129.44139881847 \tabularnewline
Winsorized Mean ( 9 / 40 ) & 7.80165289256198 & 0.058915631313346 & 132.420763703074 \tabularnewline
Winsorized Mean ( 10 / 40 ) & 7.8099173553719 & 0.0575486972933541 & 135.709715817908 \tabularnewline
Winsorized Mean ( 11 / 40 ) & 7.8099173553719 & 0.0575486972933541 & 135.709715817908 \tabularnewline
Winsorized Mean ( 12 / 40 ) & 7.8099173553719 & 0.0549029316066554 & 142.249550740296 \tabularnewline
Winsorized Mean ( 13 / 40 ) & 7.8099173553719 & 0.0549029316066554 & 142.249550740296 \tabularnewline
Winsorized Mean ( 14 / 40 ) & 7.8099173553719 & 0.0549029316066554 & 142.249550740296 \tabularnewline
Winsorized Mean ( 15 / 40 ) & 7.82231404958678 & 0.0530539462874783 & 147.440757888221 \tabularnewline
Winsorized Mean ( 16 / 40 ) & 7.82231404958678 & 0.0530539462874783 & 147.440757888221 \tabularnewline
Winsorized Mean ( 17 / 40 ) & 7.83636363636364 & 0.0510765643617231 & 153.42385953892 \tabularnewline
Winsorized Mean ( 18 / 40 ) & 7.83636363636364 & 0.0510765643617231 & 153.42385953892 \tabularnewline
Winsorized Mean ( 19 / 40 ) & 7.83636363636364 & 0.0510765643617231 & 153.42385953892 \tabularnewline
Winsorized Mean ( 20 / 40 ) & 7.83636363636364 & 0.0510765643617231 & 153.42385953892 \tabularnewline
Winsorized Mean ( 21 / 40 ) & 7.85371900826446 & 0.0487734025527831 & 161.024628121138 \tabularnewline
Winsorized Mean ( 22 / 40 ) & 7.85371900826446 & 0.0487734025527831 & 161.024628121138 \tabularnewline
Winsorized Mean ( 23 / 40 ) & 7.85371900826446 & 0.0443508631995847 & 177.081536675435 \tabularnewline
Winsorized Mean ( 24 / 40 ) & 7.85371900826446 & 0.0443508631995847 & 177.081536675435 \tabularnewline
Winsorized Mean ( 25 / 40 ) & 7.85371900826446 & 0.0443508631995847 & 177.081536675435 \tabularnewline
Winsorized Mean ( 26 / 40 ) & 7.85371900826446 & 0.0443508631995847 & 177.081536675435 \tabularnewline
Winsorized Mean ( 27 / 40 ) & 7.85371900826446 & 0.0443508631995847 & 177.081536675435 \tabularnewline
Winsorized Mean ( 28 / 40 ) & 7.85371900826446 & 0.0443508631995847 & 177.081536675435 \tabularnewline
Winsorized Mean ( 29 / 40 ) & 7.85371900826446 & 0.0443508631995847 & 177.081536675435 \tabularnewline
Winsorized Mean ( 30 / 40 ) & 7.85371900826446 & 0.0443508631995847 & 177.081536675435 \tabularnewline
Winsorized Mean ( 31 / 40 ) & 7.8793388429752 & 0.0412764207960841 & 190.892007858461 \tabularnewline
Winsorized Mean ( 32 / 40 ) & 7.8793388429752 & 0.0412764207960841 & 190.892007858461 \tabularnewline
Winsorized Mean ( 33 / 40 ) & 7.8793388429752 & 0.0412764207960841 & 190.892007858461 \tabularnewline
Winsorized Mean ( 34 / 40 ) & 7.85123966942149 & 0.0384284190651245 & 204.308162043201 \tabularnewline
Winsorized Mean ( 35 / 40 ) & 7.8801652892562 & 0.0350446357391817 & 224.860813161364 \tabularnewline
Winsorized Mean ( 36 / 40 ) & 7.8801652892562 & 0.0350446357391817 & 224.860813161364 \tabularnewline
Winsorized Mean ( 37 / 40 ) & 7.8801652892562 & 0.0350446357391817 & 224.860813161364 \tabularnewline
Winsorized Mean ( 38 / 40 ) & 7.8801652892562 & 0.0350446357391817 & 224.860813161364 \tabularnewline
Winsorized Mean ( 39 / 40 ) & 7.91239669421488 & 0.0314386509134663 & 251.677360965439 \tabularnewline
Winsorized Mean ( 40 / 40 ) & 7.8793388429752 & 0.0281651308212153 & 279.755094801126 \tabularnewline
