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R Software Module

rwasp_centraltendency.wasp

Title produced by software

Central Tendency

Date of computation

Mon, 12 Nov 2007 03:11:11 -0700

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Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2007/Nov/12/t11948619927cyup818p2qihri.htm/, Retrieved Mon, 29 Apr 2024 03:32:45 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=5157, Retrieved Mon, 29 Apr 2024 03:32:45 +0000

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Estimated Impact

200

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

-       [Central Tendency] [] [2007-11-12 10:11:11] [addc65c5fbfb06e42e5fd21f3a753dae] [Current]

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Summary of compuational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	2 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

\begin{tabular}{lllllllll}
\hline
Summary of compuational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=5157&T=0

[TABLE]
[ROW][C]Summary of compuational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=5157&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=5157&T=0

As an alternative you can also use a QR Code:

The GUIDs for individual cells are displayed in the table below:

Summary of compuational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	2 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Central Tendency - Ungrouped Data
Measure	Value	S.E.	Value/S.E.
Arithmetic Mean	89.11625	1.11582041643828	79.8661224397206
Geometric Mean	88.5567885232308
Harmonic Mean	87.987973361371
Quadratic Mean	89.6664116322272
Winsorized Mean ( 1 / 26 )	89.03	1.06282314520088	83.7674644196548
Winsorized Mean ( 2 / 26 )	89.07	1.04601020156218	85.1521331885455
Winsorized Mean ( 3 / 26 )	89.0925	1.03036919615240	86.466579486934
Winsorized Mean ( 4 / 26 )	89.0725	1.01835368349289	87.4671555117143
Winsorized Mean ( 5 / 26 )	89.01	1.00159145515423	88.8685696567704
Winsorized Mean ( 6 / 26 )	89.025	0.989995045378217	89.9246924675153
Winsorized Mean ( 7 / 26 )	89.06	0.928788171950112	95.8883873520987
Winsorized Mean ( 8 / 26 )	89.05	0.923567998634246	96.4195382816267
Winsorized Mean ( 9 / 26 )	88.96	0.855770805114358	103.953067186152
Winsorized Mean ( 10 / 26 )	88.96	0.847671046179852	104.946370883978
Winsorized Mean ( 11 / 26 )	88.9875	0.842946112592126	105.567246435666
Winsorized Mean ( 12 / 26 )	89.1225	0.815597503658933	109.272649315598
Winsorized Mean ( 13 / 26 )	89.22	0.789811305777638	112.963690627542
Winsorized Mean ( 14 / 26 )	89.185	0.784522147552253	113.680665712576
Winsorized Mean ( 15 / 26 )	89.1475	0.756030554519517	117.915207880264
Winsorized Mean ( 16 / 26 )	89.4275	0.701842004561631	127.418278499669
Winsorized Mean ( 17 / 26 )	89.44875	0.692548480572326	129.158827878850
Winsorized Mean ( 18 / 26 )	89.60625	0.657424356119385	136.298950846488
Winsorized Mean ( 19 / 26 )	89.63	0.63387845738294	141.399347076805
