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of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationMon, 08 Oct 2012 03:45:17 -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/08/t1349682431fdtxmksyv0vlp9c.htm/, Retrieved Thu, 02 May 2024 07:31:24 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=173241, Retrieved Thu, 02 May 2024 07:31:24 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact54
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [Opgave 5: oef 2 e...] [2012-10-08 07:45:17] [d241ff6d22df5f98716704005cba5463] [Current]
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Dataseries X:
7,72
7,67
7,84
7,79
7,83
7,94
8,02
8,06
8,12
8,13
7,97
8,01
8
7,9
7,99
8,02
8,08
8,02
8,07
8,11
8,19
8,16
8,08
8,22
8,15
8,19
8,31
8,3
8,34
8,31
8,38
8,34
8,44
8,64
8,6
8,61
8,54
8,69
8,73
8,91
9,01
9,08
8,94
9,03
9,02
8,96
9,03
8,94
8,95
8,95
8,99
8,93
8,98
8,95
9,02
8,92
9,1
9,06
8,97
8,89
8,99
8,79
8,83
8,61
8,71
8,91
8,91
8,89
8,98
9
8,99
8,88




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ jenkins.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 & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=173241&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]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=173241&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=173241&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'Gwilym Jenkins' @ jenkins.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean8.522638888888890.0520066780710792163.875856043732
Geometric Mean8.51125592494206
Harmonic Mean8.4997702657799
Quadratic Mean8.53389752366669
Winsorized Mean ( 1 / 24 )8.523055555555560.0518079391052991164.512538092522
Winsorized Mean ( 2 / 24 )8.524444444444440.0513167344394068166.114319969246
Winsorized Mean ( 3 / 24 )8.524861111111110.050808792296516167.783187235798
Winsorized Mean ( 4 / 24 )8.525416666666670.0507023971724191168.146224677998
Winsorized Mean ( 5 / 24 )8.528888888888890.0498383755341449171.130956767354
Winsorized Mean ( 6 / 24 )8.532222222222220.0492598671916236173.208388667217
Winsorized Mean ( 7 / 24 )8.534166666666670.0486398528936393175.456259814937
Winsorized Mean ( 8 / 24 )8.535277777777780.0481289072645997177.34202297287
Winsorized Mean ( 9 / 24 )8.535277777777780.0477617048154565178.705467293446
Winsorized Mean ( 10 / 24 )8.536666666666670.0475437365565539179.553970406011
Winsorized Mean ( 11 / 24 )8.538194444444440.0473066968582717180.485956777418
Winsorized Mean ( 12 / 24 )8.536527777777780.0470840488633246181.304029365817
Winsorized Mean ( 13 / 24 )8.536527777777780.0470840488633246181.304029365817
Winsorized Mean ( 14 / 24 )8.542361111111110.0456467577038227187.140588747571
Winsorized Mean ( 15 / 24 )8.542361111111110.0450645047400174189.55852639218
Winsorized Mean ( 16 / 24 )8.542361111111110.0444491115262788192.182943995647
Winsorized Mean ( 17 / 24 )8.542361111111110.0444491115262788192.182943995647
Winsorized Mean ( 18 / 24 )8.549861111111110.0433637907839746197.165906313494
Winsorized Mean ( 19 / 24 )8.549861111111110.0426464580661175200.482326055208
Winsorized Mean ( 20 / 24 )8.552638888888890.0422536092001197202.412031795491
Winsorized Mean ( 21 / 24 )8.555555555555560.0410612775833837208.360676020898
Winsorized Mean ( 22 / 24 )8.555555555555560.0402461561694996212.58068769408
Winsorized Mean ( 23 / 24 )8.561944444444440.038524040260194222.24938990346
Winsorized Mean ( 24 / 24 )8.561944444444440.038524040260194222.24938990346
Trimmed Mean ( 1 / 24 )8.526571428571430.0514086803033245165.858593884582
Trimmed Mean ( 2 / 24 )8.530294117647060.0509074676533069167.564691603609
Trimmed Mean ( 3 / 24 )8.533484848484850.0505860721520151168.692378859562
Trimmed Mean ( 4 / 24 )8.536718750.0503849539613711169.429920617669
Trimmed Mean ( 5 / 24 )8.540.0501357227209817170.337626277521
Trimmed Mean ( 6 / 24 )8.542666666666670.0500451020685802170.699355452609
Trimmed Mean ( 7 / 24 )8.54482758620690.0500291756253427170.796889602923
Trimmed Mean ( 8 / 24 )8.546785714285710.0500895996818644170.629946507243
Trimmed Mean ( 9 / 24 )8.54870370370370.0501987985692734170.296978161871
Trimmed Mean ( 10 / 24 )8.550769230769230.050323123449203169.917299338554
Trimmed Mean ( 11 / 24 )8.55280.0504284014566136169.602837943583
Trimmed Mean ( 12 / 24 )8.554791666666670.0505080479361842169.374822750534
Trimmed Mean ( 13 / 24 )8.557173913043480.0505435795542074169.302886509374
Trimmed Mean ( 14 / 24 )8.559772727272730.0504760515466737169.580869838002
Trimmed Mean ( 15 / 24 )8.561904761904760.050561582712264169.336169926263