Trimmed Mean ( 1 / 40 ) & 7.79327731092437 & 0.061386569488755 & 126.954110252927 \tabularnewline
Trimmed Mean ( 2 / 40 ) & 7.7974358974359 & 0.0604953218416412 & 128.893204632373 \tabularnewline
Trimmed Mean ( 3 / 40 ) & 7.80347826086957 & 0.0597340972301691 & 130.636916312655 \tabularnewline
Trimmed Mean ( 4 / 40 ) & 7.80973451327434 & 0.0588818671228164 & 132.633948189596 \tabularnewline
Trimmed Mean ( 5 / 40 ) & 7.81621621621622 & 0.0579267879388989 & 134.932670951145 \tabularnewline
Trimmed Mean ( 6 / 40 ) & 7.82110091743119 & 0.057278186776646 & 136.545888715529 \tabularnewline
Trimmed Mean ( 7 / 40 ) & 7.82616822429907 & 0.0565469743165114 & 138.401184482365 \tabularnewline
Trimmed Mean ( 8 / 40 ) & 7.83142857142857 & 0.0557222686119018 & 140.5439650344 \tabularnewline
Trimmed Mean ( 9 / 40 ) & 7.8368932038835 & 0.0547911996512886 & 143.031969618486 \tabularnewline
Trimmed Mean ( 10 / 40 ) & 7.84158415841584 & 0.0539759265505965 & 145.279287629555 \tabularnewline
Trimmed Mean ( 11 / 40 ) & 7.84545454545455 & 0.053283695346715 & 147.239310156784 \tabularnewline
Trimmed Mean ( 12 / 40 ) & 7.84948453608247 & 0.0524961893425621 & 149.524844267475 \tabularnewline
Trimmed Mean ( 13 / 40 ) & 7.85368421052632 & 0.0519886826842824 & 151.065266612356 \tabularnewline
Trimmed Mean ( 14 / 40 ) & 7.85806451612903 & 0.0514020940266571 & 152.874404534061 \tabularnewline
Trimmed Mean ( 15 / 40 ) & 7.86263736263736 & 0.0507248641963399 & 155.005587244228 \tabularnewline
Trimmed Mean ( 16 / 40 ) & 7.86629213483146 & 0.0502024456281748 & 156.691412866482 \tabularnewline
Trimmed Mean ( 17 / 40 ) & 7.87011494252874 & 0.0495937773247987 & 158.691581223707 \tabularnewline
Trimmed Mean ( 18 / 40 ) & 7.87294117647059 & 0.0491492962325158 & 160.184209743823 \tabularnewline
Trimmed Mean ( 19 / 40 ) & 7.87590361445783 & 0.0486246444001173 & 161.973495366864 \tabularnewline
Trimmed Mean ( 20 / 40 ) & 7.87901234567901 & 0.0480070741116501 & 164.121902687816 \tabularnewline
Trimmed Mean ( 21 / 40 ) & 7.88227848101266 & 0.047281141151325 & 166.710834152355 \tabularnewline
Trimmed Mean ( 22 / 40 ) & 7.88441558441558 & 0.0467342560352314 & 168.707416214603 \tabularnewline
Trimmed Mean ( 23 / 40 ) & 7.88666666666667 & 0.0460838770474417 & 171.137221344194 \tabularnewline
Trimmed Mean ( 24 / 40 ) & 7.88904109589041 & 0.0458540486119615 & 172.046773070164 \tabularnewline
Trimmed Mean ( 25 / 40 ) & 7.89154929577465 & 0.0455569813176158 & 173.223709463014 \tabularnewline
Trimmed Mean ( 26 / 40 ) & 7.89420289855072 & 0.0451805159276019 & 174.725824539068 \tabularnewline
Trimmed Mean ( 27 / 40 ) & 7.89701492537313 & 0.0447097352013154 & 176.628532685669 \tabularnewline
Trimmed Mean ( 28 / 40 ) & 7.9 & 0.0441261304060914 & 179.03224069948 \tabularnewline
Trimmed Mean ( 29 / 40 ) & 7.9031746031746 & 0.043406428600753 & 182.073827724161 \tabularnewline
Trimmed Mean ( 30 / 40 ) & 7.90655737704918 & 0.0425208950537202 & 185.945224508096 \tabularnewline
Trimmed Mean ( 31 / 40 ) & 7.90655737704918 & 0.0414307894818673 & 190.837719385231 \tabularnewline
Trimmed Mean ( 32 / 40 ) & 7.91228070175439 & 0.0405993764720102 & 194.886754165036 \tabularnewline
