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Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationWed, 04 Jan 2012 04:30:43 -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/04/t1325669469b1sra4xgrdmejch.htm/, Retrieved Sun, 28 Apr 2024 22:53:58 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=160973, Retrieved Sun, 28 Apr 2024 22:53:58 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact184
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [] [2012-01-04 09:30:43] [96d2ae1d8573cbbc1fa343dabe5aa8c1] [Current]
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Dataseries X:
6,25
6,23
6,23
6,24
6,28
6,3
6,34
6,27
6,22
6,31
6,33
6,31
6,35
6,33
6,36
6,37
6,33
6,34
6,42
6,42
6,48
6,47
6,5
6,52
6,49
6,51
6,52
6,54
6,59
6,6
6,59
6,58
6,55
6,57
6,61
6,61
6,64
6,59
6,67
6,58
6,66
6,7
6,65
6,65
6,73
6,74
6,74
6,71
6,78
6,83
6,8
6,84
6,81
6,75
6,8
6,84
6,8
6,84
6,79
6,8
6,68
6,82
6,85
6,85
6,85
6,92
6,91
6,94
6,99
7,05
6,98
6,91




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=160973&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=160973&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=160973&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 Mean6.603472222222220.0264591098900658249.572727490033
Geometric Mean6.59969849920781
Harmonic Mean6.59591596152996
Quadratic Mean6.60723477628038
Winsorized Mean ( 1 / 24 )6.602777777777780.0262453678916431251.578785446562
Winsorized Mean ( 2 / 24 )6.60250.0261883077878036252.116328152937
Winsorized Mean ( 3 / 24 )6.601250.0257819324315712256.041707405782
Winsorized Mean ( 4 / 24 )6.600694444444440.025472319497803259.132052933528
Winsorized Mean ( 5 / 24 )6.601388888888890.025086942369436263.140433444433
Winsorized Mean ( 6 / 24 )6.602222222222220.0249335754662854264.792437456456
Winsorized Mean ( 7 / 24 )6.598333333333330.0236373553859154279.148543718433
Winsorized Mean ( 8 / 24 )6.599444444444440.0234419745192646281.522550031826
Winsorized Mean ( 9 / 24 )6.599444444444440.0234419745192646281.522550031826
Winsorized Mean ( 10 / 24 )6.600833333333330.0227601892090675290.016628275815
Winsorized Mean ( 11 / 24 )6.600833333333330.0227601892090675290.016628275815
Winsorized Mean ( 12 / 24 )6.600833333333330.0227601892090675290.016628275815
Winsorized Mean ( 13 / 24 )6.600833333333330.0221945005101523297.408510289023
Winsorized Mean ( 14 / 24 )6.598888888888890.0219149333072347301.113802007803
Winsorized Mean ( 15 / 24 )6.598888888888890.0212763282132076310.151677618535
Winsorized Mean ( 16 / 24 )6.598888888888890.0206037163674815320.27663219553
Winsorized Mean ( 17 / 24 )6.601250.020220747239799326.459251070963
Winsorized Mean ( 18 / 24 )6.613750.018277162670225361.858682298339
Winsorized Mean ( 19 / 24 )6.613750.018277162670225361.858682298339
Winsorized Mean ( 20 / 24 )6.624861111111110.0158780478763751417.233980064277
Winsorized Mean ( 21 / 24 )6.624861111111110.0150546644199193440.053721977726
Winsorized Mean ( 22 / 24 )6.618750.0133376423494889496.245875138018
Winsorized Mean ( 23 / 24 )6.618750.0124658178955874530.951924329239
Winsorized Mean ( 24 / 24 )6.622083333333330.0120232844975716550.771574495372
Trimmed Mean ( 1 / 24 )6.602571428571430.0258693049877675255.228017594346
Trimmed Mean ( 2 / 24 )6.602352941176470.0254175988327774259.755179260379
Trimmed Mean ( 3 / 24 )6.602272727272730.0249108390994927265.036143539909
Trimmed Mean ( 4 / 24 )6.602656250.0244829895064637269.683416245261
Trimmed Mean ( 5 / 24 )6.603225806451610.0240732776464807274.296915585026
Trimmed Mean ( 6 / 24 )6.603666666666670.0236893342548666278.761175625273
Trimmed Mean ( 7 / 24 )6.603965517241380.0232557776715862283.970960270663
Trimmed Mean ( 8 / 24 )6.6050.0230400554653012286.674657096519
Trimmed Mean ( 9 / 24 )6.605925925925930.0228009319119418289.721751349388
Trimmed Mean ( 10 / 24 )6.606923076923080.0224843475999161293.845442815861
Trimmed Mean ( 11 / 24 )6.60780.0222202151021018297.377859288813
Trimmed Mean ( 12 / 24 )6.608750.0218648025876883302.255187235089
Trimmed Mean ( 13 / 24 )6.609782608695650.0213923304023196308.979081960091
Trimmed Mean ( 14 / 24 )6.610909090909090.0208939185691236316.403506074657
Trimmed Mean ( 15 / 24 )6.612380952380950.0202877371628306325.929939810911
Trimmed Mean ( 16 / 24 )6.6140.0196240302716482337.03576219792
Trimmed Mean ( 17 / 24 )6.615789473684210.0188866182727121350.289786035591
Trimmed Mean ( 18 / 24 )6.61750.0179742982290101368.164582321189
Trimmed Mean ( 19 / 24 )6.617941176470590.017272996305913383.137995242036
