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Author

*Unverified author*

R Software Module

rwasp_centraltendency.wasp

Title produced by software

Central Tendency

Date of computation

Mon, 21 Apr 2008 11:07:31 -0600

Cite this page as follows

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2008/Apr/21/t1208797791ysj3q2bx4mhjfxr.htm/, Retrieved Thu, 16 May 2024 07:37:56 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=10546, Retrieved Thu, 16 May 2024 07:37:56 +0000

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Original text written by user:

Centrummaten Gemiddele Prijs Zakje Frieten

IsPrivate?

No (this computation is public)

User-defined keywords

Centrummaten, gemiddele, prijs, zakje frieten

Estimated Impact

176

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)

-       [Central Tendency] [Centrummaten Gemi...] [2008-04-21 17:07:31] [d41d8cd98f00b204e9800998ecf8427e] [Current]

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Dataseries X:

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1,72
1,73
1,73
1,73
1,73
1,73
1,74
1,74
1,74
1,74
1,75
1,75
1,75
1,75
1,75
1,76
1,77
1,77
1,78
1,78
1,78
1,79
1,8
1,8
1,82
1,83
1,85
1,86
1,86
1,87
1,88
1,88
1,89
1,9
1,9
1,9
1,9
1,92
1,92
1,93
1,93
1,93
1,94
1,94
1,95
1,96
1,96
1,96
1,96
1,97
1,97
1,98
1,99
1,99
1,99
2
2
2,01
2,01
2,01
2,02
2,02
2,02
2,02
2,03
2,03
2,03
2,04
2,04
2,05
2,06
2,06

Summary of compuational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	1 seconds
R Server	'George Udny Yule' @ 72.249.76.132

\begin{tabular}{lllllllll}
\hline
Summary of compuational 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 & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=10546&T=0

[TABLE]
[ROW][C]Summary of compuational 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]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=10546&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=10546&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 compuational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	1 seconds
R Server	'George Udny Yule' @ 72.249.76.132