Trimmed Mean ( 33 / 40 ) & 7.91454545454545 & 0.0395614155645275 & 200.057185558395 \tabularnewline
Trimmed Mean ( 34 / 40 ) & 7.91698113207547 & 0.0382619351648451 & 206.915334991983 \tabularnewline
Trimmed Mean ( 35 / 40 ) & 7.92156862745098 & 0.0370811220392238 & 213.628072502004 \tabularnewline
Trimmed Mean ( 36 / 40 ) & 7.92448979591837 & 0.0362496319761869 & 218.608834460005 \tabularnewline
Trimmed Mean ( 37 / 40 ) & 7.92765957446808 & 0.0351686997720891 & 225.418045757828 \tabularnewline
Trimmed Mean ( 38 / 40 ) & 7.93111111111111 & 0.0337582346440846 & 234.938562242054 \tabularnewline
Trimmed Mean ( 39 / 40 ) & 7.93488372093023 & 0.0318988783151632 & 248.751183114749 \tabularnewline
Trimmed Mean ( 40 / 40 ) & 7.93658536585366 & 0.030394980643267 & 261.114999841651 \tabularnewline
Median & 8 &  &  \tabularnewline
Midrange & 7.55 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 7.88666666666667 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 7.88666666666667 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 7.88666666666667 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 7.88666666666667 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 7.88666666666667 &  &  \tabularnewline
Midmean - Closest Observation & 7.88666666666667 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 7.88666666666667 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 7.88666666666667 &  &  \tabularnewline
Number of observations & 121 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=115046&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]7.7892561983471[/C][C]0.0621891902958961[/C][C]125.250966627574[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]7.75818115708727[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]7.72583262373508[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]7.81899044444025[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 40 )[/C][C]7.7892561983471[/C][C]0.0621891902958961[/C][C]125.250966627574[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 40 )[/C][C]7.78595041322314[/C][C]0.0617837001105009[/C][C]126.019490566248[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 40 )[/C][C]7.78595041322314[/C][C]0.0617837001105009[/C][C]126.019490566248[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 40 )[/C][C]7.78595041322314[/C][C]0.0617837001105009[/C][C]126.019490566248[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 40 )[/C][C]7.79421487603306[/C][C]0.0602142355318931[/C][C]129.44139881847[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 40 )[/C][C]7.79421487603306[/C][C]0.0602142355318931[/C][C]129.44139881847[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 40 )[/C][C]7.79421487603306[/C][C]0.0602142355318931[/C][C]129.44139881847[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 40 )[/C][C]7.79421487603306[/C][C]0.0602142355318931[/C][C]129.44139881847[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 40 )[/C][C]7.80165289256198[/C][C]0.058915631313346[/C][C]132.420763703074[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 40 )[/C][C]7.8099173553719[/C][C]0.0575486972933541[/C][C]135.709715817908[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 40 )[/C][C]7.8099173553719[/C][C]0.0575486972933541[/C][C]135.709715817908[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 