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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 computationTue, 04 Nov 2008 01:56:27 -0700
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2008/Nov/04/t122578905374ohzqpms0lk114.htm/, Retrieved Sun, 19 May 2024 05:56:33 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=21455, Retrieved Sun, 19 May 2024 05:56:33 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact144
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [Centrummaten - ge...] [2008-11-04 08:56:27] [d41d8cd98f00b204e9800998ecf8427e] [Current]
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Dataseries X:
5,6
5,6
5,6
5,6
5,6
5,67
5,67
5,67
5,67
5,67
5,67
5,67
5,67
5,67
5,82
5,82
5,95
5,95
5,95
5,95
5,95
5,95
6,02
6,02
6,05
6,05
6,05
6,12
6,12
6,12
6,12
6,12
6,12
6,12
6,12
6,17
6,17
6,17
6,17
6,17
6,28
6,27
6,28
6,28
6,27
6,27
6,28
6,59
6,59
6,59
6,59
6,59
6,63
6,63
6,63
6,63
6,63
6,63
6,63
6,63
6,63
6,63
6,63
6,63
6,63
6,63
6,63
6,63
6,63
6,79
6,79
6,79




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' @ 72.249.76.132

\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' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=21455&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' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=21455&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=21455&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' @ 72.249.76.132







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean6.199027777777780.0445992237147183138.994073471553
Geometric Mean6.18756808021837
Harmonic Mean6.17605546329312
Quadratic Mean6.21040826623607
Winsorized Mean ( 1 / 24 )6.199027777777780.0445992237147183138.994073471553
Winsorized Mean ( 2 / 24 )6.199027777777780.0445992237147183138.994073471553
Winsorized Mean ( 3 / 24 )6.192361111111110.0435029602789771142.343442179579
Winsorized Mean ( 4 / 24 )6.192361111111110.0435029602789771142.343442179579
Winsorized Mean ( 5 / 24 )6.197222222222220.0426128356784981145.430880708773
Winsorized Mean ( 6 / 24 )6.197222222222220.0426128356784981145.430880708773
Winsorized Mean ( 7 / 24 )6.197222222222220.0426128356784981145.430880708773
Winsorized Mean ( 8 / 24 )6.197222222222220.0426128356784981145.430880708773
Winsorized Mean ( 9 / 24 )6.197222222222220.0426128356784981145.430880708773
Winsorized Mean ( 10 / 24 )6.197222222222220.0426128356784981145.430880708773
Winsorized Mean ( 11 / 24 )6.197222222222220.0426128356784981145.430880708773
Winsorized Mean ( 12 / 24 )6.197222222222220.0426128356784981145.430880708773
Winsorized Mean ( 13 / 24 )6.197222222222220.0426128356784981145.430880708773
Winsorized Mean ( 14 / 24 )6.226388888888890.0378461104128092164.518594407037
Winsorized Mean ( 15 / 24 )6.226388888888890.0378461104128092164.518594407037
Winsorized Mean ( 16 / 24 )6.255277777777780.0338047488018768185.041392096678
Winsorized Mean ( 17 / 24 )6.255277777777780.0338047488018768185.041392096678
Winsorized Mean ( 18 / 24 )6.255277777777780.0338047488018768185.041392096678
Winsorized Mean ( 19 / 24 )6.255277777777780.0338047488018768185.041392096678
Winsorized Mean ( 20 / 24 )6.244166666666670.0320935825955668194.561222576915
Winsorized Mean ( 21 / 24 )6.244166666666670.0320935825955668194.561222576915
Winsorized Mean ( 22 / 24 )6.265555555555560.0294517515366977212.739658208392
Winsorized Mean ( 23 / 24 )6.265555555555550.0294517515366977212.739658208392
Winsorized Mean ( 24 / 24 )6.275555555555550.0283028618863551221.728657008393
Trimmed Mean ( 1 / 24 )6.199142857142860.0442563316671786140.073580968309
Trimmed Mean ( 2 / 24 )6.199264705882350.0438291820396495141.441487552158
Trimmed Mean ( 3 / 24 )6.199393939393940.0433018778362271143.166861327372
Trimmed Mean ( 4 / 24 )6.202031250.0431257503313492143.812715195626
Trimmed Mean ( 5 / 24 )6.204838709677420.0428763190816903144.714817936111
Trimmed Mean ( 6 / 24 )6.206666666666670.0428033650577107145.004175683346
Trimmed Mean ( 7 / 24 )6.208620689655170.0426663133368769145.515752454033
Trimmed Mean ( 8 / 24 )6.210714285714290.0424507790934404146.303894023796
Trimmed Mean ( 9 / 24 )6.212962962962960.0421385270244752147.441389191281
Trimmed Mean ( 10 / 24 )6.215384615384620.0417061305164989149.028081445384
Trimmed Mean ( 11 / 24 )6.2180.0411230110864504151.204881056211
Trimmed Mean ( 12 / 24 )6.220833333333330.0403484746797627154.177658082660
Trimmed Mean ( 13 / 24 )6.223913043478260.0393270423130045158.260389732389
Trimmed Mean ( 14 / 24 )6.227272727272730.0379806944900912163.958895719965
Trimmed Mean ( 15 / 24 )6.227380952380950.0373420942160781166.765712612328