Trimmed Mean ( 16 / 24 )8.564250.0506469523471184169.097045391859
Trimmed Mean ( 17 / 24 )8.566842105263160.0507274328289584168.879866918333
Trimmed Mean ( 18 / 24 )8.569722222222220.0506614754720168169.156585795764
Trimmed Mean ( 19 / 24 )8.572058823529410.0506442969635409169.260101087008
Trimmed Mean ( 20 / 24 )8.57468750.050579274202292169.529666750565
Trimmed Mean ( 21 / 24 )8.577333333333330.050359474067473170.322138826176
Trimmed Mean ( 22 / 24 )8.580.0501215453888776171.183867804363
Trimmed Mean ( 23 / 24 )8.583076923076920.0497215917523819172.622730298367
Trimmed Mean ( 24 / 24 )8.585833333333330.0493689036473669173.911768320001
Median8.61
Midrange8.385
Midmean - Weighted Average at Xnp8.56425
Midmean - Weighted Average at X(n+1)p8.58973684210526
Midmean - Empirical Distribution Function8.56425
Midmean - Empirical Distribution Function - Averaging8.58973684210526
Midmean - Empirical Distribution Function - Interpolation8.58973684210526
Midmean - Closest Observation8.56425
Midmean - True Basic - Statistics Graphics Toolkit8.58973684210526
Midmean - MS Excel (old versions)8.56425
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 8.52263888888889 & 0.0520066780710792 & 163.875856043732 \tabularnewline
Geometric Mean & 8.51125592494206 &  &  \tabularnewline
Harmonic Mean & 8.4997702657799 &  &  \tabularnewline
Quadratic Mean & 8.53389752366669 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 8.52305555555556 & 0.0518079391052991 & 164.512538092522 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 8.52444444444444 & 0.0513167344394068 & 166.114319969246 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 8.52486111111111 & 0.050808792296516 & 167.783187235798 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 8.52541666666667 & 0.0507023971724191 & 168.146224677998 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 8.52888888888889 & 0.0498383755341449 & 171.130956767354 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 8.53222222222222 & 0.0492598671916236 & 173.208388667217 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 8.53416666666667 & 0.0486398528936393 & 175.456259814937 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 8.53527777777778 & 0.0481289072645997 & 177.34202297287 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 8.53527777777778 & 0.0477617048154565 & 178.705467293446 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 8.53666666666667 & 0.0475437365565539 & 179.553970406011 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 8.53819444444444 & 0.0473066968582717 & 180.485956777418 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 8.53652777777778 & 0.0470840488633246 & 181.304029365817 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 8.53652777777778 & 0.0470840488633246 & 181.304029365817 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 8.54236111111111 & 0.0456467577038227 & 187.140588747571 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 8.54236111111111 & 0.0450645047400174 & 189.55852639218 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 8.54236111111111 & 0.0444491115262788 & 192.182943995647 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 8.54236111111111 & 0.0444491115262788 & 192.182943995647 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 8.54986111111111 & 0.0433637907839746 & 197.165906313494 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 8.54986111111111 & 0.0426464580661175 & 200.482326055208 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 8.55263888888889 & 0.0422536092001197 & 202.412031795491 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 8.55555555555556 & 0.0410612775833837 & 208.360676020898 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 8.55555555555556 & 0.0402461561694996 & 212.58068769408 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 8.56194444444444 & 0.038524040260194 & 222.24938990346 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 8.56194444444444 & 0.038524040260194 & 222.24938990346 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 8.52657142857143 & 0.0514086803033245 & 165.858593884582 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 8.53029411764706 & 0.0509074676533069 & 167.564691603609 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 8.53348484848485 & 0.0505860721520151 & 168.692378859562 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 8.53671875 & 0.0503849539613711 & 169.429920617669 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 8.54 & 0.0501357227209817 & 170.337626277521 