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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 computationSat, 13 Oct 2012 10:35:52 -0400
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/Oct/13/t13501390647wtffqafqx2hn83.htm/, Retrieved Fri, 03 May 2024 13:03:16 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=175845, Retrieved Fri, 03 May 2024 13:03:16 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact119
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [Melkchocola] [2012-10-13 14:35:52] [a65efd8010de7ce8a50260769e922377] [Current]
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Dataseries X:
8,41
8,39
8,43
8,44
8,49
8,47
8,53
8,52
8,51
8,53
8,54
8,53
8,47
8,63
8,67
8,73
8,57
8,55
8,63
8,65
8,44
8,62
8,37
8,59
8,84
8,72
8,8
8,69
8,68
8,57
8,85
8,85
8,85
8,93
8,75
8,78
8,77
9,03
9,01
9,07
8,99
9,02
8,99
8,98
8,94
8,94
8,75
8,86
8,87
8,84
8,84
9,91
10,18
10,34
10,36
10,26
10,16
10,31
10,46
10,54
10,47
10,48
10,46
11,3
11,58
11,69
11,63
11,51
11,37
11,42
11,7
11,75




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'George Udny Yule' @ yule.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 & 'George Udny Yule' @ yule.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=175845&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]'George Udny Yule' @ yule.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=175845&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=175845&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'George Udny Yule' @ yule.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean9.330555555555560.1241567628291675.1514081306583
Geometric Mean9.27627651810032
Harmonic Mean9.22628382467573
Quadratic Mean9.38902151451364
Winsorized Mean ( 1 / 24 )9.330138888888890.12393797559277775.280710728606
Winsorized Mean ( 2 / 24 )9.330416666666670.12380452395846575.3641011518845
Winsorized Mean ( 3 / 24 )9.328750.12305321849255875.8106948707254
Winsorized Mean ( 4 / 24 )9.326527777777780.1222698981828876.2782002470306
Winsorized Mean ( 5 / 24 )9.321666666666670.12101988998308577.0259059727253
Winsorized Mean ( 6 / 24 )9.316666666666670.11887645643096878.3726815753204
Winsorized Mean ( 7 / 24 )9.311805555555560.11767194763796179.1336061182991
Winsorized Mean ( 8 / 24 )9.306250.11554616808918480.5413987663963
Winsorized Mean ( 9 / 24 )9.213750.094101765723107397.9126154456154
Winsorized Mean ( 10 / 24 )9.206805555555550.09231923639207699.7279214534946
Winsorized Mean ( 11 / 24 )9.206805555555550.0918636011716424100.222562996993
Winsorized Mean ( 12 / 24 )9.205138888888890.0915413127220759100.557208708992
Winsorized Mean ( 13 / 24 )9.205138888888890.0915413127220759100.557208708992
Winsorized Mean ( 14 / 24 )9.187638888888890.0876290671291747104.846932529195
Winsorized Mean ( 15 / 24 )9.185555555555560.0866293908842721106.032784737301
Winsorized Mean ( 16 / 24 )9.183333333333330.0849251718869694108.134409731379
Winsorized Mean ( 17 / 24 )9.171527777777780.0827282397248622110.863325610221
Winsorized Mean ( 18 / 24 )9.156527777777780.0785289136972613116.600718724791
Winsorized Mean ( 19 / 24 )9.159166666666670.0767660485685733119.312727924051
Winsorized Mean ( 20 / 24 )9.09250.0638384079670569142.42993034369
Winsorized Mean ( 21 / 24 )8.84750.0220592370086137401.079148682488
Winsorized Mean ( 22 / 24 )8.841388888888890.0195101449830493453.168794828045
Winsorized Mean ( 23 / 24 )8.844583333333330.0182026257155965485.896016955127
Winsorized Mean ( 24 / 24 )8.844583333333330.0173034880967101511.144532472325
Trimmed Mean ( 1 / 24 )9.309714285714290.12208861653281876.2537454358968
Trimmed Mean ( 2 / 24 )9.288088235294120.11981388430555777.5209675333371
Trimmed Mean ( 3 / 24 )9.2650.11710140446527179.1194609689567
Trimmed Mean ( 4 / 24 )9.241093750.11410954366629180.9844072028298
Trimmed Mean ( 5 / 24 )9.216290322580650.11070449702760483.2512731644731
Trimmed Mean ( 6 / 24 )9.1910.10689260146795785.9835000157156
Trimmed Mean ( 7 / 24 )9.1650.10277553231361789.1749212451974
Trimmed Mean ( 8 / 24 )9.138035714285710.097924705916111793.3169584610641
Trimmed Mean ( 9 / 24 )9.110.092330642741716898.6671350862797
Trimmed Mean ( 10 / 24 )9.094038461538460.091039439026027799.8911961544329
Trimmed Mean ( 11 / 24 )9.07780.0897085029983451101.192191337397
Trimmed Mean ( 12 / 24 )9.060208333333330.0879824539161305102.977445275282
Trimmed Mean ( 13 / 24 )9.041304347826090.0857096597105359105.487577227129
Trimmed Mean ( 14 / 24 )9.020681818181820.0826160518416998109.188004232716
Trimmed Mean ( 15 / 24 )9.00023809523810.0794555282119645113.273906772453