Winsorized Mean ( 20 / 26 )	89.405	0.57316272238267	155.985371184536
Winsorized Mean ( 21 / 26 )	89.1425	0.522923182755642	170.469588917911
Winsorized Mean ( 22 / 26 )	89.225	0.48985757423763	182.144779814545
Winsorized Mean ( 23 / 26 )	89.25375	0.486061879916122	183.626311150758
Winsorized Mean ( 24 / 26 )	89.25375	0.486061879916122	183.626311150758
Winsorized Mean ( 25 / 26 )	89.16	0.425268344174549	209.655858991952
Winsorized Mean ( 26 / 26 )	89.225	0.416880746691456	214.030033068516
Trimmed Mean ( 1 / 26 )	89.0576923076923	1.03315261527172	86.1999388969948
Trimmed Mean ( 2 / 26 )	89.0868421052632	0.998464333329312	89.2238602136233
Trimmed Mean ( 3 / 26 )	89.095945945946	0.968426853644426	92.0006974307417
Trimmed Mean ( 4 / 26 )	89.0972222222222	0.94015567464926	94.7685842086327
Trimmed Mean ( 5 / 26 )	89.1042857142857	0.911114794408023	97.7969914012638
Trimmed Mean ( 6 / 26 )	89.1264705882353	0.881876883574687	101.064527541488
Trimmed Mean ( 7 / 26 )	89.1469696969697	0.850235726800552	104.849710364949
Trimmed Mean ( 8 / 26 )	89.1625	0.828158036927122	107.663629433384
Trimmed Mean ( 9 / 26 )	89.1806451612903	0.802724863381757	111.097399905599
Trimmed Mean ( 10 / 26 )	89.2133333333333	0.787079514381215	113.347294273655
Trimmed Mean ( 11 / 26 )	89.248275862069	0.769504367396108	115.981506595047
Trimmed Mean ( 12 / 26 )	89.2821428571429	0.74875700956265	119.240476839466
Trimmed Mean ( 13 / 26 )	89.3018518518519	0.728795233894387	122.533528896256
Trimmed Mean ( 14 / 26 )	89.3115384615385	0.709170982910799	125.937948130588
Trimmed Mean ( 15 / 26 )	89.326	0.685439290096624	130.319345988188
Trimmed Mean ( 16 / 26 )	89.3458333333333	0.66137053013601	135.091948102011
Trimmed Mean ( 17 / 26 )	89.3369565217391	0.642258685641279	139.098090098289
Trimmed Mean ( 18 / 26 )	89.325	0.619333722674846	144.227573486897
Trimmed Mean ( 19 / 26 )	89.2952380952381	0.597079150510127	149.553435283993
Trimmed Mean ( 20 / 26 )	89.26	0.572912039608355	155.800531022212
Trimmed Mean ( 21 / 26 )	89.2447368421053	0.555416844836415	160.680644945852
Trimmed Mean ( 22 / 26 )	89.2555555555556	0.5433938681505	164.255728279280
Trimmed Mean ( 23 / 26 )	89.2588235294118	0.534064521846200	167.131160895793
Trimmed Mean ( 24 / 26 )	89.259375	0.520755874616485	171.403491253432
Trimmed Mean ( 25 / 26 )	89.26	0.500588159815158	178.310250152459
Trimmed Mean ( 26 / 26 )	89.2714285714286	0.489272679701249	182.457415414934
Median	89.15
Midrange	91.4
Midmean - Weighted Average at Xnp	89.1048780487805
Midmean - Weighted Average at X(n+1)p	89.26
Midmean - Empirical Distribution Function	89.1048780487805
Midmean - Empirical Distribution Function - Averaging	89.26
Midmean - Empirical Distribution Function - Interpolation	89.26
Midmean - Closest Observation	89.1048780487805
Midmean - True Basic - Statistics Graphics Toolkit	89.26
Midmean - MS Excel (old versions)	89.2952380952381
Number of observations	80