40 )[/C][C]7.8099173553719[/C][C]0.0549029316066554[/C][C]142.249550740296[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 40 )[/C][C]7.8099173553719[/C][C]0.0549029316066554[/C][C]142.249550740296[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 40 )[/C][C]7.8099173553719[/C][C]0.0549029316066554[/C][C]142.249550740296[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 40 )[/C][C]7.82231404958678[/C][C]0.0530539462874783[/C][C]147.440757888221[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 40 )[/C][C]7.82231404958678[/C][C]0.0530539462874783[/C][C]147.440757888221[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 40 )[/C][C]7.83636363636364[/C][C]0.0510765643617231[/C][C]153.42385953892[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 40 )[/C][C]7.83636363636364[/C][C]0.0510765643617231[/C][C]153.42385953892[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 40 )[/C][C]7.83636363636364[/C][C]0.0510765643617231[/C][C]153.42385953892[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 40 )[/C][C]7.83636363636364[/C][C]0.0510765643617231[/C][C]153.42385953892[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 40 )[/C][C]7.85371900826446[/C][C]0.0487734025527831[/C][C]161.024628121138[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 40 )[/C][C]7.85371900826446[/C][C]0.0487734025527831[/C][C]161.024628121138[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 40 )[/C][C]7.85371900826446[/C][C]0.0443508631995847[/C][C]177.081536675435[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 40 )[/C][C]7.85371900826446[/C][C]0.0443508631995847[/C][C]177.081536675435[/C][/ROW]
[ROW][C]Winsorized Mean ( 25 / 40 )[/C][C]7.85371900826446[/C][C]0.0443508631995847[/C][C]177.081536675435[/C][/ROW]
[ROW][C]Winsorized Mean ( 26 / 40 )[/C][C]7.85371900826446[/C][C]0.0443508631995847[/C][C]177.081536675435[/C][/ROW]
[ROW][C]Winsorized Mean ( 27 / 40 )[/C][C]7.85371900826446[/C][C]0.0443508631995847[/C][C]177.081536675435[/C][/ROW]
[ROW][C]Winsorized Mean ( 28 / 40 )[/C][C]7.85371900826446[/C][C]0.0443508631995847[/C][C]177.081536675435[/C][/ROW]
[ROW][C]Winsorized Mean ( 29 / 40 )[/C][C]7.85371900826446[/C][C]0.0443508631995847[/C][C]177.081536675435[/C][/ROW]
[ROW][C]Winsorized Mean ( 30 / 40 )[/C][C]7.85371900826446[/C][C]0.0443508631995847[/C][C]177.081536675435[/C][/ROW]
[ROW][C]Winsorized Mean ( 31 / 40 )[/C][C]7.8793388429752[/C][C]0.0412764207960841[/C][C]190.892007858461[/C][/ROW]
[ROW][C]Winsorized Mean ( 32 / 40 )[/C][C]7.8793388429752[/C][C]0.0412764207960841[/C][C]190.892007858461[/C][/ROW]
[ROW][C]Winsorized Mean ( 33 / 40 )[/C][C]7.8793388429752[/C][C]0.0412764207960841[/C][C]190.892007858461[/C][/ROW]
[ROW][C]Winsorized Mean ( 34 / 40 )[/C][C]7.85123966942149[/C][C]0.0384284190651245[/C][C]204.308162043201[/C][/ROW]
[ROW][C]Winsorized Mean ( 35 / 40 )[/C][C]7.8801652892562[/C][C]0.0350446357391817[/C][C]224.860813161364[/C][/ROW]
[ROW][C]Winsorized Mean ( 36 / 40 )[/C][C]7.8801652892562[/C][C]0.0350446357391817[/C][C]224.860813161364[/C][/ROW]
[ROW][C]Winsorized Mean ( 37 / 40 )[/C][C]7.8801652892562[/C][C]0.0350446357391817[/C][C]224.860813161364[/C][/ROW]
[ROW][C]Winsorized Mean ( 38 / 40 )[/C][C]7.8801652892562[/C][C]0.0350446357391817[/C][C]224.860813161364[/C][/ROW]
