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R Software Module

rwasp_centraltendency.wasp

Title produced by software

Central Tendency

Date of computation

Sat, 11 Oct 2014 12:04:44 +0100

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Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2014/Oct/11/t141302551369t1lwzesh3c25e.htm/, Retrieved Tue, 14 May 2024 11:57:00 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=240387, Retrieved Tue, 14 May 2024 11:57:00 +0000

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Estimated Impact

112

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

-       [Central Tendency] [] [2014-10-11 11:04:44] [5cf6a598f846f655ef95f65053f7ffc6] [Current]

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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	'Sir Maurice George Kendall' @ kendall.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 & 'Sir Maurice George Kendall' @ kendall.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=240387&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]'Sir Maurice George Kendall' @ kendall.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=240387&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=240387&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	'Sir Maurice George Kendall' @ kendall.wessa.net

Central Tendency - Ungrouped Data
Measure	Value	S.E.	Value/S.E.
Arithmetic Mean	72.6006849315068	0.186482431992055	389.316484968407
Geometric Mean	72.5835282611931
Harmonic Mean	72.5664607971695
Quadratic Mean	72.6179268689194
Winsorized Mean ( 1 / 24 )	72.5995890410959	0.1862071805616	389.886087218204
Winsorized Mean ( 2 / 24 )	72.6001369863014	0.18531715103282	391.761564332725
Winsorized Mean ( 3 / 24 )	72.5734246575343	0.179317709422154	404.719784183057
Winsorized Mean ( 4 / 24 )	72.5745205479452	0.178724770025579	406.068619014357
Winsorized Mean ( 5 / 24 )	72.5861643835616	0.176836916129744	410.469521704992
Winsorized Mean ( 6 / 24 )	72.5894520547945	0.176030656059003	412.368241304875
Winsorized Mean ( 7 / 24 )	72.578904109589	0.173903234351619	417.352238330658
Winsorized Mean ( 8 / 24 )	72.5306849315069	0.163361907943025	443.987743806242
Winsorized Mean ( 9 / 24 )	72.5220547945205	0.157860620818427	459.405609952188
Winsorized Mean ( 10 / 24 )	72.5330136986301	0.154481097952101	469.526787808825
Winsorized Mean ( 11 / 24 )	72.5541095890411	0.151467182225526	479.008776178407
Winsorized Mean ( 12 / 24 )	72.557397260274	0.150511308580287	482.072728917707
Winsorized Mean ( 13 / 24 )	72.5698630136986	0.148287855779357	489.385072245417
Winsorized Mean ( 14 / 24 )	72.5161643835616	0.139598880431376	519.460930914911
Winsorized Mean ( 15 / 24 )	72.5161643835616	0.139598880431376	519.460930914911
Winsorized Mean ( 16 / 24 )	72.5030136986301	0.136301534307665	531.931016528205
Winsorized Mean ( 17 / 24 )	72.4750684931507	0.128153245416548	565.534397959086
