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R Software Module

rwasp_centraltendency.wasp

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Central Tendency

Date of computation

Tue, 14 Mar 2017 13:21:27 +0000

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Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2017/Mar/14/t1489497753vklscwkgm7166y7.htm/, Retrieved Tue, 14 May 2024 05:52:26 +0200

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=, Retrieved Tue, 14 May 2024 05:52:26 +0200

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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	'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=&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=&T=0

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

Central Tendency - Ungrouped Data
Measure	Value	S.E.	Value/S.E.
Arithmetic Mean	100.184305555556	0.0427528959149139	2343.33378854477
Geometric Mean	100.183657416969
Harmonic Mean	100.183008821201
Quadratic Mean	100.184953232343
Winsorized Mean ( 1 / 24 )	100.183888888889	0.0425578661364989	2354.06278518669
Winsorized Mean ( 2 / 24 )	100.185277777778	0.04202054988649	2384.19720942272
Winsorized Mean ( 3 / 24 )	100.184444444444	0.041879217905383	2392.22338561311
Winsorized Mean ( 4 / 24 )	100.183333333333	0.0412822643772441	2426.78871531468
Winsorized Mean ( 5 / 24 )	100.189583333333	0.0395462514718818	2533.47863841331
Winsorized Mean ( 6 / 24 )	100.19125	0.0392421047051525	2553.15688984554
Winsorized Mean ( 7 / 24 )	100.190277777778	0.0390937900674734	2562.81822777622
Winsorized Mean ( 8 / 24 )	100.193611111111	0.0385045703624032	2602.12255761053
Winsorized Mean ( 9 / 24 )	100.192361111111	0.0379138576865695	2642.63167149575
Winsorized Mean ( 10 / 24 )	100.192361111111	0.0379138576865695	2642.63167149575
Winsorized Mean ( 11 / 24 )	100.193888888889	0.0376529512793516	2660.98368081532
Winsorized Mean ( 12 / 24 )	100.195555555556	0.0363267906031861	2758.17251928574
Winsorized Mean ( 13 / 24 )	100.21	0.034056130597866	2942.49517607497
Winsorized Mean ( 14 / 24 )	100.21	0.034056130597866	2942.49517607497
Winsorized Mean ( 15 / 24 )	100.207916666667	0.0337479713063269	2969.30193987335
Winsorized Mean ( 16 / 24 )	100.199027777778	0.032475559440344	3085.36725785551
Winsorized Mean ( 17 / 24 )	100.201388888889	0.0321201197894368	3119.58328753935
Winsorized Mean ( 18 / 24 )	100.203888888889	0.0317478299848397	3156.24371608197
Winsorized Mean ( 19 / 24 )	100.20125	0.0313799333201964	3193.16325428613
Winsorized Mean ( 20 / 24 )	100.20125	0.0282295375086084	3549.51794620951
Winsorized Mean ( 21 / 24 )	100.195416666667	0.0274574200871165	3649.11984989005
Winsorized Mean ( 22 / 24 )	100.192361111111	0.0270609734752582	3702.46699375826
Winsorized Mean ( 23 / 24 )	100.195555555556	0.0248437124928225	4033.03474005758
Winsorized Mean ( 24 / 24 )	100.198888888889	0.0225614753596736	4441.14967179781
Trimmed Mean ( 1 / 24 )	100.186428571429	0.0418545424188156	2393.68113427015
Trimmed Mean ( 2 / 24 )	100.189117647059	0.041011002664084	2442.98142300239
Trimmed Mean ( 3 / 24 )	100.191212121212	0.0403368769667073	2483.8614105873
Trimmed Mean ( 4 / 24 )	100.19375	0.0395808269883206	2531.37080813306
Trimmed Mean ( 5 / 24 )	100.196774193548	0.038874143827973	2577.4657478488
Trimmed Mean ( 6 / 24 )	100.1985	0.0385417998928833	2599.73587840929
Trimmed Mean ( 7 / 24 )	100.2	0.038191892983396	2623.59344281683
Trimmed Mean ( 8 / 24 )	100.201785714286	0.0377699006999864	2652.95337973504
Trimmed Mean ( 9 / 24 )	100.203148148148	0.0373612729329369	2682.00573165727
Trimmed Mean ( 10 / 24 )	100.204807692308	0.0369526320092959	2711.70961968555
Trimmed Mean ( 11 / 24 )	100.2066	0.0364065591757916	2752.43259095553
Trimmed Mean ( 12 / 24 )	100.208333333333	0.0357447775947132	2803.43983307241
Trimmed Mean ( 13 / 24 )	100.21	0.0351628372116493	2849.88379625978
Trimmed Mean ( 14 / 24 )	100.21	0.0348676143224803	2874.01366417522
Trimmed Mean ( 15 / 24 )	100.21	0.0344274557532206	2910.75822501422
Trimmed Mean ( 16 / 24 )	100.21025	0.0338633897692873	2959.250408265
Trimmed Mean ( 17 / 24 )	100.211578947368	0.0333427527805624	3005.49806450858
Trimmed Mean ( 18 / 24 )	100.212777777778	0.0326637780819835	3068.00938722555
Trimmed Mean ( 19 / 24 )	100.213823529412	0.0317690381280226	3154.44940843255
Trimmed Mean ( 20 / 24 )	100.2153125	0.0305592509322518	3279.37725705947
Trimmed Mean ( 21 / 24 )	100.217	0.0297157027260968	3372.52667129382