[ROW][C]Winsorized Mean ( 39 / 40 )[/C][C]7.91239669421488[/C][C]0.0314386509134663[/C][C]251.677360965439[/C][/ROW]
[ROW][C]Winsorized Mean ( 40 / 40 )[/C][C]7.8793388429752[/C][C]0.0281651308212153[/C][C]279.755094801126[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 40 )[/C][C]7.79327731092437[/C][C]0.061386569488755[/C][C]126.954110252927[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 40 )[/C][C]7.7974358974359[/C][C]0.0604953218416412[/C][C]128.893204632373[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 40 )[/C][C]7.80347826086957[/C][C]0.0597340972301691[/C][C]130.636916312655[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 40 )[/C][C]7.80973451327434[/C][C]0.0588818671228164[/C][C]132.633948189596[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 40 )[/C][C]7.81621621621622[/C][C]0.0579267879388989[/C][C]134.932670951145[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 40 )[/C][C]7.82110091743119[/C][C]0.057278186776646[/C][C]136.545888715529[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 40 )[/C][C]7.82616822429907[/C][C]0.0565469743165114[/C][C]138.401184482365[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 40 )[/C][C]7.83142857142857[/C][C]0.0557222686119018[/C][C]140.5439650344[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 40 )[/C][C]7.8368932038835[/C][C]0.0547911996512886[/C][C]143.031969618486[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 40 )[/C][C]7.84158415841584[/C][C]0.0539759265505965[/C][C]145.279287629555[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 40 )[/C][C]7.84545454545455[/C][C]0.053283695346715[/C][C]147.239310156784[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 40 )[/C][C]7.84948453608247[/C][C]0.0524961893425621[/C][C]149.524844267475[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 40 )[/C][C]7.85368421052632[/C][C]0.0519886826842824[/C][C]151.065266612356[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 40 )[/C][C]7.85806451612903[/C][C]0.0514020940266571[/C][C]152.874404534061[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 40 )[/C][C]7.86263736263736[/C][C]0.0507248641963399[/C][C]155.005587244228[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 40 )[/C][C]7.86629213483146[/C][C]0.0502024456281748[/C][C]156.691412866482[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 40 )[/C][C]7.87011494252874[/C][C]0.0495937773247987[/C][C]158.691581223707[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 40 )[/C][C]7.87294117647059[/C][C]0.0491492962325158[/C][C]160.184209743823[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 40 )[/C][C]7.87590361445783[/C][C]0.0486246444001173[/C][C]161.973495366864[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 40 )[/C][C]7.87901234567901[/C][C]0.0480070741116501[/C][C]164.121902687816[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 40 )[/C][C]7.88227848101266[/C][C]0.047281141151325[/C][C]166.710834152355[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 40 )[/C][C]7.88441558441558[/C][C]0.0467342560352314[/C][C]168.707416214603[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 40 )[/C][C]7.88666666666667[/C][C]0.0460838770474417[/C][C]171.137221344194[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 40 )[/C][C]7.88904109589041[/C][C]0.0458540486119615[/C][C]172.046773070164[/C][/ROW]