Trimmed Mean ( 20 / 24 )6.61843750.016264629735827406.922113045168
Trimmed Mean ( 21 / 24 )6.617666666666670.0155709967149607424.999554479923
Trimmed Mean ( 22 / 24 )6.616785714285710.0148007361770697447.057878413972
Trimmed Mean ( 23 / 24 )6.616538461538460.0142390828106989464.674484269938
Trimmed Mean ( 24 / 24 )6.616250.013657461993941484.442131556744
Median6.605
Midrange6.635
Midmean - Weighted Average at Xnp6.62051282051282
Midmean - Weighted Average at X(n+1)p6.6271052631579
Midmean - Empirical Distribution Function6.62051282051282
Midmean - Empirical Distribution Function - Averaging6.6271052631579
Midmean - Empirical Distribution Function - Interpolation6.6271052631579
Midmean - Closest Observation6.62051282051282
Midmean - True Basic - Statistics Graphics Toolkit6.6271052631579
Midmean - MS Excel (old versions)6.62051282051282
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 6.60347222222222 & 0.0264591098900658 & 249.572727490033 \tabularnewline
Geometric Mean & 6.59969849920781 &  &  \tabularnewline
Harmonic Mean & 6.59591596152996 &  &  \tabularnewline
Quadratic Mean & 6.60723477628038 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 6.60277777777778 & 0.0262453678916431 & 251.578785446562 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 6.6025 & 0.0261883077878036 & 252.116328152937 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 6.60125 & 0.0257819324315712 & 256.041707405782 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 6.60069444444444 & 0.025472319497803 & 259.132052933528 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 6.60138888888889 & 0.025086942369436 & 263.140433444433 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 6.60222222222222 & 0.0249335754662854 & 264.792437456456 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 6.59833333333333 & 0.0236373553859154 & 279.148543718433 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 6.59944444444444 & 0.0234419745192646 & 281.522550031826 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 6.59944444444444 & 0.0234419745192646 & 281.522550031826 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 6.60083333333333 & 0.0227601892090675 & 290.016628275815 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 6.60083333333333 & 0.0227601892090675 & 290.016628275815 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 6.60083333333333 & 0.0227601892090675 & 290.016628275815 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 6.60083333333333 & 0.0221945005101523 & 297.408510289023 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 6.59888888888889 & 0.0219149333072347 & 301.113802007803 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 6.59888888888889 & 0.0212763282132076 & 310.151677618535 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 6.59888888888889 & 0.0206037163674815 & 320.27663219553 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 6.60125 & 0.020220747239799 & 326.459251070963 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 6.61375 & 0.018277162670225 & 361.858682298339 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 6.61375 & 0.018277162670225 & 361.858682298339 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 6.62486111111111 & 0.0158780478763751 & 417.233980064277 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 6.62486111111111 & 0.0150546644199193 & 440.053721977726 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 6.61875 & 0.0133376423494889 & 496.245875138018 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 6.61875 & 0.0124658178955874 & 530.951924329239 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 6.62208333333333 & 0.0120232844975716 & 550.771574495372 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 6.60257142857143 & 0.0258693049877675 & 255.228017594346 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 6.60235294117647 & 0.0254175988327774 & 259.755179260379 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 6.60227272727273 & 0.0249108390994927 & 265.036143539909 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 6.60265625 & 0.0244829895064637 & 269.683416245261 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 6.60322580645161 & 0.0240732776464807 & 274.296915585026 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 6.60366666666667 & 0.0236893342548666 & 278.761175625273 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 6.60396551724138 & 0.0232557776715862 & 