Central Tendency - Ungrouped Data
Measure	Value	S.E.	Value/S.E.
Arithmetic Mean	1.89013888888889	0.0130748014338066	144.563487136537
Geometric Mean	1.88690491062862
Harmonic Mean	1.88365289807732
Quadratic Mean	1.89334690429409
Winsorized Mean ( 1 / 24 )	1.89027777777778	0.0130500604424550	144.848200980605
Winsorized Mean ( 2 / 24 )	1.89	0.0130005417005232	145.378557566101
Winsorized Mean ( 3 / 24 )	1.88958333333333	0.0129302896508096	146.136195271930
Winsorized Mean ( 4 / 24 )	1.88958333333333	0.0129302896508096	146.136195271930
Winsorized Mean ( 5 / 24 )	1.88888888888889	0.0128195547573488	147.344344218046
Winsorized Mean ( 6 / 24 )	1.88972222222222	0.0126774913936813	149.061211208086
Winsorized Mean ( 7 / 24 )	1.88972222222222	0.0126774913936813	149.061211208086
Winsorized Mean ( 8 / 24 )	1.88861111111111	0.0125086911187277	150.983911360920
Winsorized Mean ( 9 / 24 )	1.88861111111111	0.0125086911187277	150.983911360919
Winsorized Mean ( 10 / 24 )	1.89	0.0122809444361633	153.896958806732
Winsorized Mean ( 11 / 24 )	1.89	0.0122809444361633	153.896958806732
Winsorized Mean ( 12 / 24 )	1.88833333333333	0.0120380201035104	156.864111963286
Winsorized Mean ( 13 / 24 )	1.88833333333333	0.0120380201035104	156.864111963286
Winsorized Mean ( 14 / 24 )	1.88833333333333	0.0120380201035104	156.864111963286
Winsorized Mean ( 15 / 24 )	1.88833333333333	0.0114123865387645	165.463492400930
Winsorized Mean ( 16 / 24 )	1.89055555555556	0.0110658310549269	170.846233434389
Winsorized Mean ( 17 / 24 )	1.88819444444444	0.0107437181647453	175.748694771277
Winsorized Mean ( 18 / 24 )	1.89069444444444	0.0103618536992594	182.466815235925
Winsorized Mean ( 19 / 24 )	1.89069444444444	0.0103618536992594	182.466815235925
Winsorized Mean ( 20 / 24 )	1.88791666666667	0.00999400739848956	188.904869827492
Winsorized Mean ( 21 / 24 )	1.88791666666667	0.00917986139560759	205.658515451007
Winsorized Mean ( 22 / 24 )	1.89097222222222	0.00872587154402053	216.708693530794
Winsorized Mean ( 23 / 24 )	1.88777777777778	0.0083268101751256	226.710797781493
Winsorized Mean ( 24 / 24 )	1.89444444444444	0.00735551725921314	257.554211034113
Trimmed Mean ( 1 / 24 )	1.89014285714286	0.0129986348337872	145.410874396581
Trimmed Mean ( 2 / 24 )	1.89	0.0129291987031091	146.180752837027
Trimmed Mean ( 3 / 24 )	1.89	0.0128683489847923	146.871988180736
Trimmed Mean ( 4 / 24 )	1.89015625	0.0128164162375295	147.479312076739
Trimmed Mean ( 5 / 24 )	1.89032258064516	0.0127435921246659	148.335144608587
Trimmed Mean ( 6 / 24 )	1.89066666666667	0.0126778125210996	149.131931358035
Trimmed Mean ( 7 / 24 )	1.89086206896552	0.0126239396606796	149.783832923019
Trimmed Mean ( 8 / 24 )	1.89107142857143	0.0125451873408666	150.740788255203
Trimmed Mean ( 9 / 24 )	1.89148148148148	0.0124733325809453	151.642030644719
Trimmed Mean ( 10 / 24 )	1.89192307692308	0.0123701047619006	152.943173347255
Trimmed Mean ( 11 / 24 )	1.8922	0.0122767076620895	154.129270817706
Trimmed Mean ( 12 / 24 )	1.8925	0.0121438628226491	155.840034397487
Trimmed Mean ( 13 / 24 )	1.89304347826087	0.0120099377739859	157.623087969805
Trimmed Mean ( 14 / 24 )	1.89363636363636	0.0118218403834552	160.181181796916
Trimmed Mean ( 15 / 24 )	1.89428571428571	0.0115628005860058	163.825856910334
Trimmed Mean ( 16 / 24 )	1.895	0.0113510419718259	166.945026254288
Trimmed Mean ( 17 / 24 )	1.89552631578947	0.0111353841745237	170.225497933533
Trimmed Mean ( 18 / 24 )	1.89638888888889	0.0108974496636174	174.021348795052
Trimmed Mean ( 19 / 24 )	1.89705882352941	0.0106519178205495	178.095518148819
Trimmed Mean ( 20 / 24 )	1.8978125	0.0102855831514858	184.511900983062
Trimmed Mean ( 21 / 24 )	1.899	0.00984185292338374	192.951471108461
Trimmed Mean ( 22 / 24 )	1.90035714285714	0.0094348524052736	201.418852275309
Trimmed Mean ( 23 / 24 )	1.90153846153846	0.00897333327471857	211.90993394794
Trimmed Mean ( 24 / 24 )	1.90333333333333	0.00835504418211083	227.806495315561
Median	1.9
Midrange	1.89
Midmean - Weighted Average at Xnp	1.89230769230769
Midmean - Weighted Average at X(n+1)p	1.89891891891892
Midmean - Empirical Distribution Function	1.89230769230769
Midmean - Empirical Distribution Function - Averaging	1.89891891891892
Midmean - Empirical Distribution Function - Interpolation	1.89891891891892
Midmean - Closest Observation	1.89230769230769
Midmean - True Basic - Statistics Graphics Toolkit	1.89891891891892
Midmean - MS Excel (old versions)	1.89230769230769
Number of observations	72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 1.89013888888889 & 0.0130748014338066 & 144.563487136537 \tabularnewline
Geometric Mean & 1.88690491062862 &  &  \tabularnewline
Harmonic Mean & 1.88365289807732 &  &  \tabularnewline
