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Author

*The author of this computation has been verified*

R Software Module

rwasp_centraltendency.wasp

Title produced by software

Central Tendency

Date of computation

Tue, 08 Dec 2015 15:00:28 +0000

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/2015/Dec/08/t1449586889mit9tt9vevtxfb9.htm/, Retrieved Thu, 16 May 2024 13:32:56 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=285513, Retrieved Thu, 16 May 2024 13:32:56 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

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

-       [Central Tendency] [] [2015-12-08 15:00:28] [c64ec7a2d0db7c519901da97df98e10d] [Current]

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Dataseries X:

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-27
-29
-33
-27
-22
-23
-23
-15
-15
-24
-18
-14
-7
-12
-12
-15
-16
-17
-13
-8
-13
-13
-11
-16
-5
-3
-7
-10
-10
-11
-11
-19
-30
-38
-36
-40
-34
-35
-38
-32
-37
-39
-31
-30
-29
-36
-41
-42
-33
-43
-41
-34
-32
-36
-37
-30
-32
-30
-21
-19
-9
-8
-6
-4
-1
-2
-1
-4
-8
-6
-11
-11

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	2 seconds
R Server	'George Udny Yule' @ yule.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 & 'George Udny Yule' @ yule.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=285513&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'George Udny Yule' @ yule.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=285513&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=285513&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 Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	2 seconds
R Server	'George Udny Yule' @ yule.wessa.net