Winsorized Mean ( 18 / 24 )	72.4750684931507	0.128153245416548	565.534397959086
Winsorized Mean ( 19 / 24 )	72.41	0.118993591784788	608.520164102291
Winsorized Mean ( 20 / 24 )	72.3908219178082	0.115685165809871	625.757169564704
Winsorized Mean ( 21 / 24 )	72.3908219178082	0.115685165809871	625.757169564704
Winsorized Mean ( 22 / 24 )	72.3757534246575	0.110485285873409	655.071422882352
Winsorized Mean ( 23 / 24 )	72.4387671232877	0.098745931308486	733.587360647663
Winsorized Mean ( 24 / 24 )	72.3993150684932	0.0937300620639804	772.423633082342
Trimmed Mean ( 1 / 24 )	72.5852112676056	0.182648397168237	397.404041825496
Trimmed Mean ( 2 / 24 )	72.57	0.178399749406313	406.78308260803
Trimmed Mean ( 3 / 24 )	72.5535820895522	0.173877182528111	417.26913810455
Trimmed Mean ( 4 / 24 )	72.5461538461538	0.171185725207427	423.786234268359
Trimmed Mean ( 5 / 24 )	72.5379365079365	0.168113711841334	431.4813807478
Trimmed Mean ( 6 / 24 )	72.5263934426229	0.164927709414206	439.74656351091
Trimmed Mean ( 7 / 24 )	72.5133898305085	0.161221703767217	449.77436744626
Trimmed Mean ( 8 / 24 )	72.5014035087719	0.157211851741848	461.170088040333
Trimmed Mean ( 9 / 24 )	72.4965454545455	0.154844381135209	468.189707130812
Trimmed Mean ( 10 / 24 )	72.492641509434	0.153057885533232	473.628923180795
Trimmed Mean ( 11 / 24 )	72.486862745098	0.151416446951893	478.725159679172
Trimmed Mean ( 12 / 24 )	72.4777551020408	0.149804653214345	483.815112193727
Trimmed Mean ( 13 / 24 )	72.4674468085106	0.147778639144283	490.378360689579
Trimmed Mean ( 14 / 24 )	72.4546666666667	0.145453175498599	498.130524949348
Trimmed Mean ( 15 / 24 )	72.4472093023256	0.144181857903651	502.471048408448
Trimmed Mean ( 16 / 24 )	72.4390243902439	0.142264698703941	509.184815700435
Trimmed Mean ( 17 / 24 )	72.4315384615385	0.140230934682911	516.516121248994
Trimmed Mean ( 18 / 24 )	72.4264864864865	0.139094679129702	520.699188061328
Trimmed Mean ( 19 / 24 )	72.4208571428571	0.137186845186399	527.899428290354
Trimmed Mean ( 20 / 24 )	72.4221212121212	0.136436491480578	530.81195819544
Trimmed Mean ( 21 / 24 )	72.4258064516129	0.135674954855186	533.818541004251
Trimmed Mean ( 22 / 24 )	72.43	0.133998750086076	540.527429945978
Trimmed Mean ( 23 / 24 )	72.4366666666667	0.132451141343912	546.893487905729
Trimmed Mean ( 24 / 24 )	72.4364	0.133057481312902	544.399302356071
Median	72.56
Midrange	73.15
Midmean - Weighted Average at Xnp	72.3564864864865
Midmean - Weighted Average at X(n+1)p	72.4315384615385
Midmean - Empirical Distribution Function	72.4315384615385
Midmean - Empirical Distribution Function - Averaging	72.4315384615385
Midmean - Empirical Distribution Function - Interpolation	72.4315384615385
Midmean - Closest Observation	72.4315384615385
Midmean - True Basic - Statistics Graphics Toolkit	72.4315384615385
Midmean - MS Excel (old versions)	72.4315384615385
Number of observations	73