283.970960270663 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 6.605 & 0.0230400554653012 & 286.674657096519 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 6.60592592592593 & 0.0228009319119418 & 289.721751349388 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 6.60692307692308 & 0.0224843475999161 & 293.845442815861 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 6.6078 & 0.0222202151021018 & 297.377859288813 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 6.60875 & 0.0218648025876883 & 302.255187235089 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 6.60978260869565 & 0.0213923304023196 & 308.979081960091 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 6.61090909090909 & 0.0208939185691236 & 316.403506074657 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 6.61238095238095 & 0.0202877371628306 & 325.929939810911 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 6.614 & 0.0196240302716482 & 337.03576219792 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 6.61578947368421 & 0.0188866182727121 & 350.289786035591 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 6.6175 & 0.0179742982290101 & 368.164582321189 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 6.61794117647059 & 0.017272996305913 & 383.137995242036 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 6.6184375 & 0.016264629735827 & 406.922113045168 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 6.61766666666667 & 0.0155709967149607 & 424.999554479923 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 6.61678571428571 & 0.0148007361770697 & 447.057878413972 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 6.61653846153846 & 0.0142390828106989 & 464.674484269938 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 6.61625 & 0.013657461993941 & 484.442131556744 \tabularnewline
Median & 6.605 &  &  \tabularnewline
Midrange & 6.635 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 6.62051282051282 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 6.6271052631579 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 6.62051282051282 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 6.6271052631579 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 6.6271052631579 &  &  \tabularnewline
Midmean - Closest Observation & 6.62051282051282 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 6.6271052631579 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 6.62051282051282 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=160973&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]6.60347222222222[/C][C]0.0264591098900658[/C][C]249.572727490033[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]6.59969849920781[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]6.59591596152996[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]6.60723477628038[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]6.60277777777778[/C][C]0.0262453678916431[/C][C]251.578785446562[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]6.6025[/C][C]0.0261883077878036[/C][C]252.116328152937[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]6.60125[/C][C]0.0257819324315712[/C][C]256.041707405782[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]6.60069444444444[/C][C]0.025472319497803[/C][C]259.132052933528[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]6.60138888888889[/C][C]0.025086942369436[/C][C]263.140433444433[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]6.60222222222222[/C][C]0.0249335754662854[/C][C]264.792437456456[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]6.59833333333333[/C][C]0.0236373553859154[/C][C]279.148543718433[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]6.59944444444444[/C][C]0.0234419745192646[/C][C]281.522550031826[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]6.59944444444444[/C][C]0.0234419745192646[/C][C]281.522550031826[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]6.60083333333333[/C][C]0.0227601892090675[/C][C]290.016628275815[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]6.60083333333333[/C][C]0.0227601892090675[/C][C]290.016628275815[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]6.60083333333333[/C][C]0.0227601892090675[/C][C]290.016628275815[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]6.60083333333333[/C][C]0.0221945005101523[/C][C]297.408510289023[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]6.59888888888889[/C][C]0.0219149333072347[/C][C]301