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 89.11625 & 1.11582041643828 & 79.8661224397206 \tabularnewline
Geometric Mean & 88.5567885232308 &  &  \tabularnewline
Harmonic Mean & 87.987973361371 &  &  \tabularnewline
Quadratic Mean & 89.6664116322272 &  &  \tabularnewline
Winsorized Mean ( 1 / 26 ) & 89.03 & 1.06282314520088 & 83.7674644196548 \tabularnewline
Winsorized Mean ( 2 / 26 ) & 89.07 & 1.04601020156218 & 85.1521331885455 \tabularnewline
Winsorized Mean ( 3 / 26 ) & 89.0925 & 1.03036919615240 & 86.466579486934 \tabularnewline
Winsorized Mean ( 4 / 26 ) & 89.0725 & 1.01835368349289 & 87.4671555117143 \tabularnewline
Winsorized Mean ( 5 / 26 ) & 89.01 & 1.00159145515423 & 88.8685696567704 \tabularnewline
Winsorized Mean ( 6 / 26 ) & 89.025 & 0.989995045378217 & 89.9246924675153 \tabularnewline
Winsorized Mean ( 7 / 26 ) & 89.06 & 0.928788171950112 & 95.8883873520987 \tabularnewline
Winsorized Mean ( 8 / 26 ) & 89.05 & 0.923567998634246 & 96.4195382816267 \tabularnewline
Winsorized Mean ( 9 / 26 ) & 88.96 & 0.855770805114358 & 103.953067186152 \tabularnewline
Winsorized Mean ( 10 / 26 ) & 88.96 & 0.847671046179852 & 104.946370883978 \tabularnewline
Winsorized Mean ( 11 / 26 ) & 88.9875 & 0.842946112592126 & 105.567246435666 \tabularnewline
Winsorized Mean ( 12 / 26 ) & 89.1225 & 0.815597503658933 & 109.272649315598 \tabularnewline
Winsorized Mean ( 13 / 26 ) & 89.22 & 0.789811305777638 & 112.963690627542 \tabularnewline
Winsorized Mean ( 14 / 26 ) & 89.185 & 0.784522147552253 & 113.680665712576 \tabularnewline
Winsorized Mean ( 15 / 26 ) & 89.1475 & 0.756030554519517 & 117.915207880264 \tabularnewline
Winsorized Mean ( 16 / 26 ) & 89.4275 & 0.701842004561631 & 127.418278499669 \tabularnewline
Winsorized Mean ( 17 / 26 ) & 89.44875 & 0.692548480572326 & 129.158827878850 \tabularnewline
Winsorized Mean ( 18 / 26 ) & 89.60625 & 0.657424356119385 & 136.298950846488 \tabularnewline
Winsorized Mean ( 19 / 26 ) & 89.63 & 0.63387845738294 & 141.399347076805 \tabularnewline
Winsorized Mean ( 20 / 26 ) & 89.405 & 0.57316272238267 & 155.985371184536 \tabularnewline
Winsorized Mean ( 21 / 26 ) & 89.1425 & 0.522923182755642 & 170.469588917911 \tabularnewline
Winsorized Mean ( 22 / 26 ) & 89.225 & 0.48985757423763 & 182.144779814545 \tabularnewline
Winsorized Mean ( 23 / 26 ) & 89.25375 & 0.486061879916122 & 183.626311150758 \tabularnewline
Winsorized Mean ( 24 / 26 ) & 89.25375 & 0.486061879916122 & 183.626311150758 \tabularnewline
Winsorized Mean ( 25 / 26 ) & 89.16 & 0.425268344174549 & 209.655858991952 \tabularnewline
Winsorized Mean ( 26 / 26 ) & 89.225 & 0.416880746691456 & 214.030033068516 \tabularnewline
Trimmed Mean ( 1 / 26 ) & 89.0576923076923 & 1.03315261527172 & 86.1999388969948 \tabularnewline
Trimmed Mean ( 2 / 26 ) & 89.0868421052632 & 0.998464333329312 & 89.2238602136233 \tabularnewline
Trimmed Mean ( 3 / 26 ) & 89.095945945946 & 0.968426853644426 & 92.0006974307417 \tabularnewline
Trimmed Mean ( 4 / 26 ) & 89.0972222222222 & 0.94015567464926 & 94.7685842086327 \tabularnewline
Trimmed Mean ( 5 / 26 ) & 89.1042857142857 & 0.911114794408023 & 97.7969914012638 \tabularnewline
Trimmed Mean ( 6 / 26 ) & 89.1264705882353 & 0.881876883574687 & 101.064527541488 \tabularnewline
Trimmed Mean ( 7 / 26 ) & 89.1469696969697 & 0.850235726800552 & 104.849710364949 \tabularnewline
Trimmed Mean ( 8 / 26 ) & 89.1625 & 0.828158036927122 & 107.663629433384 \tabularnewline
Trimmed Mean ( 9 / 26 ) & 89.1806451612903 & 0.802724863381757 & 111.097399905599 \tabularnewline
Trimmed Mean ( 10 / 26 ) & 89.2133333333333 & 0.787079514381215 & 113.347294273655 \tabularnewline
Trimmed Mean ( 11 / 26 ) & 89.248275862069 & 0.769504367396108 & 115.981506595047 \tabularnewline
Trimmed Mean ( 12 / 26 ) & 89.2821428571429 & 0.74875700956265 & 119.240476839466 \tabularnewline
Trimmed Mean ( 13 / 26 ) & 89.3018518518519 & 0.728795233894387 & 122.533528896256 \tabularnewline
Trimmed Mean ( 14 / 26 ) & 89.3115384615385 & 0.709170982910799 & 125.937948130588 \tabularnewline