Quadratic Mean & 1.89334690429409 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 1.89027777777778 & 0.0130500604424550 & 144.848200980605 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 1.89 & 0.0130005417005232 & 145.378557566101 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 1.88958333333333 & 0.0129302896508096 & 146.136195271930 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 1.88958333333333 & 0.0129302896508096 & 146.136195271930 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 1.88888888888889 & 0.0128195547573488 & 147.344344218046 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 1.88972222222222 & 0.0126774913936813 & 149.061211208086 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 1.88972222222222 & 0.0126774913936813 & 149.061211208086 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 1.88861111111111 & 0.0125086911187277 & 150.983911360920 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 1.88861111111111 & 0.0125086911187277 & 150.983911360919 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 1.89 & 0.0122809444361633 & 153.896958806732 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 1.89 & 0.0122809444361633 & 153.896958806732 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 1.88833333333333 & 0.0120380201035104 & 156.864111963286 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 1.88833333333333 & 0.0120380201035104 & 156.864111963286 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 1.88833333333333 & 0.0120380201035104 & 156.864111963286 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 1.88833333333333 & 0.0114123865387645 & 165.463492400930 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 1.89055555555556 & 0.0110658310549269 & 170.846233434389 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 1.88819444444444 & 0.0107437181647453 & 175.748694771277 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 1.89069444444444 & 0.0103618536992594 & 182.466815235925 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 1.89069444444444 & 0.0103618536992594 & 182.466815235925 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 1.88791666666667 & 0.00999400739848956 & 188.904869827492 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 1.88791666666667 & 0.00917986139560759 & 205.658515451007 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 1.89097222222222 & 0.00872587154402053 & 216.708693530794 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 1.88777777777778 & 0.0083268101751256 & 226.710797781493 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 1.89444444444444 & 0.00735551725921314 & 257.554211034113 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 1.89014285714286 & 0.0129986348337872 & 145.410874396581 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 1.89 & 0.0129291987031091 & 146.180752837027 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 1.89 & 0.0128683489847923 & 146.871988180736 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 1.89015625 & 0.0128164162375295 & 147.479312076739 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 1.89032258064516 & 0.0127435921246659 & 148.335144608587 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 1.89066666666667 & 0.0126778125210996 & 149.131931358035 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 1.89086206896552 & 0.0126239396606796 & 149.783832923019 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 1.89107142857143 & 0.0125451873408666 & 150.740788255203 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 1.89148148148148 & 0.0124733325809453 & 151.642030644719 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 1.89192307692308 & 0.0123701047619006 & 152.943173347255 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 1.8922 & 0.0122767076620895 & 154.129270817706 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 1.8925 & 0.0121438628226491 & 155.840034397487 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 1.89304347826087 & 0.0120099377739859 & 157.623087969805 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 1.89363636363636 & 0.0118218403834552 & 160.181181796916 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 1.89428571428571 & 0.0115628005860058 & 163.825856910334 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 1.895 & 0.0113510419718259 & 166.945026254288 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 1.89552631578947 & 0.0111353841745237 & 170.225497933533 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 1.89638888888889 & 0.0108974496636174 & 174.021348795052 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 1.89705882352941 & 0.0106519178205495 & 178.095518148819 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 1.8978125 & 0.0102855831514858 & 184.511900983062 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 1.899 & 0.00984185292338374 & 192.951471108461 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 1.90035714285714 & 0.0094348524052736 & 201.418852275309 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 1.90153846153846 & 0.00897333327471857 & 211.90993394794 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 1.90333333333333 & 0.00835504418211083 & 227.806495315561 \tabularnewline
Median & 1.9 &  &  \tabularnewline
Midrange & 1.89 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 1.89230769230769 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 1.89891891891892 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 1.89230769230769 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 1.89891891891892 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 1.89891891891892 &  &  \tabularnewline