Trimmed Mean ( 16 / 24 )8.9780.0753361696765801119.172504237244
Trimmed Mean ( 17 / 24 )8.953684210526320.0700065238299454127.897854666744
Trimmed Mean ( 18 / 24 )8.928055555555560.0630782072452673141.539462604581
Trimmed Mean ( 19 / 24 )8.901176470588230.0542913588057736163.951992847187
Trimmed Mean ( 20 / 24 )8.8706250.0403311331655751219.944849146256
Trimmed Mean ( 21 / 24 )8.8440.0228468162222716387.099887965075
Trimmed Mean ( 22 / 24 )8.843571428571430.0217380648133447406.824227662735
Trimmed Mean ( 23 / 24 )8.843846153846150.0209400383739045422.341449233798
Trimmed Mean ( 24 / 24 )8.843750.0201337241419983439.250579655664
Median8.845
Midrange10.06
Midmean - Weighted Average at Xnp8.90921052631579
Midmean - Weighted Average at X(n+1)p8.92805555555556
Midmean - Empirical Distribution Function8.90921052631579
Midmean - Empirical Distribution Function - Averaging8.92805555555556
Midmean - Empirical Distribution Function - Interpolation8.92805555555556
Midmean - Closest Observation8.90921052631579
Midmean - True Basic - Statistics Graphics Toolkit8.92805555555556
Midmean - MS Excel (old versions)8.94384615384615
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 9.33055555555556 & 0.12415676282916 & 75.1514081306583 \tabularnewline
Geometric Mean & 9.27627651810032 &  &  \tabularnewline
Harmonic Mean & 9.22628382467573 &  &  \tabularnewline
Quadratic Mean & 9.38902151451364 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 9.33013888888889 & 0.123937975592777 & 75.280710728606 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 9.33041666666667 & 0.123804523958465 & 75.3641011518845 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 9.32875 & 0.123053218492558 & 75.8106948707254 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 9.32652777777778 & 0.12226989818288 & 76.2782002470306 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 9.32166666666667 & 0.121019889983085 & 77.0259059727253 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 9.31666666666667 & 0.118876456430968 & 78.3726815753204 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 9.31180555555556 & 0.117671947637961 & 79.1336061182991 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 9.30625 & 0.115546168089184 & 80.5413987663963 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 9.21375 & 0.0941017657231073 & 97.9126154456154 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 9.20680555555555 & 0.092319236392076 & 99.7279214534946 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 9.20680555555555 & 0.0918636011716424 & 100.222562996993 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 9.20513888888889 & 0.0915413127220759 & 100.557208708992 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 9.20513888888889 & 0.0915413127220759 & 100.557208708992 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 9.18763888888889 & 0.0876290671291747 & 104.846932529195 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 9.18555555555556 & 0.0866293908842721 & 106.032784737301 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 9.18333333333333 & 0.0849251718869694 & 108.134409731379 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 9.17152777777778 & 0.0827282397248622 & 110.863325610221 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 9.15652777777778 & 0.0785289136972613 & 116.600718724791 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 9.15916666666667 & 0.0767660485685733 & 119.312727924051 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 9.0925 & 0.0638384079670569 & 142.42993034369 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 8.8475 & 0.0220592370086137 & 401.079148682488 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 8.84138888888889 & 0.0195101449830493 & 453.168794828045 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 8.84458333333333 & 0.0182026257155965 & 485.896016955127 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 8.84458333333333 & 0.0173034880967101 & 511.144532472325 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 9.30971428571429 & 0.122088616532818 & 76.2537454358968 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 9.28808823529412 & 0.119813884305557 & 77.5209675333371 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 9.265 & 0.117101404465271 & 79.1194609689567 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 9.24109375 & 0.114109543666291 & 80.9844072028298 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 9.21629032258065 & 0.110704497027604 & 83.2512731644731 