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Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationSun, 15 Jan 2012 04:37:20 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2012/Jan/15/t1326621082za1q1o8z9hplri1.htm/, Retrieved Fri, 03 May 2024 14:07:14 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=161052, Retrieved Fri, 03 May 2024 14:07:14 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDG2011W52a
Estimated Impact112
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [] [2012-01-15 09:37:20] [f7653f7e39425878158499028a118a95] [Current]
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Dataseries X:
5,82
5,85
5,87
5,88
5,9
5,91
5,94
5,97
5,98
6
6,01
6,02
6,11
6,13
6,15
6,15
6,16
6,18
6,21
6,22
6,23
6,26
6,28
6,28
6,29
6,32
6,36
6,37
6,38
6,38
6,4
6,41
6,42
6,43
6,44
6,47
6,47
6,48
6,51
6,54
6,56
6,57
6,6
6,62
6,65
6,71
6,76
6,78
6,8
6,83
6,86
6,86
6,87
6,88
6,9
6,92
6,93
6,94
6,96
6,98
6,99
7,01
7,06
7,07
7,08
7,08
7,1
7,11
7,22
7,24
7,25
7,26




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Herman Ole Andreas Wold' @ wold.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 1 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=161052&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]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=161052&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=161052&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 time1 seconds
R Server'Herman Ole Andreas Wold' @ wold.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean6.522638888888890.0487215239474019133.87592095704
Geometric Mean6.50972534997145
Harmonic Mean6.49683413496915
Quadratic Mean6.53554565009261
Winsorized Mean ( 1 / 24 )6.522916666666670.0486091520955585134.191122154189
Winsorized Mean ( 2 / 24 )6.523194444444440.0484440315582684134.654243972209
Winsorized Mean ( 3 / 24 )6.522777777777780.0481935903691466135.345337996516
Winsorized Mean ( 4 / 24 )6.517777777777780.046817839576286139.215688651279
Winsorized Mean ( 5 / 24 )6.517777777777780.0465664678087902139.967192799352
Winsorized Mean ( 6 / 24 )6.518611111111110.0458237529703683142.25397721846
Winsorized Mean ( 7 / 24 )6.521527777777780.0453143514018069143.91749139143
Winsorized Mean ( 8 / 24 )6.521527777777780.0449328571089605145.139396810742
Winsorized Mean ( 9 / 24 )6.522777777777780.0442986654588239147.245469140392
Winsorized Mean ( 10 / 24 )6.517222222222220.0429124660518765151.872470212819
Winsorized Mean ( 11 / 24 )6.515694444444440.0421696525084039154.511456862158
Winsorized Mean ( 12 / 24 )6.529027777777780.0395386934956383165.130083989701
Winsorized Mean ( 13 / 24 )6.529027777777780.0384297418616735169.895176534851
Winsorized Mean ( 14 / 24 )6.529027777777780.0372573840357675175.241175588437
Winsorized Mean ( 15 / 24 )6.526944444444440.03693544197092176.71223345813
Winsorized Mean ( 16 / 24 )6.526944444444450.0362770803758814179.919232110637
Winsorized Mean ( 17 / 24 )6.526944444444440.0348940038663532187.050602431385
Winsorized Mean ( 18 / 24 )6.529444444444440.0331095119925577197.207510817801
Winsorized Mean ( 19 / 24 )6.529444444444440.0323601414014444201.774286565787
Winsorized Mean ( 20 / 24 )6.529444444444440.0315768982685147206.779158260612
Winsorized Mean ( 21 / 24 )6.538194444444440.0304288122184193214.868539643053
Winsorized Mean ( 22 / 24 )6.535138888888890.0282911817465239230.995613666504
Winsorized Mean ( 23 / 24 )6.525555555555560.0268988490198935242.59608843224
Winsorized Mean ( 24 / 24 )6.522222222222220.025517509271668255.597917209883
Trimmed Mean ( 1 / 24 )6.522142857142860.0479332234168334136.067270094178
Trimmed Mean ( 2 / 24 )6.521323529411760.0471202785455388138.397389207055
Trimmed Mean ( 3 / 24 )6.520303030303030.0462460076759708140.991695455929
Trimmed Mean ( 4 / 24 )6.5193750.0453036903039778143.903839979843
Trimmed Mean ( 5 / 24 )6.519838709677420.0446589354422222145.991807577064
Trimmed Mean ( 6 / 24 )6.520333333333330.0439388163892404148.395743653441
Trimmed Mean ( 7 / 24 )6.520689655172410.043251023835897150.763821913516
Trimmed Mean ( 8 / 24 )6.520535714285710.0425192237981048153.355003497885
Trimmed Mean ( 9 / 24 )6.520370370370370.041689480515734156.403253043883
Trimmed Mean ( 10 / 24 )6.520.0407887912323481159.847835716917
Trimmed Mean ( 11 / 24 )6.52040.0399591219694756163.176758612986
Trimmed Mean ( 12 / 24 )6.521041666666670.0390549253885348166.971044030749
Trimmed Mean ( 13 / 24 )6.520.0384569525322487169.54021498538
Trimmed Mean ( 14 / 24 )6.518863636363640.0378857410813401172.066414706466
Trimmed Mean ( 15 / 24 )6.517619047619050.0373494803783228174.503607054244