Central Tendency - Ungrouped Data
Measure	Value	S.E.	Value/S.E.
Arithmetic Mean	-21.1944444444444	1.47668882772624	-14.3526815172558
Geometric Mean	NaN
Harmonic Mean	-9.7098784912797
Quadratic Mean	24.5769765792658
Winsorized Mean ( 1 / 24 )	-21.1805555555556	1.47386283966464	-14.3707779214889
Winsorized Mean ( 2 / 24 )	-21.1805555555556	1.46320633049682	-14.4754400757437
Winsorized Mean ( 3 / 24 )	-21.2222222222222	1.45568635998528	-14.5788425347592
Winsorized Mean ( 4 / 24 )	-21.2222222222222	1.43566005908476	-14.7822056397888
Winsorized Mean ( 5 / 24 )	-21.1527777777778	1.42312937954227	-14.8635662237409
Winsorized Mean ( 6 / 24 )	-21.1527777777778	1.39480644691068	-15.1653857240397
Winsorized Mean ( 7 / 24 )	-21.25	1.37930574947969	-15.4063013280529
Winsorized Mean ( 8 / 24 )	-21.1388888888889	1.36067988442173	-15.5355342067636
Winsorized Mean ( 9 / 24 )	-21.2638888888889	1.34152312467427	-15.8505571002005
Winsorized Mean ( 10 / 24 )	-21.125	1.31901607410822	-16.0157259753506
Winsorized Mean ( 11 / 24 )	-21.2777777777778	1.29647140929155	-16.412068654414
Winsorized Mean ( 12 / 24 )	-21.2777777777778	1.29647140929155	-16.412068654414
Winsorized Mean ( 13 / 24 )	-21.0972222222222	1.26808663339285	-16.6370511814128
Winsorized Mean ( 14 / 24 )	-21.0972222222222	1.21063359202533	-17.4265957604296
Winsorized Mean ( 15 / 24 )	-21.3055555555556	1.1819321349184	-18.0260396736116
Winsorized Mean ( 16 / 24 )	-21.0833333333333	1.14888358410583	-18.3511485628393
Winsorized Mean ( 17 / 24 )	-21.3194444444444	1.11747857613016	-19.0781683871505
Winsorized Mean ( 18 / 24 )	-21.0694444444444	1.0812685973848	-19.4858562390547
Winsorized Mean ( 19 / 24 )	-21.0694444444444	1.0812685973848	-19.4858562390547
Winsorized Mean ( 20 / 24 )	-21.0694444444444	1.0812685973848	-19.4858562390547
Winsorized Mean ( 21 / 24 )	-20.7777777777778	1.0403108025079	-19.9726636767476
Winsorized Mean ( 22 / 24 )	-20.7777777777778	0.958493500031069	-21.6775364434963
Winsorized Mean ( 23 / 24 )	-20.7777777777778	0.958493500031069	-21.6775364434963
Winsorized Mean ( 24 / 24 )	-21.1111111111111	0.916198248982179	-23.0420775575197
Trimmed Mean ( 1 / 24 )	-21.1714285714286	1.45775166918618	-14.5233437347035
Trimmed Mean ( 2 / 24 )	-21.1617647058824	1.43816203888698	-14.7144508989125
Trimmed Mean ( 3 / 24 )	-21.1515151515152	1.42099515741928	-14.8850015716655
Trimmed Mean ( 4 / 24 )	-21.125	1.40320989729727	-15.0547683854632
Trimmed Mean ( 5 / 24 )	-21.0967741935484	1.3883076141195	-15.1960372319419
Trimmed Mean ( 6 / 24 )	-21.0833333333333	1.37333189347739	-15.351957843161
Trimmed Mean ( 7 / 24 )	-21.0689655172414	1.36188325290184	-15.4704637657807
Trimmed Mean ( 8 / 24 )	-21.0357142857143	1.35055647158175	-15.5755903054372
Trimmed Mean ( 9 / 24 )	-21.0185185185185	1.33973587015333	-15.6885539805044
Trimmed Mean ( 10 / 24 )	-20.9807692307692	1.32912903830444	-15.7853516296162
Trimmed Mean ( 11 / 24 )	-20.96	1.31923292492421	-15.8880206853571
Trimmed Mean ( 12 / 24 )	-20.9166666666667	1.30968613712514	-15.970747550692
Trimmed Mean ( 13 / 24 )	-20.8695652173913	1.29570404850276	-16.1067376778724
Trimmed Mean ( 14 / 24 )	-20.8409090909091	1.28206987018168	-16.255673404099
Trimmed Mean ( 15 / 24 )	-20.8095238095238	1.27435078105227	-16.3295099896599
Trimmed Mean ( 16 / 24 )	-20.75	1.26731596044149	-16.3731860464942
Trimmed Mean ( 17 / 24 )	-20.7105263157895	1.2621573206395	-16.4088311156775
Trimmed Mean ( 18 / 24 )	-20.6388888888889	1.2580867167842	-16.4049811619059
Trimmed Mean ( 19 / 24 )	-20.5882352941176	1.25679447313331	-16.3815450610545
Trimmed Mean ( 20 / 24 )	-20.53125	1.24998739913004	-16.4251655771005
Trimmed Mean ( 21 / 24 )	-20.4666666666667	1.23524238705983	-16.5689478284356
Trimmed Mean ( 22 / 24 )	-20.4285714285714	1.22088155701774	-16.7326398790662
Trimmed Mean ( 23 / 24 )	-20.3846153846154	1.21791362972399	-16.7373242955127
Trimmed Mean ( 24 / 24 )	-20.3333333333333	1.20486132864162	-16.8760776447672
Median	-19
Midrange	-22
Midmean - Weighted Average at Xnp	-21.025641025641
Midmean - Weighted Average at X(n+1)p	-20.3783783783784
Midmean - Empirical Distribution Function	-21.025641025641
Midmean - Empirical Distribution Function - Averaging	-20.3783783783784
Midmean - Empirical Distribution Function - Interpolation	-20.3783783783784
