Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationFri, 19 Oct 2012 08:56:42 -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/19/t1350651423hllexanak4he7mj.htm/, Retrieved Mon, 29 Apr 2024 12:30:44 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=180117, Retrieved Mon, 29 Apr 2024 12:30:44 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact78
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [] [2012-10-19 12:56:42] [119350d3baf712453a84eb36ae72814b] [Current]
Feedback Forum

Post a new message
Dataseries X:
0,47
0,47
0,47
0,47
0,47
0,47
0,48
0,48
0,48
0,48
0,48
0,49
0,49
0,49
0,49
0,49
0,49
0,49
0,5
0,5
0,5
0,5
0,5
0,5
0,5
0,5
0,51
0,51
0,5
0,51
0,5
0,51
0,51
0,52
0,53
0,53
0,53
0,53
0,53
0,54
0,55
0,54
0,55
0,55
0,55
0,54
0,55
0,55
0,55
0,55
0,56
0,56
0,56
0,56
0,55
0,55
0,56
0,56
0,56
0,56
0,56
0,55
0,55
0,55
0,54
0,54
0,54
0,54
0,55
0,54
0,54
0,54




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 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 & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=180117&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]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=180117&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=180117&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'Gwilym Jenkins' @ jenkins.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean0.5209722222222220.00357219155597884145.841065367914
Geometric Mean0.520092573969967
Harmonic Mean0.519204091253245
Quadratic Mean0.521841025174866
Winsorized Mean ( 1 / 24 )0.5209722222222220.00357219155597884145.841065367914
Winsorized Mean ( 2 / 24 )0.5209722222222220.00357219155597884145.841065367914
Winsorized Mean ( 3 / 24 )0.5209722222222220.00357219155597884145.841065367914
Winsorized Mean ( 4 / 24 )0.5209722222222220.00357219155597884145.841065367914
Winsorized Mean ( 5 / 24 )0.5209722222222220.00357219155597884145.841065367914
Winsorized Mean ( 6 / 24 )0.5218055555555560.00341637402209956152.736659446578
Winsorized Mean ( 7 / 24 )0.5218055555555560.00341637402209956152.736659446578
Winsorized Mean ( 8 / 24 )0.5218055555555560.00341637402209956152.736659446578
Winsorized Mean ( 9 / 24 )0.5205555555555560.00323740419939641160.794118835272
Winsorized Mean ( 10 / 24 )0.5205555555555560.00323740419939641160.794118835272
Winsorized Mean ( 11 / 24 )0.5220833333333330.0029862589583809174.828553253264
Winsorized Mean ( 12 / 24 )0.5220833333333330.0029862589583809174.828553253264
Winsorized Mean ( 13 / 24 )0.5220833333333330.0029862589583809174.828553253264
Winsorized Mean ( 14 / 24 )0.5220833333333330.0029862589583809174.828553253264
Winsorized Mean ( 15 / 24 )0.5220833333333330.0029862589583809174.828553253264
Winsorized Mean ( 16 / 24 )0.5220833333333330.0029862589583809174.828553253264
Winsorized Mean ( 17 / 24 )0.5220833333333330.0029862589583809174.828553253264
Winsorized Mean ( 18 / 24 )0.5245833333333330.00263105252744808199.381550866314
Winsorized Mean ( 19 / 24 )0.5245833333333330.00263105252744808199.381550866314
Winsorized Mean ( 20 / 24 )0.5245833333333330.00263105252744808199.381550866314
Winsorized Mean ( 21 / 24 )0.5245833333333330.00263105252744808199.381550866314
Winsorized Mean ( 22 / 24 )0.5245833333333330.00263105252744808199.381550866314
Winsorized Mean ( 23 / 24 )0.5213888888888890.00222295566925982234.547587295116
Winsorized Mean ( 24 / 24 )0.5213888888888890.00222295566925982234.547587295116
Trimmed Mean ( 1 / 24 )0.5211428571428570.00355694786896876146.514055403896
Trimmed Mean ( 2 / 24 )0.5213235294117650.00353649238536974147.412597739062
Trimmed Mean ( 3 / 24 )0.5215151515151510.00350984246614801148.586484021747
Trimmed Mean ( 4 / 24 )0.521718750.00347578562191113150.100957524859
Trimmed Mean ( 5 / 24 )0.5219354838709680.00343280831205588152.043294126839
Trimmed Mean ( 6 / 24 )0.5221666666666670.00337899515925258154.533120663649
Trimmed Mean ( 7 / 24 )0.5222413793103450.00335482878723613155.668563861523
Trimmed Mean ( 8 / 24 )0.5223214285714290.00332240594473276157.211802910328
Trimmed Mean ( 9 / 24 )0.5224074074074070.00327981337337415159.279613787895
Trimmed Mean ( 10 / 24 )0.5226923076923080.00326223632933456160.225150763044
Trimmed Mean ( 11 / 24 )0.5230.00323564332940175161.637098640504
Trimmed Mean ( 12 / 24 )0.5231250.00325015343336673160.953939783117
Trimmed Mean ( 13 / 24 )0.5232608695652170.00326086956521739160.466666666667
Trimmed Mean ( 14 / 24 )0.5234090909090910.00326657720240287160.231660994902
Trimmed Mean ( 15 / 24 )0.5235714285714290.00326565609125051160.326566527995
Trimmed Mean ( 16 / 24 )0.523750.00325591178296673160.861237930338
Trimmed Mean ( 17 / 24 )0.5239473684210530.00323431709445059161.996289516584