.113802007803[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]6.59888888888889[/C][C]0.0212763282132076[/C][C]310.151677618535[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]6.59888888888889[/C][C]0.0206037163674815[/C][C]320.27663219553[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]6.60125[/C][C]0.020220747239799[/C][C]326.459251070963[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]6.61375[/C][C]0.018277162670225[/C][C]361.858682298339[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]6.61375[/C][C]0.018277162670225[/C][C]361.858682298339[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]6.62486111111111[/C][C]0.0158780478763751[/C][C]417.233980064277[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]6.62486111111111[/C][C]0.0150546644199193[/C][C]440.053721977726[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]6.61875[/C][C]0.0133376423494889[/C][C]496.245875138018[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]6.61875[/C][C]0.0124658178955874[/C][C]530.951924329239[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]6.62208333333333[/C][C]0.0120232844975716[/C][C]550.771574495372[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]6.60257142857143[/C][C]0.0258693049877675[/C][C]255.228017594346[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]6.60235294117647[/C][C]0.0254175988327774[/C][C]259.755179260379[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]6.60227272727273[/C][C]0.0249108390994927[/C][C]265.036143539909[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]6.60265625[/C][C]0.0244829895064637[/C][C]269.683416245261[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]6.60322580645161[/C][C]0.0240732776464807[/C][C]274.296915585026[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]6.60366666666667[/C][C]0.0236893342548666[/C][C]278.761175625273[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]6.60396551724138[/C][C]0.0232557776715862[/C][C]283.970960270663[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]6.605[/C][C]0.0230400554653012[/C][C]286.674657096519[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]6.60592592592593[/C][C]0.0228009319119418[/C][C]289.721751349388[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]6.60692307692308[/C][C]0.0224843475999161[/C][C]293.845442815861[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]6.6078[/C][C]0.0222202151021018[/C][C]297.377859288813[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]6.60875[/C][C]0.0218648025876883[/C][C]302.255187235089[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]6.60978260869565[/C][C]0.0213923304023196[/C][C]308.979081960091[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]6.61090909090909[/C][C]0.0208939185691236[/C][C]316.403506074657[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]6.61238095238095[/C][C]0.0202877371628306[/C][C]325.929939810911[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]6.614[/C][C]0.0196240302716482[/C][C]337.03576219792[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]6.61578947368421[/C][C]0.0188866182727121[/C][C]350.289786035591[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]6.6175[/C][C]0.0179742982290101[/C][C]368.164582321189[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]6.61794117647059[/C][C]0.017272996305913[/C][C]383.137995242036[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]6.6184375[/C][C]0.016264629735827[/C][C]406.922113045168[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]6.61766666666667[/C][C]0.0155709967149607[/C][C]424.999554479923[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]6.61678571428571[/C][C]0.0148007361770697[/C][C]447.057878413972[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]6.61653846153846[/C][C]0.0142390828106989[/C][C]464.674484269938[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]6.61625[/C][C]0.013657461993941[/C][C]484.442131556744[/C][/ROW]
[ROW][C]Median[/C][C]6.605[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]6.635[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]6.62051282051282[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]6.6271052631579[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]6.62051282051282[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]6.6271052631579[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]6.6271052631579[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]6.62051282051282[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]6.6271052631579[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]6.62051282051282[/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=160973&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=160973&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 Mean6.603472222222220.0264591098900658249.572727490033