Midmean - Closest Observation & 1.89230769230769 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 1.89891891891892 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 1.89230769230769 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=10546&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]1.89013888888889[/C][C]0.0130748014338066[/C][C]144.563487136537[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]1.88690491062862[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]1.88365289807732[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]1.89334690429409[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]1.89027777777778[/C][C]0.0130500604424550[/C][C]144.848200980605[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]1.89[/C][C]0.0130005417005232[/C][C]145.378557566101[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]1.88958333333333[/C][C]0.0129302896508096[/C][C]146.136195271930[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]1.88958333333333[/C][C]0.0129302896508096[/C][C]146.136195271930[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]1.88888888888889[/C][C]0.0128195547573488[/C][C]147.344344218046[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]1.88972222222222[/C][C]0.0126774913936813[/C][C]149.061211208086[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]1.88972222222222[/C][C]0.0126774913936813[/C][C]149.061211208086[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]1.88861111111111[/C][C]0.0125086911187277[/C][C]150.983911360920[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]1.88861111111111[/C][C]0.0125086911187277[/C][C]150.983911360919[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]1.89[/C][C]0.0122809444361633[/C][C]153.896958806732[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]1.89[/C][C]0.0122809444361633[/C][C]153.896958806732[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]1.88833333333333[/C][C]0.0120380201035104[/C][C]156.864111963286[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]1.88833333333333[/C][C]0.0120380201035104[/C][C]156.864111963286[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]1.88833333333333[/C][C]0.0120380201035104[/C][C]156.864111963286[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]1.88833333333333[/C][C]0.0114123865387645[/C][C]165.463492400930[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]1.89055555555556[/C][C]0.0110658310549269[/C][C]170.846233434389[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]1.88819444444444[/C][C]0.0107437181647453[/C][C]175.748694771277[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]1.89069444444444[/C][C]0.0103618536992594[/C][C]182.466815235925[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]1.89069444444444[/C][C]0.0103618536992594[/C][C]182.466815235925[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]1.88791666666667[/C][C]0.00999400739848956[/C][C]188.904869827492[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]1.88791666666667[/C][C]0.00917986139560759[/C][C]205.658515451007[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]1.89097222222222[/C][C]0.00872587154402053[/C][C]216.708693530794[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]1.88777777777778[/C][C]0.0083268101751256[/C][C]226.710797781493[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]1.89444444444444[/C][C]0.00735551725921314[/C][C]257.554211034113[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]1.89014285714286[/C][C]0.0129986348337872[/C][C]145.410874396581[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]1.89[/C][C]0.0129291987031091[/C][C]146.180752837027[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]1.89[/C][C]0.0128683489847923[/C][C]146.871988180736[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]1.89015625[/C][C]0.0128164162375295[/C][C]147.479312076739[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]1.89032258064516[/C][C]0.0127435921246659[/C][C]148.335144608587[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]1.89066666666667[/C][C]0.0126778125210996[/C][C]149.131931358035[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]1.89086206896552[/C][C]0.0126239396606796[/C][C]149.783832923019[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]1.89107142857143[/C][C]0.0125451873408666[/C][C]150.740788255203[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]1.89148148148148[/C][C]0.0124733325809453[/C][C]151.642030644719[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]1.89192307692308[/C][C]0.0123701047619006[/C][C]152.943173347255[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]1.8922[/C][C]0.0122767076620895[/C][C]154.129270817706[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]1.8925[/C][C]0.0121438628226491[/C][C]155.840034397487[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]1.89304347826087[/C][C]0.0120099377739859[/C][C]157.623087969805[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]1.89363636363636[/C][C]0.0118218403834552[/C][C]160.181181796916[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]1.89428571428571[/C][C]0.0115628005860058[/C][C]163.825856910334[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]1.895[/C][C]0.0113510419718259[/C][C]166.945026254288[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]1.89552631578947[/C][C]0.0111353841745237[/C][C]170.225497933533[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]1.89638888888889[/C][C]0.0108974496636174[/C][C]174.021348795052[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]1.89705882352941[/C][C]0.0106519178205495[/C][C]178.095518148819[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]1.8978125[/C][C]0.0102855831514858[/C][C]184.511900983062[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]1.899[/C][C]0.00984185292338374[/C][C]192.951471108461[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]1.90035714285714[/C][C]0.0094348524052736[/C][C]201.418852275309[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]1.90153846153846[/C][C]0.00897333327471857[/C][C]211.90993394794[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]1.90333333333333[/C][C]0.00835504418211083[/C][C]227.806495315561[/C][/ROW]