Trimmed Mean ( 16 / 24 )6.51650.0366629660137185177.740666086908
Trimmed Mean ( 17 / 24 )6.515263157894740.0358492513915567181.740563749379
Trimmed Mean ( 18 / 24 )6.513888888888890.0350334936740877185.933180101499
Trimmed Mean ( 19 / 24 )6.512058823529410.034299143833254189.860681514032
Trimmed Mean ( 20 / 24 )6.510.0333964456289163194.930923857458
Trimmed Mean ( 21 / 24 )6.507666666666670.0322585935564083201.73435817303
Trimmed Mean ( 22 / 24 )6.503928571428570.0308492635197791210.82929799146
Trimmed Mean ( 23 / 24 )6.50.0294200350363228220.937874206299
Trimmed Mean ( 24 / 24 )6.496666666666670.0277127257605982234.429002862778
Median6.47
Midrange6.54
Midmean - Weighted Average at Xnp6.50486486486487
Midmean - Weighted Average at X(n+1)p6.51388888888889
Midmean - Empirical Distribution Function6.50486486486487
Midmean - Empirical Distribution Function - Averaging6.51388888888889
Midmean - Empirical Distribution Function - Interpolation6.51388888888889
Midmean - Closest Observation6.50486486486487
Midmean - True Basic - Statistics Graphics Toolkit6.51388888888889
Midmean - MS Excel (old versions)6.51526315789474
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 6.52263888888889 & 0.0487215239474019 & 133.87592095704 \tabularnewline
Geometric Mean & 6.50972534997145 &  &  \tabularnewline
Harmonic Mean & 6.49683413496915 &  &  \tabularnewline
Quadratic Mean & 6.53554565009261 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 6.52291666666667 & 0.0486091520955585 & 134.191122154189 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 6.52319444444444 & 0.0484440315582684 & 134.654243972209 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 6.52277777777778 & 0.0481935903691466 & 135.345337996516 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 6.51777777777778 & 0.046817839576286 & 139.215688651279 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 6.51777777777778 & 0.0465664678087902 & 139.967192799352 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 6.51861111111111 & 0.0458237529703683 & 142.25397721846 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 6.52152777777778 & 0.0453143514018069 & 143.91749139143 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 6.52152777777778 & 0.0449328571089605 & 145.139396810742 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 6.52277777777778 & 0.0442986654588239 & 147.245469140392 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 6.51722222222222 & 0.0429124660518765 & 151.872470212819 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 6.51569444444444 & 0.0421696525084039 & 154.511456862158 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 6.52902777777778 & 0.0395386934956383 & 165.130083989701 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 6.52902777777778 & 0.0384297418616735 & 169.895176534851 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 6.52902777777778 & 0.0372573840357675 & 175.241175588437 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 6.52694444444444 & 0.03693544197092 & 176.71223345813 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 6.52694444444445 & 0.0362770803758814 & 179.919232110637 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 6.52694444444444 & 0.0348940038663532 & 187.050602431385 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 6.52944444444444 & 0.0331095119925577 & 197.207510817801 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 6.52944444444444 & 0.0323601414014444 & 201.774286565787 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 6.52944444444444 & 0.0315768982685147 & 206.779158260612 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 6.53819444444444 & 0.0304288122184193 & 214.868539643053 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 6.53513888888889 & 0.0282911817465239 & 230.995613666504 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 6.52555555555556 & 0.0268988490198935 & 242.59608843224 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 6.52222222222222 & 0.025517509271668 & 255.597917209883 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 6.52214285714286 & 0.0479332234168334 & 136.067270094178 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 6.52132352941176 & 0.0471202785455388 & 138.397389207055 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 6.52030303030303 & 0.0462460076759708 & 140.991695455929 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 6.519375 & 0.0453036903039778 & 143.903839979843 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 6.51983870967742 & 0.0446589354422222 & 