Trimmed Mean ( 15 / 26 ) & 89.326 & 0.685439290096624 & 130.319345988188 \tabularnewline
Trimmed Mean ( 16 / 26 ) & 89.3458333333333 & 0.66137053013601 & 135.091948102011 \tabularnewline
Trimmed Mean ( 17 / 26 ) & 89.3369565217391 & 0.642258685641279 & 139.098090098289 \tabularnewline
Trimmed Mean ( 18 / 26 ) & 89.325 & 0.619333722674846 & 144.227573486897 \tabularnewline
Trimmed Mean ( 19 / 26 ) & 89.2952380952381 & 0.597079150510127 & 149.553435283993 \tabularnewline
Trimmed Mean ( 20 / 26 ) & 89.26 & 0.572912039608355 & 155.800531022212 \tabularnewline
Trimmed Mean ( 21 / 26 ) & 89.2447368421053 & 0.555416844836415 & 160.680644945852 \tabularnewline
Trimmed Mean ( 22 / 26 ) & 89.2555555555556 & 0.5433938681505 & 164.255728279280 \tabularnewline
Trimmed Mean ( 23 / 26 ) & 89.2588235294118 & 0.534064521846200 & 167.131160895793 \tabularnewline
Trimmed Mean ( 24 / 26 ) & 89.259375 & 0.520755874616485 & 171.403491253432 \tabularnewline
Trimmed Mean ( 25 / 26 ) & 89.26 & 0.500588159815158 & 178.310250152459 \tabularnewline
Trimmed Mean ( 26 / 26 ) & 89.2714285714286 & 0.489272679701249 & 182.457415414934 \tabularnewline
Median & 89.15 &  &  \tabularnewline
Midrange & 91.4 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 89.1048780487805 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 89.26 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 89.1048780487805 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 89.26 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 89.26 &  &  \tabularnewline
Midmean - Closest Observation & 89.1048780487805 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 89.26 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 89.2952380952381 &  &  \tabularnewline
Number of observations & 80 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=5157&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]89.11625[/C][C]1.11582041643828[/C][C]79.8661224397206[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]88.5567885232308[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]87.987973361371[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]89.6664116322272[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 26 )[/C][C]89.03[/C][C]1.06282314520088[/C][C]83.7674644196548[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 26 )[/C][C]89.07[/C][C]1.04601020156218[/C][C]85.1521331885455[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 26 )[/C][C]89.0925[/C][C]1.03036919615240[/C][C]86.466579486934[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 26 )[/C][C]89.0725[/C][C]1.01835368349289[/C][C]87.4671555117143[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 26 )[/C][C]89.01[/C][C]1.00159145515423[/C][C]88.8685696567704[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 26 )[/C][C]89.025[/C][C]0.989995045378217[/C][C]89.9246924675153[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 26 )[/C][C]89.06[/C][C]0.928788171950112[/C][C]95.8883873520987[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 26 )[/C][C]89.05[/C][C]0.923567998634246[/C][C]96.4195382816267[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 26 )[/C][C]88.96[/C][C]0.855770805114358[/C][C]103.953067186152[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 26 )[/C][C]88.96[/C][C]0.847671046179852[/C][C]104.946370883978[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 26 )[/C][C]88.9875[/C][C]0.842946112592126[/C][C]105.567246435666[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 26 )[/C][C]89.1225[/C][C]0.815597503658933[/C][C]109.272649315598[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 26 )[/C][C]89.22[/C][C]0.789811305777638[/C][C]112.963690627542[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 26 )[/C][C]89.185[/C][C]0.784522147552253[/C][C]113.680665712576[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 26 )[/C][C]89.1475[/C][C]0.756030554519517[/C][C]117.915207880264[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 