Trimmed Mean ( 16 / 24 )6.22750.0364546609872086170.828635662944
Trimmed Mean ( 17 / 24 )6.224210526315790.0361139172389599172.349360085510
Trimmed Mean ( 18 / 24 )6.220555555555560.0355611354748554174.925672999221
Trimmed Mean ( 19 / 24 )6.21647058823530.0347126794757881179.083570675414
Trimmed Mean ( 20 / 24 )6.2118750.0334399965151835185.761831559387
Trimmed Mean ( 21 / 24 )6.2080.0321147368327857193.30689310405
Trimmed Mean ( 22 / 24 )6.203571428571430.0300845997874138206.204219846952
Trimmed Mean ( 23 / 24 )6.195769230769230.0277248740132981223.473305155416
Trimmed Mean ( 24 / 24 )6.186666666666670.0237488875915431260.503429595150
Median6.17
Midrange6.195
Midmean - Weighted Average at Xnp6.32622641509434
Midmean - Weighted Average at X(n+1)p6.32622641509434
Midmean - Empirical Distribution Function6.32622641509434
Midmean - Empirical Distribution Function - Averaging6.32622641509434
Midmean - Empirical Distribution Function - Interpolation6.32622641509434
Midmean - Closest Observation6.32622641509434
Midmean - True Basic - Statistics Graphics Toolkit6.32622641509434
Midmean - MS Excel (old versions)6.32622641509434
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 6.19902777777778 & 0.0445992237147183 & 138.994073471553 \tabularnewline
Geometric Mean & 6.18756808021837 &  &  \tabularnewline
Harmonic Mean & 6.17605546329312 &  &  \tabularnewline
Quadratic Mean & 6.21040826623607 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 6.19902777777778 & 0.0445992237147183 & 138.994073471553 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 6.19902777777778 & 0.0445992237147183 & 138.994073471553 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 6.19236111111111 & 0.0435029602789771 & 142.343442179579 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 6.19236111111111 & 0.0435029602789771 & 142.343442179579 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 6.19722222222222 & 0.0426128356784981 & 145.430880708773 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 6.19722222222222 & 0.0426128356784981 & 145.430880708773 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 6.19722222222222 & 0.0426128356784981 & 145.430880708773 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 6.19722222222222 & 0.0426128356784981 & 145.430880708773 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 6.19722222222222 & 0.0426128356784981 & 145.430880708773 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 6.19722222222222 & 0.0426128356784981 & 145.430880708773 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 6.19722222222222 & 0.0426128356784981 & 145.430880708773 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 6.19722222222222 & 0.0426128356784981 & 145.430880708773 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 6.19722222222222 & 0.0426128356784981 & 145.430880708773 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 6.22638888888889 & 0.0378461104128092 & 164.518594407037 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 6.22638888888889 & 0.0378461104128092 & 164.518594407037 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 6.25527777777778 & 0.0338047488018768 & 185.041392096678 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 6.25527777777778 & 0.0338047488018768 & 185.041392096678 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 6.25527777777778 & 0.0338047488018768 & 185.041392096678 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 6.25527777777778 & 0.0338047488018768 & 185.041392096678 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 6.24416666666667 & 0.0320935825955668 & 194.561222576915 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 6.24416666666667 & 0.0320935825955668 & 194.561222576915 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 6.26555555555556 & 0.0294517515366977 & 212.739658208392 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 6.26555555555555 & 0.0294517515366977 & 212.739658208392 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 6.27555555555555 & 0.0283028618863551 & 221.728657008393 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 6.19914285714286 & 0.0442563316671786 & 140.073580968309 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 6.19926470588235 & 0.0438291820396495 & 141.441487552158 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 6.19939393939394 & 0.0433018778362271 & 143.166861327372 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 6.20203125 & 0.0431257503313492 & 143.812715195626 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 6.20483870967742 & 0.0428763190816903 & 144.714817936111 