Midmean - Closest Observation	-21.025641025641
Midmean - True Basic - Statistics Graphics Toolkit	-20.3783783783784
Midmean - MS Excel (old versions)	-21.025641025641
Number of observations	72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & -21.1944444444444 & 1.47668882772624 & -14.3526815172558 \tabularnewline
Geometric Mean & NaN &  &  \tabularnewline
Harmonic Mean & -9.7098784912797 &  &  \tabularnewline
Quadratic Mean & 24.5769765792658 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & -21.1805555555556 & 1.47386283966464 & -14.3707779214889 \tabularnewline
Winsorized Mean ( 2 / 24 ) & -21.1805555555556 & 1.46320633049682 & -14.4754400757437 \tabularnewline
Winsorized Mean ( 3 / 24 ) & -21.2222222222222 & 1.45568635998528 & -14.5788425347592 \tabularnewline
Winsorized Mean ( 4 / 24 ) & -21.2222222222222 & 1.43566005908476 & -14.7822056397888 \tabularnewline
Winsorized Mean ( 5 / 24 ) & -21.1527777777778 & 1.42312937954227 & -14.8635662237409 \tabularnewline
Winsorized Mean ( 6 / 24 ) & -21.1527777777778 & 1.39480644691068 & -15.1653857240397 \tabularnewline
Winsorized Mean ( 7 / 24 ) & -21.25 & 1.37930574947969 & -15.4063013280529 \tabularnewline
Winsorized Mean ( 8 / 24 ) & -21.1388888888889 & 1.36067988442173 & -15.5355342067636 \tabularnewline
Winsorized Mean ( 9 / 24 ) & -21.2638888888889 & 1.34152312467427 & -15.8505571002005 \tabularnewline
Winsorized Mean ( 10 / 24 ) & -21.125 & 1.31901607410822 & -16.0157259753506 \tabularnewline
Winsorized Mean ( 11 / 24 ) & -21.2777777777778 & 1.29647140929155 & -16.412068654414 \tabularnewline
Winsorized Mean ( 12 / 24 ) & -21.2777777777778 & 1.29647140929155 & -16.412068654414 \tabularnewline
Winsorized Mean ( 13 / 24 ) & -21.0972222222222 & 1.26808663339285 & -16.6370511814128 \tabularnewline
Winsorized Mean ( 14 / 24 ) & -21.0972222222222 & 1.21063359202533 & -17.4265957604296 \tabularnewline
Winsorized Mean ( 15 / 24 ) & -21.3055555555556 & 1.1819321349184 & -18.0260396736116 \tabularnewline
Winsorized Mean ( 16 / 24 ) & -21.0833333333333 & 1.14888358410583 & -18.3511485628393 \tabularnewline
Winsorized Mean ( 17 / 24 ) & -21.3194444444444 & 1.11747857613016 & -19.0781683871505 \tabularnewline
Winsorized Mean ( 18 / 24 ) & -21.0694444444444 & 1.0812685973848 & -19.4858562390547 \tabularnewline
Winsorized Mean ( 19 / 24 ) & -21.0694444444444 & 1.0812685973848 & -19.4858562390547 \tabularnewline
Winsorized Mean ( 20 / 24 ) & -21.0694444444444 & 1.0812685973848 & -19.4858562390547 \tabularnewline
Winsorized Mean ( 21 / 24 ) & -20.7777777777778 & 1.0403108025079 & -19.9726636767476 \tabularnewline
Winsorized Mean ( 22 / 24 ) & -20.7777777777778 & 0.958493500031069 & -21.6775364434963 \tabularnewline
Winsorized Mean ( 23 / 24 ) & -20.7777777777778 & 0.958493500031069 & -21.6775364434963 \tabularnewline
Winsorized Mean ( 24 / 24 ) & -21.1111111111111 & 0.916198248982179 & -23.0420775575197 \tabularnewline
Trimmed Mean ( 1 / 24 ) & -21.1714285714286 & 1.45775166918618 & -14.5233437347035 \tabularnewline
Trimmed Mean ( 2 / 24 ) & -21.1617647058824 & 1.43816203888698 & -14.7144508989125 \tabularnewline
Trimmed Mean ( 3 / 24 ) & -21.1515151515152 & 1.42099515741928 & -14.8850015716655 \tabularnewline
Trimmed Mean ( 4 / 24 ) & -21.125 & 1.40320989729727 & -15.0547683854632 \tabularnewline
Trimmed Mean ( 5 / 24 ) & -21.0967741935484 & 1.3883076141195 & -15.1960372319419 \tabularnewline
Trimmed Mean ( 6 / 24 ) & -21.0833333333333 & 1.37333189347739 & -15.351957843161 \tabularnewline
Trimmed Mean ( 7 / 24 ) & -21.0689655172414 & 1.36188325290184 & -15.4704637657807 \tabularnewline
Trimmed Mean ( 8 / 24 ) & -21.0357142857143 & 1.35055647158175 & -15.5755903054372 \tabularnewline
Trimmed Mean ( 9 / 24 ) & -21.0185185185185 & 1.33973587015333 & -15.6885539805044 \tabularnewline
Trimmed Mean ( 10 / 24 ) & -20.9807692307692 & 1.32912903830444 & -15.7853516296162 \tabularnewline
Trimmed Mean ( 11 / 24 ) & -20.96 & 1.31923292492421 & -15.8880206853571 \tabularnewline
Trimmed Mean ( 12 / 24 ) & -20.9166666666667 & 1.30968613712514 & -15.970747550692 \tabularnewline
Trimmed Mean ( 13 / 24 ) & -20.8695652173913 & 1.29570404850276 & -16.1067376778724 \tabularnewline
Trimmed Mean ( 14 / 24 ) & -20.8409090909091 & 1.28206987018168 & -16.255673404099 \tabularnewline