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 72.6006849315068 & 0.186482431992055 & 389.316484968407 \tabularnewline
Geometric Mean & 72.5835282611931 &  &  \tabularnewline
Harmonic Mean & 72.5664607971695 &  &  \tabularnewline
Quadratic Mean & 72.6179268689194 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 72.5995890410959 & 0.1862071805616 & 389.886087218204 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 72.6001369863014 & 0.18531715103282 & 391.761564332725 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 72.5734246575343 & 0.179317709422154 & 404.719784183057 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 72.5745205479452 & 0.178724770025579 & 406.068619014357 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 72.5861643835616 & 0.176836916129744 & 410.469521704992 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 72.5894520547945 & 0.176030656059003 & 412.368241304875 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 72.578904109589 & 0.173903234351619 & 417.352238330658 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 72.5306849315069 & 0.163361907943025 & 443.987743806242 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 72.5220547945205 & 0.157860620818427 & 459.405609952188 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 72.5330136986301 & 0.154481097952101 & 469.526787808825 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 72.5541095890411 & 0.151467182225526 & 479.008776178407 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 72.557397260274 & 0.150511308580287 & 482.072728917707 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 72.5698630136986 & 0.148287855779357 & 489.385072245417 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 72.5161643835616 & 0.139598880431376 & 519.460930914911 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 72.5161643835616 & 0.139598880431376 & 519.460930914911 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 72.5030136986301 & 0.136301534307665 & 531.931016528205 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 72.4750684931507 & 0.128153245416548 & 565.534397959086 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 72.4750684931507 & 0.128153245416548 & 565.534397959086 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 72.41 & 0.118993591784788 & 608.520164102291 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 72.3908219178082 & 0.115685165809871 & 625.757169564704 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 72.3908219178082 & 0.115685165809871 & 625.757169564704 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 72.3757534246575 & 0.110485285873409 & 655.071422882352 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 72.4387671232877 & 0.098745931308486 & 733.587360647663 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 72.3993150684932 & 0.0937300620639804 & 772.423633082342 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 72.5852112676056 & 0.182648397168237 & 397.404041825496 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 72.57 & 0.178399749406313 & 406.78308260803 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 72.5535820895522 & 0.173877182528111 & 417.26913810455 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 72.5461538461538 & 0.171185725207427 & 423.786234268359 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 72.5379365079365 & 0.168113711841334 & 431.4813807478 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 72.5263934426229 & 0.164927709414206 & 439.74656351091 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 72.5133898305085 & 0.161221703767217 & 449.77436744626 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 72.5014035087719 & 0.157211851741848 & 461.170088040333 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 72.4965454545455 & 0.154844381135209 & 468.189707130812 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 72.492641509434 & 0.153057885533232 & 473.628923180795 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 72.486862745098 & 0.151416446951893 & 478.725159679172 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 72.4777551020408 & 0.149804653214345 & 483.815112193727 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 72.4674468085106 & 0.147778639144283 & 490.378360689579 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 72.4546666666667 & 0.145453175498599 & 498.130524949348 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 72.4472093023256 & 0.144181857903651 & 502.471048408448 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 72.4390243902439 & 0.142264698703941 & 509.184815700435 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 72.4315384615385 & 0.140230934682911 & 516.516121248994 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 72.4264864864865 & 0.139094679129702 & 520.699188061328 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 72.4208571428571 & 0.137186845186399 & 527.899428290354 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 72.4221212121212 & 0.136436491480578 & 530.81195819544 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 72.4258064516129 & 0.135674954855186 & 533.818541004251 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 72.43 & 0.133998750086076 & 540.527429945978 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 72.4366666666667 & 0.132451141343912 & 546.893487905729 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 72.4364 & 0.133057481312902 & 544.399302356071 \tabularnewline
Median & 72.56 &  &  \tabularnewline
Midrange & 73.15 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 72.3564864864865 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 72.4315384615385 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 72.4315384615385 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 72.4315384615385 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 72.4315384615385 &  &  \tabularnewline