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 6.20666666666667 & 0.0428033650577107 & 145.004175683346 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 6.20862068965517 & 0.0426663133368769 & 145.515752454033 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 6.21071428571429 & 0.0424507790934404 & 146.303894023796 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 6.21296296296296 & 0.0421385270244752 & 147.441389191281 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 6.21538461538462 & 0.0417061305164989 & 149.028081445384 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 6.218 & 0.0411230110864504 & 151.204881056211 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 6.22083333333333 & 0.0403484746797627 & 154.177658082660 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 6.22391304347826 & 0.0393270423130045 & 158.260389732389 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 6.22727272727273 & 0.0379806944900912 & 163.958895719965 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 6.22738095238095 & 0.0373420942160781 & 166.765712612328 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 6.2275 & 0.0364546609872086 & 170.828635662944 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 6.22421052631579 & 0.0361139172389599 & 172.349360085510 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 6.22055555555556 & 0.0355611354748554 & 174.925672999221 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 6.2164705882353 & 0.0347126794757881 & 179.083570675414 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 6.211875 & 0.0334399965151835 & 185.761831559387 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 6.208 & 0.0321147368327857 & 193.30689310405 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 6.20357142857143 & 0.0300845997874138 & 206.204219846952 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 6.19576923076923 & 0.0277248740132981 & 223.473305155416 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 6.18666666666667 & 0.0237488875915431 & 260.503429595150 \tabularnewline
Median & 6.17 &  &  \tabularnewline
Midrange & 6.195 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 6.32622641509434 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 6.32622641509434 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 6.32622641509434 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 6.32622641509434 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 6.32622641509434 &  &  \tabularnewline
Midmean - Closest Observation & 6.32622641509434 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 6.32622641509434 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 6.32622641509434 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=21455&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]6.19902777777778[/C][C]0.0445992237147183[/C][C]138.994073471553[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]6.18756808021837[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]6.17605546329312[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]6.21040826623607[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]6.19902777777778[/C][C]0.0445992237147183[/C][C]138.994073471553[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]6.19902777777778[/C][C]0.0445992237147183[/C][C]138.994073471553[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]6.19236111111111[/C][C]0.0435029602789771[/C][C]142.343442179579[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]6.19236111111111[/C][C]0.0435029602789771[/C][C]142.343442179579[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]6.19722222222222[/C][C]0.0426128356784981[/C][C]145.430880708773[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]6.19722222222222[/C][C]0.0426128356784981[/C][C]145.430880708773[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]6.19722222222222[/C][C]0.0426128356784981[/C][C]145.430880708773[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]6.19722222222222[/C][C]0.0426128356784981[/C][C]145.430880708773[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]6.19722222222222[/C][C]0.0426128356784981[/C][C]145.430880708773[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]6.19722222222222[/C][C]0.0426128356784981[/C][C]145.430880708773[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]6.19722222222222[/C][C]0.0426128356784981[/C][C]145.430880708773[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]6.19722222222222[/C][C]0.0426128356784981[/C][C]145.430880708773[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]6.19722222222222[/C][C]0.0426128356784981[/C][C]145.430880708773[