[ROW][C]Trimmed Mean ( 25 / 40 )[/C][C]7.89154929577465[/C][C]0.0455569813176158[/C][C]173.223709463014[/C][/ROW]
[ROW][C]Trimmed Mean ( 26 / 40 )[/C][C]7.89420289855072[/C][C]0.0451805159276019[/C][C]174.725824539068[/C][/ROW]
[ROW][C]Trimmed Mean ( 27 / 40 )[/C][C]7.89701492537313[/C][C]0.0447097352013154[/C][C]176.628532685669[/C][/ROW]
[ROW][C]Trimmed Mean ( 28 / 40 )[/C][C]7.9[/C][C]0.0441261304060914[/C][C]179.03224069948[/C][/ROW]
[ROW][C]Trimmed Mean ( 29 / 40 )[/C][C]7.9031746031746[/C][C]0.043406428600753[/C][C]182.073827724161[/C][/ROW]
[ROW][C]Trimmed Mean ( 30 / 40 )[/C][C]7.90655737704918[/C][C]0.0425208950537202[/C][C]185.945224508096[/C][/ROW]
[ROW][C]Trimmed Mean ( 31 / 40 )[/C][C]7.90655737704918[/C][C]0.0414307894818673[/C][C]190.837719385231[/C][/ROW]
[ROW][C]Trimmed Mean ( 32 / 40 )[/C][C]7.91228070175439[/C][C]0.0405993764720102[/C][C]194.886754165036[/C][/ROW]
[ROW][C]Trimmed Mean ( 33 / 40 )[/C][C]7.91454545454545[/C][C]0.0395614155645275[/C][C]200.057185558395[/C][/ROW]
[ROW][C]Trimmed Mean ( 34 / 40 )[/C][C]7.91698113207547[/C][C]0.0382619351648451[/C][C]206.915334991983[/C][/ROW]
[ROW][C]Trimmed Mean ( 35 / 40 )[/C][C]7.92156862745098[/C][C]0.0370811220392238[/C][C]213.628072502004[/C][/ROW]
[ROW][C]Trimmed Mean ( 36 / 40 )[/C][C]7.92448979591837[/C][C]0.0362496319761869[/C][C]218.608834460005[/C][/ROW]
[ROW][C]Trimmed Mean ( 37 / 40 )[/C][C]7.92765957446808[/C][C]0.0351686997720891[/C][C]225.418045757828[/C][/ROW]
[ROW][C]Trimmed Mean ( 38 / 40 )[/C][C]7.93111111111111[/C][C]0.0337582346440846[/C][C]234.938562242054[/C][/ROW]
[ROW][C]Trimmed Mean ( 39 / 40 )[/C][C]7.93488372093023[/C][C]0.0318988783151632[/C][C]248.751183114749[/C][/ROW]
[ROW][C]Trimmed Mean ( 40 / 40 )[/C][C]7.93658536585366[/C][C]0.030394980643267[/C][C]261.114999841651[/C][/ROW]
[ROW][C]Median[/C][C]8[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]7.55[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]7.88666666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]7.88666666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]7.88666666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]7.88666666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]7.88666666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]7.88666666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]7.88666666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]7.88666666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]121[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=115046&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=115046&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 Mean7.78925619834710.0621891902958961125.250966627574
Geometric Mean7.75818115708727
Harmonic Mean7.72583262373508
Quadratic Mean7.81899044444025
Winsorized Mean ( 1 / 40 )7.78925619834710.0621891902958961125.250966627574
Winsorized Mean ( 2 / 40 )7.785950413223140.0617837001105009126.019490566248
Winsorized Mean ( 3 / 40 )7.785950413223140.0617837001105009126.019490566248
Winsorized Mean ( 4 / 40 )7.785950413223140.0617837001105009126.019490566248
Winsorized Mean ( 5 / 40 )7.794214876033060.0602142355318931129.44139881847