Geometric Mean6.59969849920781
Harmonic Mean6.59591596152996
Quadratic Mean6.60723477628038
Winsorized Mean ( 1 / 24 )6.602777777777780.0262453678916431251.578785446562
Winsorized Mean ( 2 / 24 )6.60250.0261883077878036252.116328152937
Winsorized Mean ( 3 / 24 )6.601250.0257819324315712256.041707405782
Winsorized Mean ( 4 / 24 )6.600694444444440.025472319497803259.132052933528
Winsorized Mean ( 5 / 24 )6.601388888888890.025086942369436263.140433444433
Winsorized Mean ( 6 / 24 )6.602222222222220.0249335754662854264.792437456456
Winsorized Mean ( 7 / 24 )6.598333333333330.0236373553859154279.148543718433
Winsorized Mean ( 8 / 24 )6.599444444444440.0234419745192646281.522550031826
Winsorized Mean ( 9 / 24 )6.599444444444440.0234419745192646281.522550031826
Winsorized Mean ( 10 / 24 )6.600833333333330.0227601892090675290.016628275815
Winsorized Mean ( 11 / 24 )6.600833333333330.0227601892090675290.016628275815
Winsorized Mean ( 12 / 24 )6.600833333333330.0227601892090675290.016628275815
Winsorized Mean ( 13 / 24 )6.600833333333330.0221945005101523297.408510289023
Winsorized Mean ( 14 / 24 )6.598888888888890.0219149333072347301.113802007803
Winsorized Mean ( 15 / 24 )6.598888888888890.0212763282132076310.151677618535
Winsorized Mean ( 16 / 24 )6.598888888888890.0206037163674815320.27663219553
Winsorized Mean ( 17 / 24 )6.601250.020220747239799326.459251070963
Winsorized Mean ( 18 / 24 )6.613750.018277162670225361.858682298339
Winsorized Mean ( 19 / 24 )6.613750.018277162670225361.858682298339
Winsorized Mean ( 20 / 24 )6.624861111111110.0158780478763751417.233980064277
Winsorized Mean ( 21 / 24 )6.624861111111110.0150546644199193440.053721977726
Winsorized Mean ( 22 / 24 )6.618750.0133376423494889496.245875138018
Winsorized Mean ( 23 / 24 )6.618750.0124658178955874530.951924329239
Winsorized Mean ( 24 / 24 )6.622083333333330.0120232844975716550.771574495372
Trimmed Mean ( 1 / 24 )6.602571428571430.0258693049877675255.228017594346
Trimmed Mean ( 2 / 24 )6.602352941176470.0254175988327774259.755179260379
Trimmed Mean ( 3 / 24 )6.602272727272730.0249108390994927265.036143539909
Trimmed Mean ( 4 / 24 )6.602656250.0244829895064637269.683416245261
Trimmed Mean ( 5 / 24 )6.603225806451610.0240732776464807274.296915585026
Trimmed Mean ( 6 / 24 )6.603666666666670.0236893342548666278.761175625273
Trimmed Mean ( 7 / 24 )6.603965517241380.0232557776715862283.970960270663
Trimmed Mean ( 8 / 24 )6.6050.0230400554653012286.674657096519
Trimmed Mean ( 9 / 24 )6.605925925925930.0228009319119418289.721751349388
Trimmed Mean ( 10 / 24 )6.606923076923080.0224843475999161293.845442815861
Trimmed Mean ( 11 / 24 )6.60780.0222202151021018297.377859288813
Trimmed Mean ( 12 / 24 )6.608750.0218648025876883302.255187235089
Trimmed Mean ( 13 / 24 )6.609782608695650.0213923304023196308.979081960091
Trimmed Mean ( 14 / 24 )6.610909090909090.0208939185691236316.403506074657
Trimmed Mean ( 15 / 24 )6.612380952380950.0202877371628306325.929939810911
Trimmed Mean ( 16 / 24 )6.6140.0196240302716482337.03576219792
Trimmed Mean ( 17 / 24 )6.615789473684210.0188866182727121350.289786035591
Trimmed Mean ( 18 / 24 )6.61750.0179742982290101368.164582321189
Trimmed Mean ( 19 / 24 )6.617941176470590.017272996305913383.137995242036
Trimmed Mean ( 20 / 24 )6.61843750.016264629735827406.922113045168
Trimmed Mean ( 21 / 24 )6.617666666666670.0155709967149607424.999554479923
Trimmed Mean ( 22 / 24 )6.616785714285710.0148007361770697447.057878413972
Trimmed Mean ( 23 / 24 )6.616538461538460.0142390828106989464.674484269938
Trimmed Mean ( 24 / 24 )6.616250.013657461993941484.442131556744
Median6.605
Midrange6.635
Midmean - Weighted Average at Xnp6.62051282051282
Midmean - Weighted Average at X(n+1)p6.6271052631579
Midmean - Empirical Distribution Function6.62051282051282
Midmean - Empirical Distribution Function - Averaging6.6271052631579
Midmean - Empirical Distribution Function - Interpolation6.6271052631579
Midmean - Closest Observation6.62051282051282
Midmean - True Basic - Statistics Graphics Toolkit6.6271052631579
Midmean - MS Excel (old versions)6.62051282051282
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')