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]6.22638888888889[/C][C]0.0378461104128092[/C][C]164.518594407037[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]6.22638888888889[/C][C]0.0378461104128092[/C][C]164.518594407037[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]6.25527777777778[/C][C]0.0338047488018768[/C][C]185.041392096678[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]6.25527777777778[/C][C]0.0338047488018768[/C][C]185.041392096678[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]6.25527777777778[/C][C]0.0338047488018768[/C][C]185.041392096678[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]6.25527777777778[/C][C]0.0338047488018768[/C][C]185.041392096678[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]6.24416666666667[/C][C]0.0320935825955668[/C][C]194.561222576915[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]6.24416666666667[/C][C]0.0320935825955668[/C][C]194.561222576915[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]6.26555555555556[/C][C]0.0294517515366977[/C][C]212.739658208392[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]6.26555555555555[/C][C]0.0294517515366977[/C][C]212.739658208392[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]6.27555555555555[/C][C]0.0283028618863551[/C][C]221.728657008393[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]6.19914285714286[/C][C]0.0442563316671786[/C][C]140.073580968309[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]6.19926470588235[/C][C]0.0438291820396495[/C][C]141.441487552158[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]6.19939393939394[/C][C]0.0433018778362271[/C][C]143.166861327372[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]6.20203125[/C][C]0.0431257503313492[/C][C]143.812715195626[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]6.20483870967742[/C][C]0.0428763190816903[/C][C]144.714817936111[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]6.20666666666667[/C][C]0.0428033650577107[/C][C]145.004175683346[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]6.20862068965517[/C][C]0.0426663133368769[/C][C]145.515752454033[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]6.21071428571429[/C][C]0.0424507790934404[/C][C]146.303894023796[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]6.21296296296296[/C][C]0.0421385270244752[/C][C]147.441389191281[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]6.21538461538462[/C][C]0.0417061305164989[/C][C]149.028081445384[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]6.218[/C][C]0.0411230110864504[/C][C]151.204881056211[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]6.22083333333333[/C][C]0.0403484746797627[/C][C]154.177658082660[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]6.22391304347826[/C][C]0.0393270423130045[/C][C]158.260389732389[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]6.22727272727273[/C][C]0.0379806944900912[/C][C]163.958895719965[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]6.22738095238095[/C][C]0.0373420942160781[/C][C]166.765712612328[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]6.2275[/C][C]0.0364546609872086[/C][C]170.828635662944[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]6.22421052631579[/C][C]0.0361139172389599[/C][C]172.349360085510[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]6.22055555555556[/C][C]0.0355611354748554[/C][C]174.925672999221[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]6.2164705882353[/C][C]0.0347126794757881[/C][C]179.083570675414[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]6.211875[/C][C]0.0334399965151835[/C][C]185.761831559387[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]6.208[/C][C]0.0321147368327857[/C][C]193.30689310405[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]6.20357142857143[/C][C]0.0300845997874138[/C][C]206.204219846952[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]6.19576923076923[/C][C]0.0277248740132981[/C][C]223.473305155416[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]6.18666666666667[/C][C]0.0237488875915431[/C][C]260.503429595150[/C][/ROW]
[ROW][C]Median[/C][C]6.17[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]6.195[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]6.32622641509434[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]6.32622641509434[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]6.32622641509434[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]6.32622641509434[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]6.32622641509434[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]6.32622641509434[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]6.32622641509434[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]6.32622641509434[/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=21455&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=21455&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 Mean6.199027777777780.0445992237147183138.994073471553