Trimmed Mean ( 18 / 24 )0.5241666666666670.0031966003766899163.976288837657
Trimmed Mean ( 19 / 24 )0.5241176470588240.00321864130995413162.83816573096
Trimmed Mean ( 20 / 24 )0.52406250.00323349952114204162.072855299173
Trimmed Mean ( 21 / 24 )0.5240.00323770885360152161.842841247792
Trimmed Mean ( 22 / 24 )0.5239285714285710.00322602207725439162.407001217573
Trimmed Mean ( 23 / 24 )0.5238461538461540.00319022174666581164.203680949025
Trimmed Mean ( 24 / 24 )0.5241666666666670.00323682763521579161.93839330951
Median0.53
Midrange0.515
Midmean - Weighted Average at Xnp0.524038461538461
Midmean - Weighted Average at X(n+1)p0.529333333333333
Midmean - Empirical Distribution Function0.524038461538461
Midmean - Empirical Distribution Function - Averaging0.529333333333333
Midmean - Empirical Distribution Function - Interpolation0.529333333333333
Midmean - Closest Observation0.524038461538461
Midmean - True Basic - Statistics Graphics Toolkit0.529333333333333
Midmean - MS Excel (old versions)0.524038461538461
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 0.520972222222222 & 0.00357219155597884 & 145.841065367914 \tabularnewline
Geometric Mean & 0.520092573969967 &  &  \tabularnewline
Harmonic Mean & 0.519204091253245 &  &  \tabularnewline
Quadratic Mean & 0.521841025174866 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 0.520972222222222 & 0.00357219155597884 & 145.841065367914 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 0.520972222222222 & 0.00357219155597884 & 145.841065367914 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 0.520972222222222 & 0.00357219155597884 & 145.841065367914 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 0.520972222222222 & 0.00357219155597884 & 145.841065367914 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 0.520972222222222 & 0.00357219155597884 & 145.841065367914 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 0.521805555555556 & 0.00341637402209956 & 152.736659446578 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 0.521805555555556 & 0.00341637402209956 & 152.736659446578 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 0.521805555555556 & 0.00341637402209956 & 152.736659446578 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 0.520555555555556 & 0.00323740419939641 & 160.794118835272 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 0.520555555555556 & 0.00323740419939641 & 160.794118835272 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 0.522083333333333 & 0.0029862589583809 & 174.828553253264 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 0.522083333333333 & 0.0029862589583809 & 174.828553253264 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 0.522083333333333 & 0.0029862589583809 & 174.828553253264 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 0.522083333333333 & 0.0029862589583809 & 174.828553253264 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 0.522083333333333 & 0.0029862589583809 & 174.828553253264 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 0.522083333333333 & 0.0029862589583809 & 174.828553253264 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 0.522083333333333 & 0.0029862589583809 & 174.828553253264 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 0.524583333333333 & 0.00263105252744808 & 199.381550866314 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 0.524583333333333 & 0.00263105252744808 & 199.381550866314 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 0.524583333333333 & 0.00263105252744808 & 199.381550866314 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 0.524583333333333 & 0.00263105252744808 & 199.381550866314 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 0.524583333333333 & 0.00263105252744808 & 199.381550866314 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 0.521388888888889 & 0.00222295566925982 & 234.547587295116 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 0.521388888888889 & 0.00222295566925982 & 234.547587295116 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 0.521142857142857 & 0.00355694786896876 & 146.514055403896 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 0.521323529411765 & 0.00353649238536974 & 147.412597739062 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 0.521515151515151 & 0.00350984246614801 & 148.586484021747 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 0.52171875 & 0.00347578562191113 & 150.100957524859 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 0.521935483870968 & 0.00343280831205588 & 152.043294126839 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 0.522166666666667 & 0.00337899515925258 & 154.533120663649 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 0.522241379310345 & 0.00335482878723613 & 155.668563861523 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 0.522321428571429 & 0.00332240594473276 & 157.211802910328 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 0.522407407407407 & 0.00327981337337415 & 159.279613787895 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 0.522692307692308 & 0.00326223632933456 & 160.225150763044 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 0.523 & 0.00323564332940175 & 161.637098640504 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 0.523125 & 0.00325015343336673 & 160.953939783117 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 0.523260869565217 & 0.00326086956521739 & 160.466666666667 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 0.523409090909091 & 0.00326657720240287 & 160.231660994902 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 0.523571428571429 & 0.00326565609125051 & 160.326566527995 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 0.52375 & 0.00325591178296673 & 160.861237930338 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 0.523947368421053 & 0.00323431709445059 & 161.996289516584 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 0.524166666666667 & 0.0031966003766899 & 163.976288837657 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 0.524117647058824 & 0.00321864130995413 & 162.83816573096 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 0.5240625 & 0.00323349952114204 & 162.072855299173 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 0.524 & 0.00323770885360152 & 161.842841247792 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 0.523928571428571 & 0.00322602207725439 & 162.407001217573 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 0.523846153846154 & 0.00319022174666581 & 164.203680949025 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 0.524166666666667 & 0.00323682763521579 & 161.93839330951 \tabularnewline
Median & 0.53 &  &  \tabularnewline
Midrange & 0.515 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 0.524038461538461 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 0.529333333333333 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 0.524038461538461 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 0.529333333333333 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 0.529333333333333 &  &  \tabularnewline
Midmean - Closest Observation & 0.524038461538461 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 0.529333333333333 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 0.524038461538461 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=180117&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]0.520972222222222[/C][C]0.00357219155597884[/C][C]145.841065367914[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]0.520092573969967[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]0.519204091253245[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]0.521841025174866[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]0.520972222222222[/C][C]0.00357219155597884[/C][C]145.841065367914[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]0.520972222222222[/C][C]0.00357219155597884[/C][C]145.841065367914[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]0.520972222222222[/C][C]0.00357219155597884[/C][C]145.841065367914[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]0.520972222222222[/C][C]0.00357219155597884[/C][C]145.841065367914[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]0.520972222222222[/C][C]0.00357219155597884[/C][C]145.841065367914[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]0.521805555555556[/C][C]0.00341637402209956[/C][C]152.736659446578[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]0.521805555555556[/C][C]0.00341637402209956[/C][C]152.736659446578[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]0.521805555555556[/C][C]0.00341637402209956[/C][C]152.736659446578[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]0.520555555555556[/C][C]0.00323740419939641[/C][C]160.794118835272[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]0.520555555555556[/C][C]0.00323740419939641[/C][C]160.794118835272[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]0.522083333333333[/C][C]0.0029862589583809[/C][C]174.828553253264[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]0.522083333333333[/C][C]0.0029862589583809[/C][C]174.828553253264[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]0.522083333333333[/C][C]0.0029862589583809[/C][C]174.828553253264[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