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 8.54266666666667 & 0.0500451020685802 & 170.699355452609 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 8.5448275862069 & 0.0500291756253427 & 170.796889602923 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 8.54678571428571 & 0.0500895996818644 & 170.629946507243 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 8.5487037037037 & 0.0501987985692734 & 170.296978161871 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 8.55076923076923 & 0.050323123449203 & 169.917299338554 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 8.5528 & 0.0504284014566136 & 169.602837943583 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 8.55479166666667 & 0.0505080479361842 & 169.374822750534 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 8.55717391304348 & 0.0505435795542074 & 169.302886509374 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 8.55977272727273 & 0.0504760515466737 & 169.580869838002 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 8.56190476190476 & 0.050561582712264 & 169.336169926263 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 8.56425 & 0.0506469523471184 & 169.097045391859 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 8.56684210526316 & 0.0507274328289584 & 168.879866918333 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 8.56972222222222 & 0.0506614754720168 & 169.156585795764 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 8.57205882352941 & 0.0506442969635409 & 169.260101087008 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 8.5746875 & 0.050579274202292 & 169.529666750565 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 8.57733333333333 & 0.050359474067473 & 170.322138826176 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 8.58 & 0.0501215453888776 & 171.183867804363 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 8.58307692307692 & 0.0497215917523819 & 172.622730298367 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 8.58583333333333 & 0.0493689036473669 & 173.911768320001 \tabularnewline
Median & 8.61 &  &  \tabularnewline
Midrange & 8.385 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 8.56425 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 8.58973684210526 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 8.56425 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 8.58973684210526 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 8.58973684210526 &  &  \tabularnewline
Midmean - Closest Observation & 8.56425 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 8.58973684210526 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 8.56425 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=173241&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]8.52263888888889[/C][C]0.0520066780710792[/C][C]163.875856043732[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]8.51125592494206[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]8.4997702657799[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]8.53389752366669[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]8.52305555555556[/C][C]0.0518079391052991[/C][C]164.512538092522[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]8.52444444444444[/C][C]0.0513167344394068[/C][C]166.114319969246[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]8.52486111111111[/C][C]0.050808792296516[/C][C]167.783187235798[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]8.52541666666667[/C][C]0.0507023971724191[/C][C]168.146224677998[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]8.52888888888889[/C][C]0.0498383755341449[/C][C]171.130956767354[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]8.53222222222222[/C][C]0.0492598671916236[/C][C]173.208388667217[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]8.53416666666667[/C][C]0.0486398528936393[/C][C]175.456259814937[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]8.53527777777778[/C][C]0.0481289072645997[/C][C]177.34202297287[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]8.53527777777778[/C][C]0.0477617048154565[/C][C]178.705467293446[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]8.53666666666667[/C][C]0.0475437365565539[/C][C]179.553970406011[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]8.53819444444444[/C][C]0.0473066968582717[/C][C]180.485956777418[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]8.53652777777778[/C][C]0.0470840488633246[/C][C]181.304029365817[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]8.53652777777778[/C][C]0.0470840488633246[/C][C]181.304029365