Geometric Mean6.18756808021837
Harmonic Mean6.17605546329312
Quadratic Mean6.21040826623607
Winsorized Mean ( 1 / 24 )6.199027777777780.0445992237147183138.994073471553
Winsorized Mean ( 2 / 24 )6.199027777777780.0445992237147183138.994073471553
Winsorized Mean ( 3 / 24 )6.192361111111110.0435029602789771142.343442179579
Winsorized Mean ( 4 / 24 )6.192361111111110.0435029602789771142.343442179579
Winsorized Mean ( 5 / 24 )6.197222222222220.0426128356784981145.430880708773
Winsorized Mean ( 6 / 24 )6.197222222222220.0426128356784981145.430880708773
Winsorized Mean ( 7 / 24 )6.197222222222220.0426128356784981145.430880708773
Winsorized Mean ( 8 / 24 )6.197222222222220.0426128356784981145.430880708773
Winsorized Mean ( 9 / 24 )6.197222222222220.0426128356784981145.430880708773
Winsorized Mean ( 10 / 24 )6.197222222222220.0426128356784981145.430880708773
Winsorized Mean ( 11 / 24 )6.197222222222220.0426128356784981145.430880708773
Winsorized Mean ( 12 / 24 )6.197222222222220.0426128356784981145.430880708773
Winsorized Mean ( 13 / 24 )6.197222222222220.0426128356784981145.430880708773
Winsorized Mean ( 14 / 24 )6.226388888888890.0378461104128092164.518594407037
Winsorized Mean ( 15 / 24 )6.226388888888890.0378461104128092164.518594407037
Winsorized Mean ( 16 / 24 )6.255277777777780.0338047488018768185.041392096678
Winsorized Mean ( 17 / 24 )6.255277777777780.0338047488018768185.041392096678
Winsorized Mean ( 18 / 24 )6.255277777777780.0338047488018768185.041392096678
Winsorized Mean ( 19 / 24 )6.255277777777780.0338047488018768185.041392096678
Winsorized Mean ( 20 / 24 )6.244166666666670.0320935825955668194.561222576915
Winsorized Mean ( 21 / 24 )6.244166666666670.0320935825955668194.561222576915
Winsorized Mean ( 22 / 24 )6.265555555555560.0294517515366977212.739658208392
Winsorized Mean ( 23 / 24 )6.265555555555550.0294517515366977212.739658208392
Winsorized Mean ( 24 / 24 )6.275555555555550.0283028618863551221.728657008393
Trimmed Mean ( 1 / 24 )6.199142857142860.0442563316671786140.073580968309
Trimmed Mean ( 2 / 24 )6.199264705882350.0438291820396495141.441487552158
Trimmed Mean ( 3 / 24 )6.199393939393940.0433018778362271143.166861327372
Trimmed Mean ( 4 / 24 )6.202031250.0431257503313492143.812715195626
Trimmed Mean ( 5 / 24 )6.204838709677420.0428763190816903144.714817936111
Trimmed Mean ( 6 / 24 )6.206666666666670.0428033650577107145.004175683346
Trimmed Mean ( 7 / 24 )6.208620689655170.0426663133368769145.515752454033
Trimmed Mean ( 8 / 24 )6.210714285714290.0424507790934404146.303894023796
Trimmed Mean ( 9 / 24 )6.212962962962960.0421385270244752147.441389191281
Trimmed Mean ( 10 / 24 )6.215384615384620.0417061305164989149.028081445384
Trimmed Mean ( 11 / 24 )6.2180.0411230110864504151.204881056211
Trimmed Mean ( 12 / 24 )6.220833333333330.0403484746797627154.177658082660
Trimmed Mean ( 13 / 24 )6.223913043478260.0393270423130045158.260389732389
Trimmed Mean ( 14 / 24 )6.227272727272730.0379806944900912163.958895719965
Trimmed Mean ( 15 / 24 )6.227380952380950.0373420942160781166.765712612328
Trimmed Mean ( 16 / 24 )6.22750.0364546609872086170.828635662944
Trimmed Mean ( 17 / 24 )6.224210526315790.0361139172389599172.349360085510
Trimmed Mean ( 18 / 24 )6.220555555555560.0355611354748554174.925672999221
Trimmed Mean ( 19 / 24 )6.21647058823530.0347126794757881179.083570675414
Trimmed Mean ( 20 / 24 )6.2118750.0334399965151835185.761831559387
Trimmed Mean ( 21 / 24 )6.2080.0321147368327857193.30689310405
Trimmed Mean ( 22 / 24 )6.203571428571430.0300845997874138206.204219846952
Trimmed Mean ( 23 / 24 )6.195769230769230.0277248740132981223.473305155416
Trimmed Mean ( 24 / 24 )6.186666666666670.0237488875915431260.503429595150
Median6.17
Midrange6.195
Midmean - Weighted Average at Xnp6.32622641509434
Midmean - Weighted Average at X(n+1)p6.32622641509434
Midmean - Empirical Distribution Function6.32622641509434
Midmean - Empirical Distribution Function - Averaging6.32622641509434
Midmean - Empirical Distribution Function - Interpolation6.32622641509434
Midmean - Closest Observation6.32622641509434
Midmean - True Basic - Statistics Graphics Toolkit6.32622641509434
Midmean - MS Excel (old versions)6.32622641509434
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')