26 )[/C][C]89.4275[/C][C]0.701842004561631[/C][C]127.418278499669[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 26 )[/C][C]89.44875[/C][C]0.692548480572326[/C][C]129.158827878850[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 26 )[/C][C]89.60625[/C][C]0.657424356119385[/C][C]136.298950846488[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 26 )[/C][C]89.63[/C][C]0.63387845738294[/C][C]141.399347076805[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 26 )[/C][C]89.405[/C][C]0.57316272238267[/C][C]155.985371184536[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 26 )[/C][C]89.1425[/C][C]0.522923182755642[/C][C]170.469588917911[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 26 )[/C][C]89.225[/C][C]0.48985757423763[/C][C]182.144779814545[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 26 )[/C][C]89.25375[/C][C]0.486061879916122[/C][C]183.626311150758[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 26 )[/C][C]89.25375[/C][C]0.486061879916122[/C][C]183.626311150758[/C][/ROW]
[ROW][C]Winsorized Mean ( 25 / 26 )[/C][C]89.16[/C][C]0.425268344174549[/C][C]209.655858991952[/C][/ROW]
[ROW][C]Winsorized Mean ( 26 / 26 )[/C][C]89.225[/C][C]0.416880746691456[/C][C]214.030033068516[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 26 )[/C][C]89.0576923076923[/C][C]1.03315261527172[/C][C]86.1999388969948[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 26 )[/C][C]89.0868421052632[/C][C]0.998464333329312[/C][C]89.2238602136233[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 26 )[/C][C]89.095945945946[/C][C]0.968426853644426[/C][C]92.0006974307417[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 26 )[/C][C]89.0972222222222[/C][C]0.94015567464926[/C][C]94.7685842086327[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 26 )[/C][C]89.1042857142857[/C][C]0.911114794408023[/C][C]97.7969914012638[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 26 )[/C][C]89.1264705882353[/C][C]0.881876883574687[/C][C]101.064527541488[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 26 )[/C][C]89.1469696969697[/C][C]0.850235726800552[/C][C]104.849710364949[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 26 )[/C][C]89.1625[/C][C]0.828158036927122[/C][C]107.663629433384[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 26 )[/C][C]89.1806451612903[/C][C]0.802724863381757[/C][C]111.097399905599[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 26 )[/C][C]89.2133333333333[/C][C]0.787079514381215[/C][C]113.347294273655[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 26 )[/C][C]89.248275862069[/C][C]0.769504367396108[/C][C]115.981506595047[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 26 )[/C][C]89.2821428571429[/C][C]0.74875700956265[/C][C]119.240476839466[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 26 )[/C][C]89.3018518518519[/C][C]0.728795233894387[/C][C]122.533528896256[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 26 )[/C][C]89.3115384615385[/C][C]0.709170982910799[/C][C]125.937948130588[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 26 )[/C][C]89.326[/C][C]0.685439290096624[/C][C]130.319345988188[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 26 )[/C][C]89.3458333333333[/C][C]0.66137053013601[/C][C]135.091948102011[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 26 )[/C][C]89.3369565217391[/C][C]0.642258685641279[/C][C]139.098090098289[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 26 )[/C][C]89.325[/C][C]0.619333722674846[/C][C]144.227573486897[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 26 )[/C][C]89.2952380952381[/C][C]0.597079150510127[/C][C]149.553435283993[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 26 )[/C][C]89.26[/C][C]0.572912039608355[/C][C]155.800531022212[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 26 )[/C][C]89.2447368421053[/C][C]0.555416844836415[/C][C]160.680644945852[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 26 )[/C][C]89.2555555555556[/C][C]0.5433938681505[/C][C]164.255728279280[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 26 )[/C][C]89.2588235294118[/C][C]0.534064521846200[/C][C]167.131160895793[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 26 )[/C][C]89.259375[/C][C]0.520755874616485[/C][C]171.403491253432[/C][/ROW]