Midmean - Closest Observation & 72.4315384615385 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 72.4315384615385 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 72.4315384615385 &  &  \tabularnewline
Number of observations & 73 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=240387&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]72.6006849315068[/C][C]0.186482431992055[/C][C]389.316484968407[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]72.5835282611931[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]72.5664607971695[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]72.6179268689194[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]72.5995890410959[/C][C]0.1862071805616[/C][C]389.886087218204[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]72.6001369863014[/C][C]0.18531715103282[/C][C]391.761564332725[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]72.5734246575343[/C][C]0.179317709422154[/C][C]404.719784183057[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]72.5745205479452[/C][C]0.178724770025579[/C][C]406.068619014357[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]72.5861643835616[/C][C]0.176836916129744[/C][C]410.469521704992[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]72.5894520547945[/C][C]0.176030656059003[/C][C]412.368241304875[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]72.578904109589[/C][C]0.173903234351619[/C][C]417.352238330658[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]72.5306849315069[/C][C]0.163361907943025[/C][C]443.987743806242[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]72.5220547945205[/C][C]0.157860620818427[/C][C]459.405609952188[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]72.5330136986301[/C][C]0.154481097952101[/C][C]469.526787808825[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]72.5541095890411[/C][C]0.151467182225526[/C][C]479.008776178407[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]72.557397260274[/C][C]0.150511308580287[/C][C]482.072728917707[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]72.5698630136986[/C][C]0.148287855779357[/C][C]489.385072245417[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]72.5161643835616[/C][C]0.139598880431376[/C][C]519.460930914911[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]72.5161643835616[/C][C]0.139598880431376[/C][C]519.460930914911[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]72.5030136986301[/C][C]0.136301534307665[/C][C]531.931016528205[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]72.4750684931507[/C][C]0.128153245416548[/C][C]565.534397959086[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]72.4750684931507[/C][C]0.128153245416548[/C][C]565.534397959086[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]72.41[/C][C]0.118993591784788[/C][C]608.520164102291[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]72.3908219178082[/C][C]0.115685165809871[/C][C]625.757169564704[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]72.3908219178082[/C][C]0.115685165809871[/C][C]625.757169564704[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]72.3757534246575[/C][C]0.110485285873409[/C][C]655.071422882352[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]72.4387671232877[/C][C]0.098745931308486[/C][C]733.587360647663[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]72.3993150684932[/C][C]0.0937300620639804[/C][C]772.423633082342[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]72.5852112676056[/C][C]0.182648397168237[/C][C]397.404041825496[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]72.57[/C][C]0.178399749406313[/C][C]406.78308260803[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]72.5535820895522[/C][C]0.173877182528111[/C][C]417.26913810455[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]72.5461538461538[/C][C]0.171185725207427[/C][C]423.786234268359[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]72.5379365079365[/C][C]0.168113711841334[/C][C]431.4813807478[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]72.5263934426229[/C][C]0.164927709414206[/C][C]439.74656351091[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]72.5133898305085[/C][C]0.161221703767217[/C][C]449.77436744626[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]72.5014035087719[/C][C]0.157211851741848[/C][C]461.170088040333[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]72.4965454545455[/C][C]0.154844381135209[/C][C]468.189707130812[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]72.492641509434[/C][C]0.153057885533232[/C][C]473.628923180795[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]72.486862745098[/C][C]0.151416446951893[/C][C]478.725159679172[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]72.4777551020408[/C][C]0.149804653214345[/C][C]483.815112193727[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]72.4674468085106[/C][C]0.147778639144283[/C][C]490.378360689579[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]72.4546666666667[/C][C]0.145453175498599[/C][C]498.130524949348[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]72.4472093023256[/C][C]0.144181857903651[/C][C]502.471048408448[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]72.4390243902439[/C][C]0.142264698703941[/C][C]509.184815700435[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]72.4315384615385[/C][C]0.140230934682911[/C][C]516.516121248994[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]72.4264864864865[/C][C]0.139094679129702[/C][C]520.699188061328[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]72.4208571428571[/C][C]0.137186845186399[/C][C]527.899428290354[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]72.4221212121212[/C][C]0.136436491480578[/C][C]530.81195819544[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]72.4258064516129[/C][C]0.135674954855186[/C][C]533.818541004251[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]72.43[/C][C]0.133998750086076[/C][C]540.527429945978[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]72.4366666666667[/C][C]0.132451141343912[/C][C]546.893487905729[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]72.4364[/C][C]0.133057481312902[/C][C]544.399302356071[/C][/ROW]