817[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]8.54236111111111[/C][C]0.0456467577038227[/C][C]187.140588747571[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]8.54236111111111[/C][C]0.0450645047400174[/C][C]189.55852639218[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]8.54236111111111[/C][C]0.0444491115262788[/C][C]192.182943995647[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]8.54236111111111[/C][C]0.0444491115262788[/C][C]192.182943995647[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]8.54986111111111[/C][C]0.0433637907839746[/C][C]197.165906313494[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]8.54986111111111[/C][C]0.0426464580661175[/C][C]200.482326055208[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]8.55263888888889[/C][C]0.0422536092001197[/C][C]202.412031795491[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]8.55555555555556[/C][C]0.0410612775833837[/C][C]208.360676020898[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]8.55555555555556[/C][C]0.0402461561694996[/C][C]212.58068769408[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]8.56194444444444[/C][C]0.038524040260194[/C][C]222.24938990346[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]8.56194444444444[/C][C]0.038524040260194[/C][C]222.24938990346[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]8.52657142857143[/C][C]0.0514086803033245[/C][C]165.858593884582[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]8.53029411764706[/C][C]0.0509074676533069[/C][C]167.564691603609[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]8.53348484848485[/C][C]0.0505860721520151[/C][C]168.692378859562[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]8.53671875[/C][C]0.0503849539613711[/C][C]169.429920617669[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]8.54[/C][C]0.0501357227209817[/C][C]170.337626277521[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]8.54266666666667[/C][C]0.0500451020685802[/C][C]170.699355452609[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]8.5448275862069[/C][C]0.0500291756253427[/C][C]170.796889602923[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]8.54678571428571[/C][C]0.0500895996818644[/C][C]170.629946507243[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]8.5487037037037[/C][C]0.0501987985692734[/C][C]170.296978161871[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]8.55076923076923[/C][C]0.050323123449203[/C][C]169.917299338554[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]8.5528[/C][C]0.0504284014566136[/C][C]169.602837943583[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]8.55479166666667[/C][C]0.0505080479361842[/C][C]169.374822750534[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]8.55717391304348[/C][C]0.0505435795542074[/C][C]169.302886509374[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]8.55977272727273[/C][C]0.0504760515466737[/C][C]169.580869838002[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]8.56190476190476[/C][C]0.050561582712264[/C][C]169.336169926263[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]8.56425[/C][C]0.0506469523471184[/C][C]169.097045391859[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]8.56684210526316[/C][C]0.0507274328289584[/C][C]168.879866918333[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]8.56972222222222[/C][C]0.0506614754720168[/C][C]169.156585795764[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]8.57205882352941[/C][C]0.0506442969635409[/C][C]169.260101087008[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]8.5746875[/C][C]0.050579274202292[/C][C]169.529666750565[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]8.57733333333333[/C][C]0.050359474067473[/C][C]170.322138826176[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]8.58[/C][C]0.0501215453888776[/C][C]171.183867804363[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]8.58307692307692[/C][C]0.0497215917523819[/C][C]172.622730298367[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]8.58583333333333[/C][C]0.0493689036473669[/C][C]173.911768320001[/C][/ROW]
[ROW][C]Median[/C][C]8.61[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]8.385[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]8.56425[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]8.58973684210526[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]8.56425[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]8.58973684210526[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]8.58973684210526[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]8.56425[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]8.58973684210526[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]8.56425[/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=173241&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=173241&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 Mean8.522638888888890.0520066780710792163.875856043732