]0.522083333333333[/C][C]0.0029862589583809[/C][C]174.828553253264[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]0.522083333333333[/C][C]0.0029862589583809[/C][C]174.828553253264[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]0.522083333333333[/C][C]0.0029862589583809[/C][C]174.828553253264[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]0.522083333333333[/C][C]0.0029862589583809[/C][C]174.828553253264[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]0.524583333333333[/C][C]0.00263105252744808[/C][C]199.381550866314[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]0.524583333333333[/C][C]0.00263105252744808[/C][C]199.381550866314[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]0.524583333333333[/C][C]0.00263105252744808[/C][C]199.381550866314[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]0.524583333333333[/C][C]0.00263105252744808[/C][C]199.381550866314[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]0.524583333333333[/C][C]0.00263105252744808[/C][C]199.381550866314[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]0.521388888888889[/C][C]0.00222295566925982[/C][C]234.547587295116[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]0.521388888888889[/C][C]0.00222295566925982[/C][C]234.547587295116[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]0.521142857142857[/C][C]0.00355694786896876[/C][C]146.514055403896[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]0.521323529411765[/C][C]0.00353649238536974[/C][C]147.412597739062[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]0.521515151515151[/C][C]0.00350984246614801[/C][C]148.586484021747[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]0.52171875[/C][C]0.00347578562191113[/C][C]150.100957524859[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]0.521935483870968[/C][C]0.00343280831205588[/C][C]152.043294126839[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]0.522166666666667[/C][C]0.00337899515925258[/C][C]154.533120663649[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]0.522241379310345[/C][C]0.00335482878723613[/C][C]155.668563861523[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]0.522321428571429[/C][C]0.00332240594473276[/C][C]157.211802910328[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]0.522407407407407[/C][C]0.00327981337337415[/C][C]159.279613787895[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]0.522692307692308[/C][C]0.00326223632933456[/C][C]160.225150763044[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]0.523[/C][C]0.00323564332940175[/C][C]161.637098640504[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]0.523125[/C][C]0.00325015343336673[/C][C]160.953939783117[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]0.523260869565217[/C][C]0.00326086956521739[/C][C]160.466666666667[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]0.523409090909091[/C][C]0.00326657720240287[/C][C]160.231660994902[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]0.523571428571429[/C][C]0.00326565609125051[/C][C]160.326566527995[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]0.52375[/C][C]0.00325591178296673[/C][C]160.861237930338[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]0.523947368421053[/C][C]0.00323431709445059[/C][C]161.996289516584[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]0.524166666666667[/C][C]0.0031966003766899[/C][C]163.976288837657[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]0.524117647058824[/C][C]0.00321864130995413[/C][C]162.83816573096[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]0.5240625[/C][C]0.00323349952114204[/C][C]162.072855299173[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]0.524[/C][C]0.00323770885360152[/C][C]161.842841247792[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]0.523928571428571[/C][C]0.00322602207725439[/C][C]162.407001217573[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]0.523846153846154[/C][C]0.00319022174666581[/C][C]164.203680949025[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]0.524166666666667[/C][C]0.00323682763521579[/C][C]161.93839330951[/C][/ROW]
[ROW][C]Median[/C][C]0.53[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]0.515[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]0.524038461538461[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]0.529333333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]0.524038461538461[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]0.529333333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]0.529333333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]0.524038461538461[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]0.529333333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]0.524038461538461[/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=180117&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=180117&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 Mean0.5209722222222220.00357219155597884145.841065367914