[ROW][C]Median[/C][C]72.56[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]73.15[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]72.3564864864865[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]72.4315384615385[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]72.4315384615385[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]72.4315384615385[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]72.4315384615385[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]72.4315384615385[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]72.4315384615385[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]72.4315384615385[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]73[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=240387&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=240387&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	72.6006849315068	0.186482431992055	389.316484968407
Geometric Mean	72.5835282611931
Harmonic Mean	72.5664607971695
Quadratic Mean	72.6179268689194
Winsorized Mean ( 1 / 24 )	72.5995890410959	0.1862071805616	389.886087218204
Winsorized Mean ( 2 / 24 )	72.6001369863014	0.18531715103282	391.761564332725
Winsorized Mean ( 3 / 24 )	72.5734246575343	0.179317709422154	404.719784183057
Winsorized Mean ( 4 / 24 )	72.5745205479452	0.178724770025579	406.068619014357
Winsorized Mean ( 5 / 24 )	72.5861643835616	0.176836916129744	410.469521704992
Winsorized Mean ( 6 / 24 )	72.5894520547945	0.176030656059003	412.368241304875
Winsorized Mean ( 7 / 24 )	72.578904109589	0.173903234351619	417.352238330658
Winsorized Mean ( 8 / 24 )	72.5306849315069	0.163361907943025	443.987743806242
Winsorized Mean ( 9 / 24 )	72.5220547945205	0.157860620818427	459.405609952188
Winsorized Mean ( 10 / 24 )	72.5330136986301	0.154481097952101	469.526787808825
Winsorized Mean ( 11 / 24 )	72.5541095890411	0.151467182225526	479.008776178407
Winsorized Mean ( 12 / 24 )	72.557397260274	0.150511308580287	482.072728917707
Winsorized Mean ( 13 / 24 )	72.5698630136986	0.148287855779357	489.385072245417
Winsorized Mean ( 14 / 24 )	72.5161643835616	0.139598880431376	519.460930914911
Winsorized Mean ( 15 / 24 )	72.5161643835616	0.139598880431376	519.460930914911
Winsorized Mean ( 16 / 24 )	72.5030136986301	0.136301534307665	531.931016528205
Winsorized Mean ( 17 / 24 )	72.4750684931507	0.128153245416548	565.534397959086
Winsorized Mean ( 18 / 24 )	72.4750684931507	0.128153245416548	565.534397959086
Winsorized Mean ( 19 / 24 )	72.41	0.118993591784788	608.520164102291
Winsorized Mean ( 20 / 24 )	72.3908219178082	0.115685165809871	625.757169564704
Winsorized Mean ( 21 / 24 )	72.3908219178082	0.115685165809871	625.757169564704
Winsorized Mean ( 22 / 24 )	72.3757534246575	0.110485285873409	655.071422882352
Winsorized Mean ( 23 / 24 )	72.4387671232877	0.098745931308486	733.587360647663
Winsorized Mean ( 24 / 24 )	72.3993150684932	0.0937300620639804	772.423633082342
Trimmed Mean ( 1 / 24 )	72.5852112676056	0.182648397168237	397.404041825496
Trimmed Mean ( 2 / 24 )	72.57	0.178399749406313	406.78308260803
Trimmed Mean ( 3 / 24 )	72.5535820895522	0.173877182528111	417.26913810455
Trimmed Mean ( 4 / 24 )	72.5461538461538	0.171185725207427	423.786234268359
Trimmed Mean ( 5 / 24 )	72.5379365079365	0.168113711841334	431.4813807478
Trimmed Mean ( 6 / 24 )	72.5263934426229	0.164927709414206	439.74656351091
Trimmed Mean ( 7 / 24 )	72.5133898305085	0.161221703767217	449.77436744626
Trimmed Mean ( 8 / 24 )	72.5014035087719	0.157211851741848	461.170088040333
Trimmed Mean ( 9 / 24 )	72.4965454545455	0.154844381135209	468.189707130812
Trimmed Mean ( 10 / 24 )	72.492641509434	0.153057885533232	473.628923180795
Trimmed Mean ( 11 / 24 )	72.486862745098	0.151416446951893	478.725159679172
Trimmed Mean ( 12 / 24 )	72.4777551020408	0.149804653214345	483.815112193727
Trimmed Mean ( 13 / 24 )	72.4674468085106	0.147778639144283	490.378360689579
Trimmed Mean ( 14 / 24 )	72.4546666666667	0.145453175498599	498.130524949348
Trimmed Mean ( 15 / 24 )	72.4472093023256	0.144181857903651	502.471048408448
Trimmed Mean ( 16 / 24 )	72.4390243902439	0.142264698703941	509.184815700435
Trimmed Mean ( 17 / 24 )	72.4315384615385	0.140230934682911	516.516121248994
Trimmed Mean ( 18 / 24 )	72.4264864864865	0.139094679129702	520.699188061328
Trimmed Mean ( 19 / 24 )	72.4208571428571	0.137186845186399	527.899428290354
Trimmed Mean ( 20 / 24 )	72.4221212121212	0.136436491480578	530.81195819544
Trimmed Mean ( 21 / 24 )	72.4258064516129	0.135674954855186	533.818541004251
Trimmed Mean ( 22 / 24 )	72.43	0.133998750086076	540.527429945978
Trimmed Mean ( 23 / 24 )	72.4366666666667	0.132451141343912	546.893487905729
Trimmed Mean ( 24 / 24 )	72.4364	0.133057481312902	544.399302356071
Median	72.56
Midrange	73.15
Midmean - Weighted Average at Xnp	72.3564864864865
Midmean - Weighted Average at X(n+1)p	72.4315384615385
Midmean - Empirical Distribution Function	72.4315384615385
Midmean - Empirical Distribution Function - Averaging	72.4315384615385
Midmean - Empirical Distribution Function - Interpolation	72.4315384615385
Midmean - Closest Observation	72.4315384615385
Midmean - True Basic - Statistics Graphics Toolkit	72.4315384615385
Midmean - MS Excel (old versions)	72.4315384615385
Number of observations	73

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