Trimmed Mean ( 15 / 24 ) & -20.8095238095238 & 1.27435078105227 & -16.3295099896599 \tabularnewline
Trimmed Mean ( 16 / 24 ) & -20.75 & 1.26731596044149 & -16.3731860464942 \tabularnewline
Trimmed Mean ( 17 / 24 ) & -20.7105263157895 & 1.2621573206395 & -16.4088311156775 \tabularnewline
Trimmed Mean ( 18 / 24 ) & -20.6388888888889 & 1.2580867167842 & -16.4049811619059 \tabularnewline
Trimmed Mean ( 19 / 24 ) & -20.5882352941176 & 1.25679447313331 & -16.3815450610545 \tabularnewline
Trimmed Mean ( 20 / 24 ) & -20.53125 & 1.24998739913004 & -16.4251655771005 \tabularnewline
Trimmed Mean ( 21 / 24 ) & -20.4666666666667 & 1.23524238705983 & -16.5689478284356 \tabularnewline
Trimmed Mean ( 22 / 24 ) & -20.4285714285714 & 1.22088155701774 & -16.7326398790662 \tabularnewline
Trimmed Mean ( 23 / 24 ) & -20.3846153846154 & 1.21791362972399 & -16.7373242955127 \tabularnewline
Trimmed Mean ( 24 / 24 ) & -20.3333333333333 & 1.20486132864162 & -16.8760776447672 \tabularnewline
Median & -19 &  &  \tabularnewline
Midrange & -22 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & -21.025641025641 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & -20.3783783783784 &  &  \tabularnewline
Midmean - Empirical Distribution Function & -21.025641025641 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & -20.3783783783784 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & -20.3783783783784 &  &  \tabularnewline
Midmean - Closest Observation & -21.025641025641 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & -20.3783783783784 &  &  \tabularnewline
Midmean - MS Excel (old versions) & -21.025641025641 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=285513&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]-21.1944444444444[/C][C]1.47668882772624[/C][C]-14.3526815172558[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]NaN[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]-9.7098784912797[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]24.5769765792658[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]-21.1805555555556[/C][C]1.47386283966464[/C][C]-14.3707779214889[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]-21.1805555555556[/C][C]1.46320633049682[/C][C]-14.4754400757437[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]-21.2222222222222[/C][C]1.45568635998528[/C][C]-14.5788425347592[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]-21.2222222222222[/C][C]1.43566005908476[/C][C]-14.7822056397888[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]-21.1527777777778[/C][C]1.42312937954227[/C][C]-14.8635662237409[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]-21.1527777777778[/C][C]1.39480644691068[/C][C]-15.1653857240397[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]-21.25[/C][C]1.37930574947969[/C][C]-15.4063013280529[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]-21.1388888888889[/C][C]1.36067988442173[/C][C]-15.5355342067636[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]-21.2638888888889[/C][C]1.34152312467427[/C][C]-15.8505571002005[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]-21.125[/C][C]1.31901607410822[/C][C]-16.0157259753506[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]-21.2777777777778[/C][C]1.29647140929155[/C][C]-16.412068654414[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]-21.2777777777778[/C][C]1.29647140929155[/C][C]-16.412068654414[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]-21.0972222222222[/C][C]1.26808663339285[/C][C]-16.6370511814128[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]-21.0972222222222[/C][C]1.21063359202533[/C][C]-17.4265957604296[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]-21.3055555555556[/C][C]1.1819321349184[/C][C]-18.0260396736116[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]-21.0833333333333[/C][C]1.14888358410583[/C][C]-18.3511485628393[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]-21.3194444444444[/C][C]1.11747857613016[/C][C]-19.0781683871505[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]-21.0694444444444[/C][C]1.0812685973848[/C][C]-19.4858562390547[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]-21.0694444444444[/C][C]1.0812685973848[/C][C]-19.4858562390547[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]-21.0694444444444[/C][C]1.0