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 9.191 & 0.106892601467957 & 85.9835000157156 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 9.165 & 0.102775532313617 & 89.1749212451974 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 9.13803571428571 & 0.0979247059161117 & 93.3169584610641 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 9.11 & 0.0923306427417168 & 98.6671350862797 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 9.09403846153846 & 0.0910394390260277 & 99.8911961544329 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 9.0778 & 0.0897085029983451 & 101.192191337397 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 9.06020833333333 & 0.0879824539161305 & 102.977445275282 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 9.04130434782609 & 0.0857096597105359 & 105.487577227129 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 9.02068181818182 & 0.0826160518416998 & 109.188004232716 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 9.0002380952381 & 0.0794555282119645 & 113.273906772453 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 8.978 & 0.0753361696765801 & 119.172504237244 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 8.95368421052632 & 0.0700065238299454 & 127.897854666744 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 8.92805555555556 & 0.0630782072452673 & 141.539462604581 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 8.90117647058823 & 0.0542913588057736 & 163.951992847187 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 8.870625 & 0.0403311331655751 & 219.944849146256 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 8.844 & 0.0228468162222716 & 387.099887965075 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 8.84357142857143 & 0.0217380648133447 & 406.824227662735 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 8.84384615384615 & 0.0209400383739045 & 422.341449233798 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 8.84375 & 0.0201337241419983 & 439.250579655664 \tabularnewline
Median & 8.845 &  &  \tabularnewline
Midrange & 10.06 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 8.90921052631579 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 8.92805555555556 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 8.90921052631579 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 8.92805555555556 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 8.92805555555556 &  &  \tabularnewline
Midmean - Closest Observation & 8.90921052631579 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 8.92805555555556 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 8.94384615384615 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=175845&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]9.33055555555556[/C][C]0.12415676282916[/C][C]75.1514081306583[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]9.27627651810032[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]9.22628382467573[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]9.38902151451364[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]9.33013888888889[/C][C]0.123937975592777[/C][C]75.280710728606[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]9.33041666666667[/C][C]0.123804523958465[/C][C]75.3641011518845[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]9.32875[/C][C]0.123053218492558[/C][C]75.8106948707254[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]9.32652777777778[/C][C]0.12226989818288[/C][C]76.2782002470306[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]9.32166666666667[/C][C]0.121019889983085[/C][C]77.0259059727253[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]9.31666666666667[/C][C]0.118876456430968[/C][C]78.3726815753204[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]9.31180555555556[/C][C]0.117671947637961[/C][C]79.1336061182991[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]9.30625[/C][C]0.115546168089184[/C][C]80.5413987663963[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]9.21375[/C][C]0.0941017657231073[/C][C]97.9126154456154[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]9.20680555555555[/C][C]0.092319236392076[/C][C]99.7279214534946[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]9.20680555555555[/C][C]0.0918636011716424[/C][C]100.222562996993[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]9.20513888888889[/C][C]0.0915413127220759[/C][C]100.557208708992[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]9.20513888888889[/C][C]0.0915413127220759[/C][C]100.557208708992[