Trimmed Mean ( 22 / 24 )	100.219642857143	0.0286258575475493	3501.01801109965
Trimmed Mean ( 23 / 24 )	100.223076923077	0.0270257383348612	3708.43067009928
Trimmed Mean ( 24 / 24 )	100.226666666667	0.0253787731303912	3949.23214576691
Median	100.235
Midrange	100.11
Midmean - Weighted Average at Xnp	100.219487179487
Midmean - Weighted Average at X(n+1)p	100.228947368421
Midmean - Empirical Distribution Function	100.219487179487
Midmean - Empirical Distribution Function - Averaging	100.228947368421
Midmean - Empirical Distribution Function - Interpolation	100.228947368421
Midmean - Closest Observation	100.219487179487
Midmean - True Basic - Statistics Graphics Toolkit	100.228947368421
Midmean - MS Excel (old versions)	100.219487179487
Number of observations	72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 100.184305555556 & 0.0427528959149139 & 2343.33378854477 \tabularnewline
Geometric Mean & 100.183657416969 &  &  \tabularnewline
Harmonic Mean & 100.183008821201 &  &  \tabularnewline
Quadratic Mean & 100.184953232343 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 100.183888888889 & 0.0425578661364989 & 2354.06278518669 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 100.185277777778 & 0.04202054988649 & 2384.19720942272 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 100.184444444444 & 0.041879217905383 & 2392.22338561311 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 100.183333333333 & 0.0412822643772441 & 2426.78871531468 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 100.189583333333 & 0.0395462514718818 & 2533.47863841331 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 100.19125 & 0.0392421047051525 & 2553.15688984554 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 100.190277777778 & 0.0390937900674734 & 2562.81822777622 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 100.193611111111 & 0.0385045703624032 & 2602.12255761053 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 100.192361111111 & 0.0379138576865695 & 2642.63167149575 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 100.192361111111 & 0.0379138576865695 & 2642.63167149575 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 100.193888888889 & 0.0376529512793516 & 2660.98368081532 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 100.195555555556 & 0.0363267906031861 & 2758.17251928574 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 100.21 & 0.034056130597866 & 2942.49517607497 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 100.21 & 0.034056130597866 & 2942.49517607497 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 100.207916666667 & 0.0337479713063269 & 2969.30193987335 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 100.199027777778 & 0.032475559440344 & 3085.36725785551 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 100.201388888889 & 0.0321201197894368 & 3119.58328753935 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 100.203888888889 & 0.0317478299848397 & 3156.24371608197 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 100.20125 & 0.0313799333201964 & 3193.16325428613 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 100.20125 & 0.0282295375086084 & 3549.51794620951 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 100.195416666667 & 0.0274574200871165 & 3649.11984989005 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 100.192361111111 & 0.0270609734752582 & 3702.46699375826 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 100.195555555556 & 0.0248437124928225 & 4033.03474005758 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 100.198888888889 & 0.0225614753596736 & 4441.14967179781 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 100.186428571429 & 0.0418545424188156 & 2393.68113427015 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 100.189117647059 & 0.041011002664084 & 2442.98142300239 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 100.191212121212 & 0.0403368769667073 & 2483.8614105873 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 100.19375 & 0.0395808269883206 & 2531.37080813306 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 100.196774193548 & 0.038874143827973 & 2577.4657478488 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 100.1985 & 0.0385417998928833 & 2599.73587840929 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 100.2 & 0.038191892983396 & 2623.59344281683 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 100.201785714286 & 0.0377699006999864 & 2652.95337973504 