812685973848[/C][C]-19.4858562390547[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]-20.7777777777778[/C][C]1.0403108025079[/C][C]-19.9726636767476[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]-20.7777777777778[/C][C]0.958493500031069[/C][C]-21.6775364434963[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]-20.7777777777778[/C][C]0.958493500031069[/C][C]-21.6775364434963[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]-21.1111111111111[/C][C]0.916198248982179[/C][C]-23.0420775575197[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]-21.1714285714286[/C][C]1.45775166918618[/C][C]-14.5233437347035[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]-21.1617647058824[/C][C]1.43816203888698[/C][C]-14.7144508989125[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]-21.1515151515152[/C][C]1.42099515741928[/C][C]-14.8850015716655[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]-21.125[/C][C]1.40320989729727[/C][C]-15.0547683854632[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]-21.0967741935484[/C][C]1.3883076141195[/C][C]-15.1960372319419[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]-21.0833333333333[/C][C]1.37333189347739[/C][C]-15.351957843161[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]-21.0689655172414[/C][C]1.36188325290184[/C][C]-15.4704637657807[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]-21.0357142857143[/C][C]1.35055647158175[/C][C]-15.5755903054372[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]-21.0185185185185[/C][C]1.33973587015333[/C][C]-15.6885539805044[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]-20.9807692307692[/C][C]1.32912903830444[/C][C]-15.7853516296162[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]-20.96[/C][C]1.31923292492421[/C][C]-15.8880206853571[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]-20.9166666666667[/C][C]1.30968613712514[/C][C]-15.970747550692[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]-20.8695652173913[/C][C]1.29570404850276[/C][C]-16.1067376778724[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]-20.8409090909091[/C][C]1.28206987018168[/C][C]-16.255673404099[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]-20.8095238095238[/C][C]1.27435078105227[/C][C]-16.3295099896599[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]-20.75[/C][C]1.26731596044149[/C][C]-16.3731860464942[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]-20.7105263157895[/C][C]1.2621573206395[/C][C]-16.4088311156775[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]-20.6388888888889[/C][C]1.2580867167842[/C][C]-16.4049811619059[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]-20.5882352941176[/C][C]1.25679447313331[/C][C]-16.3815450610545[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]-20.53125[/C][C]1.24998739913004[/C][C]-16.4251655771005[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]-20.4666666666667[/C][C]1.23524238705983[/C][C]-16.5689478284356[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]-20.4285714285714[/C][C]1.22088155701774[/C][C]-16.7326398790662[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]-20.3846153846154[/C][C]1.21791362972399[/C][C]-16.7373242955127[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]-20.3333333333333[/C][C]1.20486132864162[/C][C]-16.8760776447672[/C][/ROW]
[ROW][C]Median[/C][C]-19[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]-22[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]-21.025641025641[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]-20.3783783783784[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]-21.025641025641[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]-20.3783783783784[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]-20.3783783783784[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]-21.025641025641[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]-20.3783783783784[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]-21.025641025641[/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=285513&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=285513&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	-21.1944444444444	1.47668882772624	-14.3526815172558
Geometric Mean	NaN
Harmonic Mean	-9.7098784912797
Quadratic Mean	24.5769765792658