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]9.18763888888889[/C][C]0.0876290671291747[/C][C]104.846932529195[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]9.18555555555556[/C][C]0.0866293908842721[/C][C]106.032784737301[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]9.18333333333333[/C][C]0.0849251718869694[/C][C]108.134409731379[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]9.17152777777778[/C][C]0.0827282397248622[/C][C]110.863325610221[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]9.15652777777778[/C][C]0.0785289136972613[/C][C]116.600718724791[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]9.15916666666667[/C][C]0.0767660485685733[/C][C]119.312727924051[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]9.0925[/C][C]0.0638384079670569[/C][C]142.42993034369[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]8.8475[/C][C]0.0220592370086137[/C][C]401.079148682488[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]8.84138888888889[/C][C]0.0195101449830493[/C][C]453.168794828045[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]8.84458333333333[/C][C]0.0182026257155965[/C][C]485.896016955127[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]8.84458333333333[/C][C]0.0173034880967101[/C][C]511.144532472325[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]9.30971428571429[/C][C]0.122088616532818[/C][C]76.2537454358968[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]9.28808823529412[/C][C]0.119813884305557[/C][C]77.5209675333371[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]9.265[/C][C]0.117101404465271[/C][C]79.1194609689567[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]9.24109375[/C][C]0.114109543666291[/C][C]80.9844072028298[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]9.21629032258065[/C][C]0.110704497027604[/C][C]83.2512731644731[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]9.191[/C][C]0.106892601467957[/C][C]85.9835000157156[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]9.165[/C][C]0.102775532313617[/C][C]89.1749212451974[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]9.13803571428571[/C][C]0.0979247059161117[/C][C]93.3169584610641[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]9.11[/C][C]0.0923306427417168[/C][C]98.6671350862797[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]9.09403846153846[/C][C]0.0910394390260277[/C][C]99.8911961544329[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]9.0778[/C][C]0.0897085029983451[/C][C]101.192191337397[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]9.06020833333333[/C][C]0.0879824539161305[/C][C]102.977445275282[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]9.04130434782609[/C][C]0.0857096597105359[/C][C]105.487577227129[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]9.02068181818182[/C][C]0.0826160518416998[/C][C]109.188004232716[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]9.0002380952381[/C][C]0.0794555282119645[/C][C]113.273906772453[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]8.978[/C][C]0.0753361696765801[/C][C]119.172504237244[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]8.95368421052632[/C][C]0.0700065238299454[/C][C]127.897854666744[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]8.92805555555556[/C][C]0.0630782072452673[/C][C]141.539462604581[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]8.90117647058823[/C][C]0.0542913588057736[/C][C]163.951992847187[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]8.870625[/C][C]0.0403311331655751[/C][C]219.944849146256[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]8.844[/C][C]0.0228468162222716[/C][C]387.099887965075[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]8.84357142857143[/C][C]0.0217380648133447[/C][C]406.824227662735[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]8.84384615384615[/C][C]0.0209400383739045[/C][C]422.341449233798[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]8.84375[/C][C]0.0201337241419983[/C][C]439.250579655664[/C][/ROW]
[ROW][C]Median[/C][C]8.845[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]10.06[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]8.90921052631579[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]8.92805555555556[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]8.90921052631579[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]8.92805555555556[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]8.92805555555556[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]8.90921052631579[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]8.92805555555556[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]8.94384615384615[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]72[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=175845&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=175845&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 Mean9.330555555555560.1241567628291675.1514081306583