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 100.203148148148 & 0.0373612729329369 & 2682.00573165727 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 100.204807692308 & 0.0369526320092959 & 2711.70961968555 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 100.2066 & 0.0364065591757916 & 2752.43259095553 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 100.208333333333 & 0.0357447775947132 & 2803.43983307241 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 100.21 & 0.0351628372116493 & 2849.88379625978 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 100.21 & 0.0348676143224803 & 2874.01366417522 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 100.21 & 0.0344274557532206 & 2910.75822501422 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 100.21025 & 0.0338633897692873 & 2959.250408265 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 100.211578947368 & 0.0333427527805624 & 3005.49806450858 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 100.212777777778 & 0.0326637780819835 & 3068.00938722555 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 100.213823529412 & 0.0317690381280226 & 3154.44940843255 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 100.2153125 & 0.0305592509322518 & 3279.37725705947 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 100.217 & 0.0297157027260968 & 3372.52667129382 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 100.219642857143 & 0.0286258575475493 & 3501.01801109965 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 100.223076923077 & 0.0270257383348612 & 3708.43067009928 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 100.226666666667 & 0.0253787731303912 & 3949.23214576691 \tabularnewline
Median & 100.235 &  &  \tabularnewline
Midrange & 100.11 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 100.219487179487 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 100.228947368421 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 100.219487179487 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 100.228947368421 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 100.228947368421 &  &  \tabularnewline
Midmean - Closest Observation & 100.219487179487 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 100.228947368421 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 100.219487179487 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]100.184305555556[/C][C]0.0427528959149139[/C][C]2343.33378854477[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]100.183657416969[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]100.183008821201[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]100.184953232343[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]100.183888888889[/C][C]0.0425578661364989[/C][C]2354.06278518669[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]100.185277777778[/C][C]0.04202054988649[/C][C]2384.19720942272[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]100.184444444444[/C][C]0.041879217905383[/C][C]2392.22338561311[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]100.183333333333[/C][C]0.0412822643772441[/C][C]2426.78871531468[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]100.189583333333[/C][C]0.0395462514718818[/C][C]2533.47863841331[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]100.19125[/C][C]0.0392421047051525[/C][C]2553.15688984554[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]100.190277777778[/C][C]0.0390937900674734[/C][C]2562.81822777622[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]100.193611111111[/C][C]0.0385045703624032[/C][C]2602.12255761053[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]100.192361111111[/C][C]0.0379138576865695[/C][C]2642.63167149575[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]100.192361111111[/C][C]0.0379138576865695[/C][C]2642.63167149575[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]100.193888888889[/C][C]0.0376529512793516[/C][C]2660.98368081532[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]100.195555555556[/C][C]0.0363267906031861[/C][C]2758.17251928574[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]100.21[/C][C]0.034056130597866[/C][C]2942.49517607497[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]100.21[/C][C]0.034056130597866[/C][C]2942.49517607497[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]100.207916666667[/C][C]0.0337479713063269[/C][C]2969.30193987335[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