Winsorized Mean ( 6 / 40 )7.794214876033060.0602142355318931129.44139881847
Winsorized Mean ( 7 / 40 )7.794214876033060.0602142355318931129.44139881847
Winsorized Mean ( 8 / 40 )7.794214876033060.0602142355318931129.44139881847
Winsorized Mean ( 9 / 40 )7.801652892561980.058915631313346132.420763703074
Winsorized Mean ( 10 / 40 )7.80991735537190.0575486972933541135.709715817908
Winsorized Mean ( 11 / 40 )7.80991735537190.0575486972933541135.709715817908
Winsorized Mean ( 12 / 40 )7.80991735537190.0549029316066554142.249550740296
Winsorized Mean ( 13 / 40 )7.80991735537190.0549029316066554142.249550740296
Winsorized Mean ( 14 / 40 )7.80991735537190.0549029316066554142.249550740296
Winsorized Mean ( 15 / 40 )7.822314049586780.0530539462874783147.440757888221
Winsorized Mean ( 16 / 40 )7.822314049586780.0530539462874783147.440757888221
Winsorized Mean ( 17 / 40 )7.836363636363640.0510765643617231153.42385953892
Winsorized Mean ( 18 / 40 )7.836363636363640.0510765643617231153.42385953892
Winsorized Mean ( 19 / 40 )7.836363636363640.0510765643617231153.42385953892
Winsorized Mean ( 20 / 40 )7.836363636363640.0510765643617231153.42385953892
Winsorized Mean ( 21 / 40 )7.853719008264460.0487734025527831161.024628121138
Winsorized Mean ( 22 / 40 )7.853719008264460.0487734025527831161.024628121138
Winsorized Mean ( 23 / 40 )7.853719008264460.0443508631995847177.081536675435
Winsorized Mean ( 24 / 40 )7.853719008264460.0443508631995847177.081536675435
Winsorized Mean ( 25 / 40 )7.853719008264460.0443508631995847177.081536675435
Winsorized Mean ( 26 / 40 )7.853719008264460.0443508631995847177.081536675435
Winsorized Mean ( 27 / 40 )7.853719008264460.0443508631995847177.081536675435
Winsorized Mean ( 28 / 40 )7.853719008264460.0443508631995847177.081536675435
Winsorized Mean ( 29 / 40 )7.853719008264460.0443508631995847177.081536675435
Winsorized Mean ( 30 / 40 )7.853719008264460.0443508631995847177.081536675435
Winsorized Mean ( 31 / 40 )7.87933884297520.0412764207960841190.892007858461
Winsorized Mean ( 32 / 40 )7.87933884297520.0412764207960841190.892007858461
Winsorized Mean ( 33 / 40 )7.87933884297520.0412764207960841190.892007858461
Winsorized Mean ( 34 / 40 )7.851239669421490.0384284190651245204.308162043201
Winsorized Mean ( 35 / 40 )7.88016528925620.0350446357391817224.860813161364
Winsorized Mean ( 36 / 40 )7.88016528925620.0350446357391817224.860813161364
Winsorized Mean ( 37 / 40 )7.88016528925620.0350446357391817224.860813161364
Winsorized Mean ( 38 / 40 )7.88016528925620.0350446357391817224.860813161364
Winsorized Mean ( 39 / 40 )7.912396694214880.0314386509134663251.677360965439
Winsorized Mean ( 40 / 40 )7.87933884297520.0281651308212153279.755094801126
Trimmed Mean ( 1 / 40 )7.793277310924370.061386569488755126.954110252927
Trimmed Mean ( 2 / 40 )7.79743589743590.0604953218416412128.893204632373
Trimmed Mean ( 3 / 40 )7.803478260869570.0597340972301691130.636916312655
Trimmed Mean ( 4 / 40 )7.809734513274340.0588818671228164132.633948189596
Trimmed Mean ( 5 / 40 )7.816216216216220.0579267879388989134.932670951145
Trimmed Mean ( 6 / 40 )7.821100917431190.057278186776646136.545888715529
Trimmed Mean ( 7 / 40 )7.826168224299070.0565469743165114138.401184482365