145.991807577064 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 6.52033333333333 & 0.0439388163892404 & 148.395743653441 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 6.52068965517241 & 0.043251023835897 & 150.763821913516 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 6.52053571428571 & 0.0425192237981048 & 153.355003497885 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 6.52037037037037 & 0.041689480515734 & 156.403253043883 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 6.52 & 0.0407887912323481 & 159.847835716917 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 6.5204 & 0.0399591219694756 & 163.176758612986 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 6.52104166666667 & 0.0390549253885348 & 166.971044030749 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 6.52 & 0.0384569525322487 & 169.54021498538 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 6.51886363636364 & 0.0378857410813401 & 172.066414706466 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 6.51761904761905 & 0.0373494803783228 & 174.503607054244 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 6.5165 & 0.0366629660137185 & 177.740666086908 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 6.51526315789474 & 0.0358492513915567 & 181.740563749379 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 6.51388888888889 & 0.0350334936740877 & 185.933180101499 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 6.51205882352941 & 0.034299143833254 & 189.860681514032 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 6.51 & 0.0333964456289163 & 194.930923857458 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 6.50766666666667 & 0.0322585935564083 & 201.73435817303 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 6.50392857142857 & 0.0308492635197791 & 210.82929799146 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 6.5 & 0.0294200350363228 & 220.937874206299 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 6.49666666666667 & 0.0277127257605982 & 234.429002862778 \tabularnewline
Median & 6.47 &  &  \tabularnewline
Midrange & 6.54 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 6.50486486486487 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 6.51388888888889 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 6.50486486486487 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 6.51388888888889 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 6.51388888888889 &  &  \tabularnewline
Midmean - Closest Observation & 6.50486486486487 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 6.51388888888889 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 6.51526315789474 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=161052&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]6.52263888888889[/C][C]0.0487215239474019[/C][C]133.87592095704[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]6.50972534997145[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]6.49683413496915[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]6.53554565009261[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]6.52291666666667[/C][C]0.0486091520955585[/C][C]134.191122154189[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]6.52319444444444[/C][C]0.0484440315582684[/C][C]134.654243972209[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]6.52277777777778[/C][C]0.0481935903691466[/C][C]135.345337996516[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]6.51777777777778[/C][C]0.046817839576286[/C][C]139.215688651279[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]6.51777777777778[/C][C]0.0465664678087902[/C][C]139.967192799352[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]6.51861111111111[/C][C]0.0458237529703683[/C][C]142.25397721846[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]6.52152777777778[/C][C]0.0453143514018069[/C][C]143.91749139143[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]6.52152777777778[/C][C]0.0449328571089605[/C][C]145.139396810742[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]6.52277777777778[/C][C]0.0442986654588239[/C][C]147.245469140392[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]6.51722222222222[/C][C]0.0429124660518765[/C][C]151.872470212819[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]6.51569444444444[/C][C]0.0421696525084039[/C][C]154.511456862158[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]6.52902777777778[/C][C]0.0395386934956383[/C][C]165.130083989701[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]6.52902777777778[/C][C]0.0384297418616735[