]100.199027777778[/C][C]0.032475559440344[/C][C]3085.36725785551[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]100.201388888889[/C][C]0.0321201197894368[/C][C]3119.58328753935[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]100.203888888889[/C][C]0.0317478299848397[/C][C]3156.24371608197[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]100.20125[/C][C]0.0313799333201964[/C][C]3193.16325428613[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]100.20125[/C][C]0.0282295375086084[/C][C]3549.51794620951[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]100.195416666667[/C][C]0.0274574200871165[/C][C]3649.11984989005[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]100.192361111111[/C][C]0.0270609734752582[/C][C]3702.46699375826[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]100.195555555556[/C][C]0.0248437124928225[/C][C]4033.03474005758[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]100.198888888889[/C][C]0.0225614753596736[/C][C]4441.14967179781[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]100.186428571429[/C][C]0.0418545424188156[/C][C]2393.68113427015[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]100.189117647059[/C][C]0.041011002664084[/C][C]2442.98142300239[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]100.191212121212[/C][C]0.0403368769667073[/C][C]2483.8614105873[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]100.19375[/C][C]0.0395808269883206[/C][C]2531.37080813306[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]100.196774193548[/C][C]0.038874143827973[/C][C]2577.4657478488[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]100.1985[/C][C]0.0385417998928833[/C][C]2599.73587840929[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]100.2[/C][C]0.038191892983396[/C][C]2623.59344281683[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]100.201785714286[/C][C]0.0377699006999864[/C][C]2652.95337973504[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]100.203148148148[/C][C]0.0373612729329369[/C][C]2682.00573165727[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]100.204807692308[/C][C]0.0369526320092959[/C][C]2711.70961968555[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]100.2066[/C][C]0.0364065591757916[/C][C]2752.43259095553[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]100.208333333333[/C][C]0.0357447775947132[/C][C]2803.43983307241[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]100.21[/C][C]0.0351628372116493[/C][C]2849.88379625978[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]100.21[/C][C]0.0348676143224803[/C][C]2874.01366417522[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]100.21[/C][C]0.0344274557532206[/C][C]2910.75822501422[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]100.21025[/C][C]0.0338633897692873[/C][C]2959.250408265[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]100.211578947368[/C][C]0.0333427527805624[/C][C]3005.49806450858[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]100.212777777778[/C][C]0.0326637780819835[/C][C]3068.00938722555[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]100.213823529412[/C][C]0.0317690381280226[/C][C]3154.44940843255[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]100.2153125[/C][C]0.0305592509322518[/C][C]3279.37725705947[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]100.217[/C][C]0.0297157027260968[/C][C]3372.52667129382[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]100.219642857143[/C][C]0.0286258575475493[/C][C]3501.01801109965[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]100.223076923077[/C][C]0.0270257383348612[/C][C]3708.43067009928[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]100.226666666667[/C][C]0.0253787731303912[/C][C]3949.23214576691[/C][/ROW]
[ROW][C]Median[/C][C]100.235[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]100.11[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]100.219487179487[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]100.228947368421[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]100.219487179487[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]100.228947368421[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]100.228947368421[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]100.219487179487[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]100.228947368421[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]100.219487179487[/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=&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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	100.184305555556	0.0427528959149139	2343.33378854477