Winsorized Mean ( 1 / 24 )	-21.1805555555556	1.47386283966464	-14.3707779214889
Winsorized Mean ( 2 / 24 )	-21.1805555555556	1.46320633049682	-14.4754400757437
Winsorized Mean ( 3 / 24 )	-21.2222222222222	1.45568635998528	-14.5788425347592
Winsorized Mean ( 4 / 24 )	-21.2222222222222	1.43566005908476	-14.7822056397888
Winsorized Mean ( 5 / 24 )	-21.1527777777778	1.42312937954227	-14.8635662237409
Winsorized Mean ( 6 / 24 )	-21.1527777777778	1.39480644691068	-15.1653857240397
Winsorized Mean ( 7 / 24 )	-21.25	1.37930574947969	-15.4063013280529
Winsorized Mean ( 8 / 24 )	-21.1388888888889	1.36067988442173	-15.5355342067636
Winsorized Mean ( 9 / 24 )	-21.2638888888889	1.34152312467427	-15.8505571002005
Winsorized Mean ( 10 / 24 )	-21.125	1.31901607410822	-16.0157259753506
Winsorized Mean ( 11 / 24 )	-21.2777777777778	1.29647140929155	-16.412068654414
Winsorized Mean ( 12 / 24 )	-21.2777777777778	1.29647140929155	-16.412068654414
Winsorized Mean ( 13 / 24 )	-21.0972222222222	1.26808663339285	-16.6370511814128
Winsorized Mean ( 14 / 24 )	-21.0972222222222	1.21063359202533	-17.4265957604296
Winsorized Mean ( 15 / 24 )	-21.3055555555556	1.1819321349184	-18.0260396736116
Winsorized Mean ( 16 / 24 )	-21.0833333333333	1.14888358410583	-18.3511485628393
Winsorized Mean ( 17 / 24 )	-21.3194444444444	1.11747857613016	-19.0781683871505
Winsorized Mean ( 18 / 24 )	-21.0694444444444	1.0812685973848	-19.4858562390547
Winsorized Mean ( 19 / 24 )	-21.0694444444444	1.0812685973848	-19.4858562390547
Winsorized Mean ( 20 / 24 )	-21.0694444444444	1.0812685973848	-19.4858562390547
Winsorized Mean ( 21 / 24 )	-20.7777777777778	1.0403108025079	-19.9726636767476
Winsorized Mean ( 22 / 24 )	-20.7777777777778	0.958493500031069	-21.6775364434963
Winsorized Mean ( 23 / 24 )	-20.7777777777778	0.958493500031069	-21.6775364434963
Winsorized Mean ( 24 / 24 )	-21.1111111111111	0.916198248982179	-23.0420775575197
Trimmed Mean ( 1 / 24 )	-21.1714285714286	1.45775166918618	-14.5233437347035
Trimmed Mean ( 2 / 24 )	-21.1617647058824	1.43816203888698	-14.7144508989125
Trimmed Mean ( 3 / 24 )	-21.1515151515152	1.42099515741928	-14.8850015716655
Trimmed Mean ( 4 / 24 )	-21.125	1.40320989729727	-15.0547683854632
Trimmed Mean ( 5 / 24 )	-21.0967741935484	1.3883076141195	-15.1960372319419
Trimmed Mean ( 6 / 24 )	-21.0833333333333	1.37333189347739	-15.351957843161
Trimmed Mean ( 7 / 24 )	-21.0689655172414	1.36188325290184	-15.4704637657807
Trimmed Mean ( 8 / 24 )	-21.0357142857143	1.35055647158175	-15.5755903054372
Trimmed Mean ( 9 / 24 )	-21.0185185185185	1.33973587015333	-15.6885539805044
Trimmed Mean ( 10 / 24 )	-20.9807692307692	1.32912903830444	-15.7853516296162
Trimmed Mean ( 11 / 24 )	-20.96	1.31923292492421	-15.8880206853571
Trimmed Mean ( 12 / 24 )	-20.9166666666667	1.30968613712514	-15.970747550692
Trimmed Mean ( 13 / 24 )	-20.8695652173913	1.29570404850276	-16.1067376778724
Trimmed Mean ( 14 / 24 )	-20.8409090909091	1.28206987018168	-16.255673404099
Trimmed Mean ( 15 / 24 )	-20.8095238095238	1.27435078105227	-16.3295099896599
Trimmed Mean ( 16 / 24 )	-20.75	1.26731596044149	-16.3731860464942
Trimmed Mean ( 17 / 24 )	-20.7105263157895	1.2621573206395	-16.4088311156775
Trimmed Mean ( 18 / 24 )	-20.6388888888889	1.2580867167842	-16.4049811619059
Trimmed Mean ( 19 / 24 )	-20.5882352941176	1.25679447313331	-16.3815450610545
Trimmed Mean ( 20 / 24 )	-20.53125	1.24998739913004	-16.4251655771005
Trimmed Mean ( 21 / 24 )	-20.4666666666667	1.23524238705983	-16.5689478284356
Trimmed Mean ( 22 / 24 )	-20.4285714285714	1.22088155701774	-16.7326398790662
Trimmed Mean ( 23 / 24 )	-20.3846153846154	1.21791362972399	-16.7373242955127
Trimmed Mean ( 24 / 24 )	-20.3333333333333	1.20486132864162	-16.8760776447672
Median	-19
Midrange	-22
Midmean - Weighted Average at Xnp	-21.025641025641
Midmean - Weighted Average at X(n+1)p	-20.3783783783784
Midmean - Empirical Distribution Function	-21.025641025641
Midmean - Empirical Distribution Function - Averaging	-20.3783783783784
Midmean - Empirical Distribution Function - Interpolation	-20.3783783783784
Midmean - Closest Observation	-21.025641025641
Midmean - True Basic - Statistics Graphics Toolkit	-20.3783783783784
Midmean - MS Excel (old versions)	-21.025641025641
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