/C][C]169.895176534851[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]6.52902777777778[/C][C]0.0372573840357675[/C][C]175.241175588437[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]6.52694444444444[/C][C]0.03693544197092[/C][C]176.71223345813[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]6.52694444444445[/C][C]0.0362770803758814[/C][C]179.919232110637[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]6.52694444444444[/C][C]0.0348940038663532[/C][C]187.050602431385[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]6.52944444444444[/C][C]0.0331095119925577[/C][C]197.207510817801[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]6.52944444444444[/C][C]0.0323601414014444[/C][C]201.774286565787[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]6.52944444444444[/C][C]0.0315768982685147[/C][C]206.779158260612[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]6.53819444444444[/C][C]0.0304288122184193[/C][C]214.868539643053[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]6.53513888888889[/C][C]0.0282911817465239[/C][C]230.995613666504[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]6.52555555555556[/C][C]0.0268988490198935[/C][C]242.59608843224[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]6.52222222222222[/C][C]0.025517509271668[/C][C]255.597917209883[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]6.52214285714286[/C][C]0.0479332234168334[/C][C]136.067270094178[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]6.52132352941176[/C][C]0.0471202785455388[/C][C]138.397389207055[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]6.52030303030303[/C][C]0.0462460076759708[/C][C]140.991695455929[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]6.519375[/C][C]0.0453036903039778[/C][C]143.903839979843[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]6.51983870967742[/C][C]0.0446589354422222[/C][C]145.991807577064[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]6.52033333333333[/C][C]0.0439388163892404[/C][C]148.395743653441[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]6.52068965517241[/C][C]0.043251023835897[/C][C]150.763821913516[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]6.52053571428571[/C][C]0.0425192237981048[/C][C]153.355003497885[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]6.52037037037037[/C][C]0.041689480515734[/C][C]156.403253043883[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]6.52[/C][C]0.0407887912323481[/C][C]159.847835716917[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]6.5204[/C][C]0.0399591219694756[/C][C]163.176758612986[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]6.52104166666667[/C][C]0.0390549253885348[/C][C]166.971044030749[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]6.52[/C][C]0.0384569525322487[/C][C]169.54021498538[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]6.51886363636364[/C][C]0.0378857410813401[/C][C]172.066414706466[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]6.51761904761905[/C][C]0.0373494803783228[/C][C]174.503607054244[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]6.5165[/C][C]0.0366629660137185[/C][C]177.740666086908[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]6.51526315789474[/C][C]0.0358492513915567[/C][C]181.740563749379[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]6.51388888888889[/C][C]0.0350334936740877[/C][C]185.933180101499[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]6.51205882352941[/C][C]0.034299143833254[/C][C]189.860681514032[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]6.51[/C][C]0.0333964456289163[/C][C]194.930923857458[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]6.50766666666667[/C][C]0.0322585935564083[/C][C]201.73435817303[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]6.50392857142857[/C][C]0.0308492635197791[/C][C]210.82929799146[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]6.5[/C][C]0.0294200350363228[/C][C]220.937874206299[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]6.49666666666667[/C][C]0.0277127257605982[/C][C]234.429002862778[/C][/ROW]
[ROW][C]Median[/C][C]6.47[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]6.54[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]6.50486486486487[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]6.51388888888889[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]6.50486486486487[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]6.51388888888889[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]6.51388888888889[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]6.50486486486487[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]6.51388888888889[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]6.51526315789474[/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=161052&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=161052&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 Mean6.522638888888890.0487215239474019133.87592095704