Geometric Mean	100.183657416969
Harmonic Mean	100.183008821201
Quadratic Mean	100.184953232343
Winsorized Mean ( 1 / 24 )	100.183888888889	0.0425578661364989	2354.06278518669
Winsorized Mean ( 2 / 24 )	100.185277777778	0.04202054988649	2384.19720942272
Winsorized Mean ( 3 / 24 )	100.184444444444	0.041879217905383	2392.22338561311
Winsorized Mean ( 4 / 24 )	100.183333333333	0.0412822643772441	2426.78871531468
Winsorized Mean ( 5 / 24 )	100.189583333333	0.0395462514718818	2533.47863841331
Winsorized Mean ( 6 / 24 )	100.19125	0.0392421047051525	2553.15688984554
Winsorized Mean ( 7 / 24 )	100.190277777778	0.0390937900674734	2562.81822777622
Winsorized Mean ( 8 / 24 )	100.193611111111	0.0385045703624032	2602.12255761053
Winsorized Mean ( 9 / 24 )	100.192361111111	0.0379138576865695	2642.63167149575
Winsorized Mean ( 10 / 24 )	100.192361111111	0.0379138576865695	2642.63167149575
Winsorized Mean ( 11 / 24 )	100.193888888889	0.0376529512793516	2660.98368081532
Winsorized Mean ( 12 / 24 )	100.195555555556	0.0363267906031861	2758.17251928574
Winsorized Mean ( 13 / 24 )	100.21	0.034056130597866	2942.49517607497
Winsorized Mean ( 14 / 24 )	100.21	0.034056130597866	2942.49517607497
Winsorized Mean ( 15 / 24 )	100.207916666667	0.0337479713063269	2969.30193987335
Winsorized Mean ( 16 / 24 )	100.199027777778	0.032475559440344	3085.36725785551
Winsorized Mean ( 17 / 24 )	100.201388888889	0.0321201197894368	3119.58328753935
Winsorized Mean ( 18 / 24 )	100.203888888889	0.0317478299848397	3156.24371608197
Winsorized Mean ( 19 / 24 )	100.20125	0.0313799333201964	3193.16325428613
Winsorized Mean ( 20 / 24 )	100.20125	0.0282295375086084	3549.51794620951
Winsorized Mean ( 21 / 24 )	100.195416666667	0.0274574200871165	3649.11984989005
Winsorized Mean ( 22 / 24 )	100.192361111111	0.0270609734752582	3702.46699375826
Winsorized Mean ( 23 / 24 )	100.195555555556	0.0248437124928225	4033.03474005758
Winsorized Mean ( 24 / 24 )	100.198888888889	0.0225614753596736	4441.14967179781
Trimmed Mean ( 1 / 24 )	100.186428571429	0.0418545424188156	2393.68113427015
Trimmed Mean ( 2 / 24 )	100.189117647059	0.041011002664084	2442.98142300239
Trimmed Mean ( 3 / 24 )	100.191212121212	0.0403368769667073	2483.8614105873
Trimmed Mean ( 4 / 24 )	100.19375	0.0395808269883206	2531.37080813306
Trimmed Mean ( 5 / 24 )	100.196774193548	0.038874143827973	2577.4657478488
Trimmed Mean ( 6 / 24 )	100.1985	0.0385417998928833	2599.73587840929
Trimmed Mean ( 7 / 24 )	100.2	0.038191892983396	2623.59344281683
Trimmed Mean ( 8 / 24 )	100.201785714286	0.0377699006999864	2652.95337973504
Trimmed Mean ( 9 / 24 )	100.203148148148	0.0373612729329369	2682.00573165727
Trimmed Mean ( 10 / 24 )	100.204807692308	0.0369526320092959	2711.70961968555
Trimmed Mean ( 11 / 24 )	100.2066	0.0364065591757916	2752.43259095553
Trimmed Mean ( 12 / 24 )	100.208333333333	0.0357447775947132	2803.43983307241
Trimmed Mean ( 13 / 24 )	100.21	0.0351628372116493	2849.88379625978
Trimmed Mean ( 14 / 24 )	100.21	0.0348676143224803	2874.01366417522
Trimmed Mean ( 15 / 24 )	100.21	0.0344274557532206	2910.75822501422
Trimmed Mean ( 16 / 24 )	100.21025	0.0338633897692873	2959.250408265
Trimmed Mean ( 17 / 24 )	100.211578947368	0.0333427527805624	3005.49806450858
Trimmed Mean ( 18 / 24 )	100.212777777778	0.0326637780819835	3068.00938722555
Trimmed Mean ( 19 / 24 )	100.213823529412	0.0317690381280226	3154.44940843255
Trimmed Mean ( 20 / 24 )	100.2153125	0.0305592509322518	3279.37725705947
Trimmed Mean ( 21 / 24 )	100.217	0.0297157027260968	3372.52667129382
Trimmed Mean ( 22 / 24 )	100.219642857143	0.0286258575475493	3501.01801109965
Trimmed Mean ( 23 / 24 )	100.223076923077	0.0270257383348612	3708.43067009928
Trimmed Mean ( 24 / 24 )	100.226666666667	0.0253787731303912	3949.23214576691
Median	100.235
Midrange	100.11
Midmean - Weighted Average at Xnp	100.219487179487
Midmean - Weighted Average at X(n+1)p	100.228947368421
Midmean - Empirical Distribution Function	100.219487179487
Midmean - Empirical Distribution Function - Averaging	100.228947368421
Midmean - Empirical Distribution Function - Interpolation	100.228947368421
Midmean - Closest Observation	100.219487179487
Midmean - True Basic - Statistics Graphics Toolkit	100.228947368421
Midmean - MS Excel (old versions)	100.219487179487
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