Geometric Mean8.51125592494206
Harmonic Mean8.4997702657799
Quadratic Mean8.53389752366669
Winsorized Mean ( 1 / 24 )8.523055555555560.0518079391052991164.512538092522
Winsorized Mean ( 2 / 24 )8.524444444444440.0513167344394068166.114319969246
Winsorized Mean ( 3 / 24 )8.524861111111110.050808792296516167.783187235798
Winsorized Mean ( 4 / 24 )8.525416666666670.0507023971724191168.146224677998
Winsorized Mean ( 5 / 24 )8.528888888888890.0498383755341449171.130956767354
Winsorized Mean ( 6 / 24 )8.532222222222220.0492598671916236173.208388667217
Winsorized Mean ( 7 / 24 )8.534166666666670.0486398528936393175.456259814937
Winsorized Mean ( 8 / 24 )8.535277777777780.0481289072645997177.34202297287
Winsorized Mean ( 9 / 24 )8.535277777777780.0477617048154565178.705467293446
Winsorized Mean ( 10 / 24 )8.536666666666670.0475437365565539179.553970406011
Winsorized Mean ( 11 / 24 )8.538194444444440.0473066968582717180.485956777418
Winsorized Mean ( 12 / 24 )8.536527777777780.0470840488633246181.304029365817
Winsorized Mean ( 13 / 24 )8.536527777777780.0470840488633246181.304029365817
Winsorized Mean ( 14 / 24 )8.542361111111110.0456467577038227187.140588747571
Winsorized Mean ( 15 / 24 )8.542361111111110.0450645047400174189.55852639218
Winsorized Mean ( 16 / 24 )8.542361111111110.0444491115262788192.182943995647
Winsorized Mean ( 17 / 24 )8.542361111111110.0444491115262788192.182943995647
Winsorized Mean ( 18 / 24 )8.549861111111110.0433637907839746197.165906313494
Winsorized Mean ( 19 / 24 )8.549861111111110.0426464580661175200.482326055208
Winsorized Mean ( 20 / 24 )8.552638888888890.0422536092001197202.412031795491
Winsorized Mean ( 21 / 24 )8.555555555555560.0410612775833837208.360676020898
Winsorized Mean ( 22 / 24 )8.555555555555560.0402461561694996212.58068769408
Winsorized Mean ( 23 / 24 )8.561944444444440.038524040260194222.24938990346
Winsorized Mean ( 24 / 24 )8.561944444444440.038524040260194222.24938990346
Trimmed Mean ( 1 / 24 )8.526571428571430.0514086803033245165.858593884582
Trimmed Mean ( 2 / 24 )8.530294117647060.0509074676533069167.564691603609
Trimmed Mean ( 3 / 24 )8.533484848484850.0505860721520151168.692378859562
Trimmed Mean ( 4 / 24 )8.536718750.0503849539613711169.429920617669
Trimmed Mean ( 5 / 24 )8.540.0501357227209817170.337626277521
Trimmed Mean ( 6 / 24 )8.542666666666670.0500451020685802170.699355452609
Trimmed Mean ( 7 / 24 )8.54482758620690.0500291756253427170.796889602923
Trimmed Mean ( 8 / 24 )8.546785714285710.0500895996818644170.629946507243
Trimmed Mean ( 9 / 24 )8.54870370370370.0501987985692734170.296978161871
Trimmed Mean ( 10 / 24 )8.550769230769230.050323123449203169.917299338554
Trimmed Mean ( 11 / 24 )8.55280.0504284014566136169.602837943583
Trimmed Mean ( 12 / 24 )8.554791666666670.0505080479361842169.374822750534
Trimmed Mean ( 13 / 24 )8.557173913043480.0505435795542074169.302886509374
Trimmed Mean ( 14 / 24 )8.559772727272730.0504760515466737169.580869838002
Trimmed Mean ( 15 / 24 )8.561904761904760.050561582712264169.336169926263
Trimmed Mean ( 16 / 24 )8.564250.0506469523471184169.097045391859
Trimmed Mean ( 17 / 24 )8.566842105263160.0507274328289584168.879866918333
Trimmed Mean ( 18 / 24 )8.569722222222220.0506614754720168169.156585795764
Trimmed Mean ( 19 / 24 )8.572058823529410.0506442969635409169.260101087008
Trimmed Mean ( 20 / 24 )8.57468750.050579274202292169.529666750565
Trimmed Mean ( 21 / 24 )8.577333333333330.050359474067473170.322138826176
Trimmed Mean ( 22 / 24 )8.580.0501215453888776171.183867804363
Trimmed Mean ( 23 / 24 )8.583076923076920.0497215917523819172.622730298367
Trimmed Mean ( 24 / 24 )8.585833333333330.0493689036473669173.911768320001
Median8.61
Midrange8.385
Midmean - Weighted Average at Xnp8.56425
Midmean - Weighted Average at X(n+1)p8.58973684210526
Midmean - Empirical Distribution Function8.56425
Midmean - Empirical Distribution Function - Averaging8.58973684210526
Midmean - Empirical Distribution Function - Interpolation8.58973684210526
Midmean - Closest Observation8.56425
Midmean - True Basic - Statistics Graphics Toolkit8.58973684210526
Midmean - MS Excel (old versions)8.56425
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')