Trimmed Mean ( 8 / 40 )7.831428571428570.0557222686119018140.5439650344
Trimmed Mean ( 9 / 40 )7.83689320388350.0547911996512886143.031969618486
Trimmed Mean ( 10 / 40 )7.841584158415840.0539759265505965145.279287629555
Trimmed Mean ( 11 / 40 )7.845454545454550.053283695346715147.239310156784
Trimmed Mean ( 12 / 40 )7.849484536082470.0524961893425621149.524844267475
Trimmed Mean ( 13 / 40 )7.853684210526320.0519886826842824151.065266612356
Trimmed Mean ( 14 / 40 )7.858064516129030.0514020940266571152.874404534061
Trimmed Mean ( 15 / 40 )7.862637362637360.0507248641963399155.005587244228
Trimmed Mean ( 16 / 40 )7.866292134831460.0502024456281748156.691412866482
Trimmed Mean ( 17 / 40 )7.870114942528740.0495937773247987158.691581223707
Trimmed Mean ( 18 / 40 )7.872941176470590.0491492962325158160.184209743823
Trimmed Mean ( 19 / 40 )7.875903614457830.0486246444001173161.973495366864
Trimmed Mean ( 20 / 40 )7.879012345679010.0480070741116501164.121902687816
Trimmed Mean ( 21 / 40 )7.882278481012660.047281141151325166.710834152355
Trimmed Mean ( 22 / 40 )7.884415584415580.0467342560352314168.707416214603
Trimmed Mean ( 23 / 40 )7.886666666666670.0460838770474417171.137221344194
Trimmed Mean ( 24 / 40 )7.889041095890410.0458540486119615172.046773070164
Trimmed Mean ( 25 / 40 )7.891549295774650.0455569813176158173.223709463014
Trimmed Mean ( 26 / 40 )7.894202898550720.0451805159276019174.725824539068
Trimmed Mean ( 27 / 40 )7.897014925373130.0447097352013154176.628532685669
Trimmed Mean ( 28 / 40 )7.90.0441261304060914179.03224069948
Trimmed Mean ( 29 / 40 )7.90317460317460.043406428600753182.073827724161
Trimmed Mean ( 30 / 40 )7.906557377049180.0425208950537202185.945224508096
Trimmed Mean ( 31 / 40 )7.906557377049180.0414307894818673190.837719385231
Trimmed Mean ( 32 / 40 )7.912280701754390.0405993764720102194.886754165036
Trimmed Mean ( 33 / 40 )7.914545454545450.0395614155645275200.057185558395
Trimmed Mean ( 34 / 40 )7.916981132075470.0382619351648451206.915334991983
Trimmed Mean ( 35 / 40 )7.921568627450980.0370811220392238213.628072502004
Trimmed Mean ( 36 / 40 )7.924489795918370.0362496319761869218.608834460005
Trimmed Mean ( 37 / 40 )7.927659574468080.0351686997720891225.418045757828
Trimmed Mean ( 38 / 40 )7.931111111111110.0337582346440846234.938562242054
Trimmed Mean ( 39 / 40 )7.934883720930230.0318988783151632248.751183114749
Trimmed Mean ( 40 / 40 )7.936585365853660.030394980643267261.114999841651
Median8
Midrange7.55
Midmean - Weighted Average at Xnp7.88666666666667
Midmean - Weighted Average at X(n+1)p7.88666666666667
Midmean - Empirical Distribution Function7.88666666666667
Midmean - Empirical Distribution Function - Averaging7.88666666666667
Midmean - Empirical Distribution Function - Interpolation7.88666666666667
Midmean - Closest Observation7.88666666666667
Midmean - True Basic - Statistics Graphics Toolkit7.88666666666667
Midmean - MS Excel (old versions)7.88666666666667
Number of observations121



Parameters (Session):
Parameters (R input):
par1 = ; par2 = ; par3 = ; par4 = ; par5 = ; par6 = ; par7 = ; par8 = ; par9 = ; par10 = ; par11 = ; par12 = ; par13 = ; par14 = ; par15 = ; par16 = ; par17 = ; par18 = ; par19 = ; par20 = ;
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')