Geometric Mean6.50972534997145
Harmonic Mean6.49683413496915
Quadratic Mean6.53554565009261
Winsorized Mean ( 1 / 24 )6.522916666666670.0486091520955585134.191122154189
Winsorized Mean ( 2 / 24 )6.523194444444440.0484440315582684134.654243972209
Winsorized Mean ( 3 / 24 )6.522777777777780.0481935903691466135.345337996516
Winsorized Mean ( 4 / 24 )6.517777777777780.046817839576286139.215688651279
Winsorized Mean ( 5 / 24 )6.517777777777780.0465664678087902139.967192799352
Winsorized Mean ( 6 / 24 )6.518611111111110.0458237529703683142.25397721846
Winsorized Mean ( 7 / 24 )6.521527777777780.0453143514018069143.91749139143
Winsorized Mean ( 8 / 24 )6.521527777777780.0449328571089605145.139396810742
Winsorized Mean ( 9 / 24 )6.522777777777780.0442986654588239147.245469140392
Winsorized Mean ( 10 / 24 )6.517222222222220.0429124660518765151.872470212819
Winsorized Mean ( 11 / 24 )6.515694444444440.0421696525084039154.511456862158
Winsorized Mean ( 12 / 24 )6.529027777777780.0395386934956383165.130083989701
Winsorized Mean ( 13 / 24 )6.529027777777780.0384297418616735169.895176534851
Winsorized Mean ( 14 / 24 )6.529027777777780.0372573840357675175.241175588437
Winsorized Mean ( 15 / 24 )6.526944444444440.03693544197092176.71223345813
Winsorized Mean ( 16 / 24 )6.526944444444450.0362770803758814179.919232110637
Winsorized Mean ( 17 / 24 )6.526944444444440.0348940038663532187.050602431385
Winsorized Mean ( 18 / 24 )6.529444444444440.0331095119925577197.207510817801
Winsorized Mean ( 19 / 24 )6.529444444444440.0323601414014444201.774286565787
Winsorized Mean ( 20 / 24 )6.529444444444440.0315768982685147206.779158260612
Winsorized Mean ( 21 / 24 )6.538194444444440.0304288122184193214.868539643053
Winsorized Mean ( 22 / 24 )6.535138888888890.0282911817465239230.995613666504
Winsorized Mean ( 23 / 24 )6.525555555555560.0268988490198935242.59608843224
Winsorized Mean ( 24 / 24 )6.522222222222220.025517509271668255.597917209883
Trimmed Mean ( 1 / 24 )6.522142857142860.0479332234168334136.067270094178
Trimmed Mean ( 2 / 24 )6.521323529411760.0471202785455388138.397389207055
Trimmed Mean ( 3 / 24 )6.520303030303030.0462460076759708140.991695455929
Trimmed Mean ( 4 / 24 )6.5193750.0453036903039778143.903839979843
Trimmed Mean ( 5 / 24 )6.519838709677420.0446589354422222145.991807577064
Trimmed Mean ( 6 / 24 )6.520333333333330.0439388163892404148.395743653441
Trimmed Mean ( 7 / 24 )6.520689655172410.043251023835897150.763821913516
Trimmed Mean ( 8 / 24 )6.520535714285710.0425192237981048153.355003497885
Trimmed Mean ( 9 / 24 )6.520370370370370.041689480515734156.403253043883
Trimmed Mean ( 10 / 24 )6.520.0407887912323481159.847835716917
Trimmed Mean ( 11 / 24 )6.52040.0399591219694756163.176758612986
Trimmed Mean ( 12 / 24 )6.521041666666670.0390549253885348166.971044030749
Trimmed Mean ( 13 / 24 )6.520.0384569525322487169.54021498538
Trimmed Mean ( 14 / 24 )6.518863636363640.0378857410813401172.066414706466
Trimmed Mean ( 15 / 24 )6.517619047619050.0373494803783228174.503607054244
Trimmed Mean ( 16 / 24 )6.51650.0366629660137185177.740666086908
Trimmed Mean ( 17 / 24 )6.515263157894740.0358492513915567181.740563749379
Trimmed Mean ( 18 / 24 )6.513888888888890.0350334936740877185.933180101499
Trimmed Mean ( 19 / 24 )6.512058823529410.034299143833254189.860681514032
Trimmed Mean ( 20 / 24 )6.510.0333964456289163194.930923857458
Trimmed Mean ( 21 / 24 )6.507666666666670.0322585935564083201.73435817303
Trimmed Mean ( 22 / 24 )6.503928571428570.0308492635197791210.82929799146
Trimmed Mean ( 23 / 24 )6.50.0294200350363228220.937874206299
Trimmed Mean ( 24 / 24 )6.496666666666670.0277127257605982234.429002862778
Median6.47
Midrange6.54
Midmean - Weighted Average at Xnp6.50486486486487
Midmean - Weighted Average at X(n+1)p6.51388888888889
Midmean - Empirical Distribution Function6.50486486486487
Midmean - Empirical Distribution Function - Averaging6.51388888888889
Midmean - Empirical Distribution Function - Interpolation6.51388888888889
Midmean - Closest Observation6.50486486486487
Midmean - True Basic - Statistics Graphics Toolkit6.51388888888889
Midmean - MS Excel (old versions)6.51526315789474
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')