Geometric Mean0.520092573969967
Harmonic Mean0.519204091253245
Quadratic Mean0.521841025174866
Winsorized Mean ( 1 / 24 )0.5209722222222220.00357219155597884145.841065367914
Winsorized Mean ( 2 / 24 )0.5209722222222220.00357219155597884145.841065367914
Winsorized Mean ( 3 / 24 )0.5209722222222220.00357219155597884145.841065367914
Winsorized Mean ( 4 / 24 )0.5209722222222220.00357219155597884145.841065367914
Winsorized Mean ( 5 / 24 )0.5209722222222220.00357219155597884145.841065367914
Winsorized Mean ( 6 / 24 )0.5218055555555560.00341637402209956152.736659446578
Winsorized Mean ( 7 / 24 )0.5218055555555560.00341637402209956152.736659446578
Winsorized Mean ( 8 / 24 )0.5218055555555560.00341637402209956152.736659446578
Winsorized Mean ( 9 / 24 )0.5205555555555560.00323740419939641160.794118835272
Winsorized Mean ( 10 / 24 )0.5205555555555560.00323740419939641160.794118835272
Winsorized Mean ( 11 / 24 )0.5220833333333330.0029862589583809174.828553253264
Winsorized Mean ( 12 / 24 )0.5220833333333330.0029862589583809174.828553253264
Winsorized Mean ( 13 / 24 )0.5220833333333330.0029862589583809174.828553253264
Winsorized Mean ( 14 / 24 )0.5220833333333330.0029862589583809174.828553253264
Winsorized Mean ( 15 / 24 )0.5220833333333330.0029862589583809174.828553253264
Winsorized Mean ( 16 / 24 )0.5220833333333330.0029862589583809174.828553253264
Winsorized Mean ( 17 / 24 )0.5220833333333330.0029862589583809174.828553253264
Winsorized Mean ( 18 / 24 )0.5245833333333330.00263105252744808199.381550866314
Winsorized Mean ( 19 / 24 )0.5245833333333330.00263105252744808199.381550866314
Winsorized Mean ( 20 / 24 )0.5245833333333330.00263105252744808199.381550866314
Winsorized Mean ( 21 / 24 )0.5245833333333330.00263105252744808199.381550866314
Winsorized Mean ( 22 / 24 )0.5245833333333330.00263105252744808199.381550866314
Winsorized Mean ( 23 / 24 )0.5213888888888890.00222295566925982234.547587295116
Winsorized Mean ( 24 / 24 )0.5213888888888890.00222295566925982234.547587295116
Trimmed Mean ( 1 / 24 )0.5211428571428570.00355694786896876146.514055403896
Trimmed Mean ( 2 / 24 )0.5213235294117650.00353649238536974147.412597739062
Trimmed Mean ( 3 / 24 )0.5215151515151510.00350984246614801148.586484021747
Trimmed Mean ( 4 / 24 )0.521718750.00347578562191113150.100957524859
Trimmed Mean ( 5 / 24 )0.5219354838709680.00343280831205588152.043294126839
Trimmed Mean ( 6 / 24 )0.5221666666666670.00337899515925258154.533120663649
Trimmed Mean ( 7 / 24 )0.5222413793103450.00335482878723613155.668563861523
Trimmed Mean ( 8 / 24 )0.5223214285714290.00332240594473276157.211802910328
Trimmed Mean ( 9 / 24 )0.5224074074074070.00327981337337415159.279613787895
Trimmed Mean ( 10 / 24 )0.5226923076923080.00326223632933456160.225150763044
Trimmed Mean ( 11 / 24 )0.5230.00323564332940175161.637098640504
Trimmed Mean ( 12 / 24 )0.5231250.00325015343336673160.953939783117
Trimmed Mean ( 13 / 24 )0.5232608695652170.00326086956521739160.466666666667
Trimmed Mean ( 14 / 24 )0.5234090909090910.00326657720240287160.231660994902
Trimmed Mean ( 15 / 24 )0.5235714285714290.00326565609125051160.326566527995
Trimmed Mean ( 16 / 24 )0.523750.00325591178296673160.861237930338
Trimmed Mean ( 17 / 24 )0.5239473684210530.00323431709445059161.996289516584
Trimmed Mean ( 18 / 24 )0.5241666666666670.0031966003766899163.976288837657
Trimmed Mean ( 19 / 24 )0.5241176470588240.00321864130995413162.83816573096
Trimmed Mean ( 20 / 24 )0.52406250.00323349952114204162.072855299173
Trimmed Mean ( 21 / 24 )0.5240.00323770885360152161.842841247792
Trimmed Mean ( 22 / 24 )0.5239285714285710.00322602207725439162.407001217573
Trimmed Mean ( 23 / 24 )0.5238461538461540.00319022174666581164.203680949025
Trimmed Mean ( 24 / 24 )0.5241666666666670.00323682763521579161.93839330951
Median0.53
Midrange0.515
Midmean - Weighted Average at Xnp0.524038461538461
Midmean - Weighted Average at X(n+1)p0.529333333333333
Midmean - Empirical Distribution Function0.524038461538461
Midmean - Empirical Distribution Function - Averaging0.529333333333333
Midmean - Empirical Distribution Function - Interpolation0.529333333333333
Midmean - Closest Observation0.524038461538461
Midmean - True Basic - Statistics Graphics Toolkit0.529333333333333
Midmean - MS Excel (old versions)0.524038461538461
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')