[ROW][C]Median[/C][C]1.9[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]1.89[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]1.89230769230769[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]1.89891891891892[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]1.89230769230769[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]1.89891891891892[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]1.89891891891892[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]1.89230769230769[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]1.89891891891892[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]1.89230769230769[/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=10546&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=10546&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
Measure	Value	S.E.	Value/S.E.
Arithmetic Mean	1.89013888888889	0.0130748014338066	144.563487136537
Geometric Mean	1.88690491062862
Harmonic Mean	1.88365289807732
Quadratic Mean	1.89334690429409
Winsorized Mean ( 1 / 24 )	1.89027777777778	0.0130500604424550	144.848200980605
Winsorized Mean ( 2 / 24 )	1.89	0.0130005417005232	145.378557566101
Winsorized Mean ( 3 / 24 )	1.88958333333333	0.0129302896508096	146.136195271930
Winsorized Mean ( 4 / 24 )	1.88958333333333	0.0129302896508096	146.136195271930
Winsorized Mean ( 5 / 24 )	1.88888888888889	0.0128195547573488	147.344344218046
Winsorized Mean ( 6 / 24 )	1.88972222222222	0.0126774913936813	149.061211208086
Winsorized Mean ( 7 / 24 )	1.88972222222222	0.0126774913936813	149.061211208086
Winsorized Mean ( 8 / 24 )	1.88861111111111	0.0125086911187277	150.983911360920
Winsorized Mean ( 9 / 24 )	1.88861111111111	0.0125086911187277	150.983911360919
Winsorized Mean ( 10 / 24 )	1.89	0.0122809444361633	153.896958806732
Winsorized Mean ( 11 / 24 )	1.89	0.0122809444361633	153.896958806732
Winsorized Mean ( 12 / 24 )	1.88833333333333	0.0120380201035104	156.864111963286
Winsorized Mean ( 13 / 24 )	1.88833333333333	0.0120380201035104	156.864111963286
Winsorized Mean ( 14 / 24 )	1.88833333333333	0.0120380201035104	156.864111963286
Winsorized Mean ( 15 / 24 )	1.88833333333333	0.0114123865387645	165.463492400930
Winsorized Mean ( 16 / 24 )	1.89055555555556	0.0110658310549269	170.846233434389
Winsorized Mean ( 17 / 24 )	1.88819444444444	0.0107437181647453	175.748694771277
Winsorized Mean ( 18 / 24 )	1.89069444444444	0.0103618536992594	182.466815235925
Winsorized Mean ( 19 / 24 )	1.89069444444444	0.0103618536992594	182.466815235925
Winsorized Mean ( 20 / 24 )	1.88791666666667	0.00999400739848956	188.904869827492
Winsorized Mean ( 21 / 24 )	1.88791666666667	0.00917986139560759	205.658515451007
Winsorized Mean ( 22 / 24 )	1.89097222222222	0.00872587154402053	216.708693530794
Winsorized Mean ( 23 / 24 )	1.88777777777778	0.0083268101751256	226.710797781493
Winsorized Mean ( 24 / 24 )	1.89444444444444	0.00735551725921314	257.554211034113
Trimmed Mean ( 1 / 24 )	1.89014285714286	0.0129986348337872	145.410874396581
Trimmed Mean ( 2 / 24 )	1.89	0.0129291987031091	146.180752837027
Trimmed Mean ( 3 / 24 )	1.89	0.0128683489847923	146.871988180736
Trimmed Mean ( 4 / 24 )	1.89015625	0.0128164162375295	147.479312076739
Trimmed Mean ( 5 / 24 )	1.89032258064516	0.0127435921246659	148.335144608587
Trimmed Mean ( 6 / 24 )	1.89066666666667	0.0126778125210996	149.131931358035
Trimmed Mean ( 7 / 24 )	1.89086206896552	0.0126239396606796	149.783832923019
Trimmed Mean ( 8 / 24 )	1.89107142857143	0.0125451873408666	150.740788255203
Trimmed Mean ( 9 / 24 )	1.89148148148148	0.0124733325809453	151.642030644719
Trimmed Mean ( 10 / 24 )	1.89192307692308	0.0123701047619006	152.943173347255
Trimmed Mean ( 11 / 24 )	1.8922	0.0122767076620895	154.129270817706
Trimmed Mean ( 12 / 24 )	1.8925	0.0121438628226491	155.840034397487
Trimmed Mean ( 13 / 24 )	1.89304347826087	0.0120099377739859	157.623087969805
Trimmed Mean ( 14 / 24 )	1.89363636363636	0.0118218403834552	160.181181796916
Trimmed Mean ( 15 / 24 )	1.89428571428571	0.0115628005860058	163.825856910334
Trimmed Mean ( 16 / 24 )	1.895	0.0113510419718259	166.945026254288
Trimmed Mean ( 17 / 24 )	1.89552631578947	0.0111353841745237	170.225497933533
Trimmed Mean ( 18 / 24 )	1.89638888888889	0.0108974496636174	174.021348795052
Trimmed Mean ( 19 / 24 )	1.89705882352941	0.0106519178205495	178.095518148819
Trimmed Mean ( 20 / 24 )	1.8978125	0.0102855831514858	184.511900983062
Trimmed Mean ( 21 / 24 )	1.899	0.00984185292338374	192.951471108461
Trimmed Mean ( 22 / 24 )	1.90035714285714	0.0094348524052736	201.418852275309
Trimmed Mean ( 23 / 24 )	1.90153846153846	0.00897333327471857	211.90993394794
Trimmed Mean ( 24 / 24 )	1.90333333333333	0.00835504418211083	227.806495315561
Median	1.9
Midrange	1.89
Midmean - Weighted Average at Xnp	1.89230769230769
Midmean - Weighted Average at X(n+1)p	1.89891891891892
Midmean - Empirical Distribution Function	1.89230769230769
Midmean - Empirical Distribution Function - Averaging	1.89891891891892
Midmean - Empirical Distribution Function - Interpolation	1.89891891891892
Midmean - Closest Observation	1.89230769230769
Midmean - True Basic - Statistics Graphics Toolkit	1.89891891891892
Midmean - MS Excel (old versions)	1.89230769230769
Number of observations	72

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

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')

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code