Geometric Mean9.27627651810032
Harmonic Mean9.22628382467573
Quadratic Mean9.38902151451364
Winsorized Mean ( 1 / 24 )9.330138888888890.12393797559277775.280710728606
Winsorized Mean ( 2 / 24 )9.330416666666670.12380452395846575.3641011518845
Winsorized Mean ( 3 / 24 )9.328750.12305321849255875.8106948707254
Winsorized Mean ( 4 / 24 )9.326527777777780.1222698981828876.2782002470306
Winsorized Mean ( 5 / 24 )9.321666666666670.12101988998308577.0259059727253
Winsorized Mean ( 6 / 24 )9.316666666666670.11887645643096878.3726815753204
Winsorized Mean ( 7 / 24 )9.311805555555560.11767194763796179.1336061182991
Winsorized Mean ( 8 / 24 )9.306250.11554616808918480.5413987663963
Winsorized Mean ( 9 / 24 )9.213750.094101765723107397.9126154456154
Winsorized Mean ( 10 / 24 )9.206805555555550.09231923639207699.7279214534946
Winsorized Mean ( 11 / 24 )9.206805555555550.0918636011716424100.222562996993
Winsorized Mean ( 12 / 24 )9.205138888888890.0915413127220759100.557208708992
Winsorized Mean ( 13 / 24 )9.205138888888890.0915413127220759100.557208708992
Winsorized Mean ( 14 / 24 )9.187638888888890.0876290671291747104.846932529195
Winsorized Mean ( 15 / 24 )9.185555555555560.0866293908842721106.032784737301
Winsorized Mean ( 16 / 24 )9.183333333333330.0849251718869694108.134409731379
Winsorized Mean ( 17 / 24 )9.171527777777780.0827282397248622110.863325610221
Winsorized Mean ( 18 / 24 )9.156527777777780.0785289136972613116.600718724791
Winsorized Mean ( 19 / 24 )9.159166666666670.0767660485685733119.312727924051
Winsorized Mean ( 20 / 24 )9.09250.0638384079670569142.42993034369
Winsorized Mean ( 21 / 24 )8.84750.0220592370086137401.079148682488
Winsorized Mean ( 22 / 24 )8.841388888888890.0195101449830493453.168794828045
Winsorized Mean ( 23 / 24 )8.844583333333330.0182026257155965485.896016955127
Winsorized Mean ( 24 / 24 )8.844583333333330.0173034880967101511.144532472325
Trimmed Mean ( 1 / 24 )9.309714285714290.12208861653281876.2537454358968
Trimmed Mean ( 2 / 24 )9.288088235294120.11981388430555777.5209675333371
Trimmed Mean ( 3 / 24 )9.2650.11710140446527179.1194609689567
Trimmed Mean ( 4 / 24 )9.241093750.11410954366629180.9844072028298
Trimmed Mean ( 5 / 24 )9.216290322580650.11070449702760483.2512731644731
Trimmed Mean ( 6 / 24 )9.1910.10689260146795785.9835000157156
Trimmed Mean ( 7 / 24 )9.1650.10277553231361789.1749212451974
Trimmed Mean ( 8 / 24 )9.138035714285710.097924705916111793.3169584610641
Trimmed Mean ( 9 / 24 )9.110.092330642741716898.6671350862797
Trimmed Mean ( 10 / 24 )9.094038461538460.091039439026027799.8911961544329
Trimmed Mean ( 11 / 24 )9.07780.0897085029983451101.192191337397
Trimmed Mean ( 12 / 24 )9.060208333333330.0879824539161305102.977445275282
Trimmed Mean ( 13 / 24 )9.041304347826090.0857096597105359105.487577227129
Trimmed Mean ( 14 / 24 )9.020681818181820.0826160518416998109.188004232716
Trimmed Mean ( 15 / 24 )9.00023809523810.0794555282119645113.273906772453
Trimmed Mean ( 16 / 24 )8.9780.0753361696765801119.172504237244
Trimmed Mean ( 17 / 24 )8.953684210526320.0700065238299454127.897854666744
Trimmed Mean ( 18 / 24 )8.928055555555560.0630782072452673141.539462604581
Trimmed Mean ( 19 / 24 )8.901176470588230.0542913588057736163.951992847187
Trimmed Mean ( 20 / 24 )8.8706250.0403311331655751219.944849146256
Trimmed Mean ( 21 / 24 )8.8440.0228468162222716387.099887965075
Trimmed Mean ( 22 / 24 )8.843571428571430.0217380648133447406.824227662735
Trimmed Mean ( 23 / 24 )8.843846153846150.0209400383739045422.341449233798
Trimmed Mean ( 24 / 24 )8.843750.0201337241419983439.250579655664
Median8.845
Midrange10.06
Midmean - Weighted Average at Xnp8.90921052631579
Midmean - Weighted Average at X(n+1)p8.92805555555556
Midmean - Empirical Distribution Function8.90921052631579
Midmean - Empirical Distribution Function - Averaging8.92805555555556
Midmean - Empirical Distribution Function - Interpolation8.92805555555556
Midmean - Closest Observation8.90921052631579
Midmean - True Basic - Statistics Graphics Toolkit8.92805555555556
Midmean - MS Excel (old versions)8.94384615384615
Number of observations72



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')