[ROW][C]Trimmed Mean ( 25 / 26 )[/C][C]89.26[/C][C]0.500588159815158[/C][C]178.310250152459[/C][/ROW]
[ROW][C]Trimmed Mean ( 26 / 26 )[/C][C]89.2714285714286[/C][C]0.489272679701249[/C][C]182.457415414934[/C][/ROW]
[ROW][C]Median[/C][C]89.15[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]91.4[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]89.1048780487805[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]89.26[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]89.1048780487805[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]89.26[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]89.26[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]89.1048780487805[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]89.26[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]89.2952380952381[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]80[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=5157&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=5157&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	89.11625	1.11582041643828	79.8661224397206
Geometric Mean	88.5567885232308
Harmonic Mean	87.987973361371
Quadratic Mean	89.6664116322272
Winsorized Mean ( 1 / 26 )	89.03	1.06282314520088	83.7674644196548
Winsorized Mean ( 2 / 26 )	89.07	1.04601020156218	85.1521331885455
Winsorized Mean ( 3 / 26 )	89.0925	1.03036919615240	86.466579486934
Winsorized Mean ( 4 / 26 )	89.0725	1.01835368349289	87.4671555117143
Winsorized Mean ( 5 / 26 )	89.01	1.00159145515423	88.8685696567704
Winsorized Mean ( 6 / 26 )	89.025	0.989995045378217	89.9246924675153
Winsorized Mean ( 7 / 26 )	89.06	0.928788171950112	95.8883873520987
Winsorized Mean ( 8 / 26 )	89.05	0.923567998634246	96.4195382816267
Winsorized Mean ( 9 / 26 )	88.96	0.855770805114358	103.953067186152
Winsorized Mean ( 10 / 26 )	88.96	0.847671046179852	104.946370883978
Winsorized Mean ( 11 / 26 )	88.9875	0.842946112592126	105.567246435666
Winsorized Mean ( 12 / 26 )	89.1225	0.815597503658933	109.272649315598
Winsorized Mean ( 13 / 26 )	89.22	0.789811305777638	112.963690627542
Winsorized Mean ( 14 / 26 )	89.185	0.784522147552253	113.680665712576
Winsorized Mean ( 15 / 26 )	89.1475	0.756030554519517	117.915207880264
Winsorized Mean ( 16 / 26 )	89.4275	0.701842004561631	127.418278499669
Winsorized Mean ( 17 / 26 )	89.44875	0.692548480572326	129.158827878850
Winsorized Mean ( 18 / 26 )	89.60625	0.657424356119385	136.298950846488
Winsorized Mean ( 19 / 26 )	89.63	0.63387845738294	141.399347076805
Winsorized Mean ( 20 / 26 )	89.405	0.57316272238267	155.985371184536
Winsorized Mean ( 21 / 26 )	89.1425	0.522923182755642	170.469588917911
Winsorized Mean ( 22 / 26 )	89.225	0.48985757423763	182.144779814545
Winsorized Mean ( 23 / 26 )	89.25375	0.486061879916122	183.626311150758
Winsorized Mean ( 24 / 26 )	89.25375	0.486061879916122	183.626311150758
Winsorized Mean ( 25 / 26 )	89.16	0.425268344174549	209.655858991952
Winsorized Mean ( 26 / 26 )	89.225	0.416880746691456	214.030033068516
Trimmed Mean ( 1 / 26 )	89.0576923076923	1.03315261527172	86.1999388969948
Trimmed Mean ( 2 / 26 )	89.0868421052632	0.998464333329312	89.2238602136233
Trimmed Mean ( 3 / 26 )	89.095945945946	0.968426853644426	92.0006974307417
Trimmed Mean ( 4 / 26 )	89.0972222222222	0.94015567464926	94.7685842086327
Trimmed Mean ( 5 / 26 )	89.1042857142857	0.911114794408023	97.7969914012638
Trimmed Mean ( 6 / 26 )	89.1264705882353	0.881876883574687	101.064527541488
Trimmed Mean ( 7 / 26 )	89.1469696969697	0.850235726800552	104.849710364949
Trimmed Mean ( 8 / 26 )	89.1625	0.828158036927122	107.663629433384
Trimmed Mean ( 9 / 26 )	89.1806451612903	0.802724863381757	111.097399905599
Trimmed Mean ( 10 / 26 )	89.2133333333333	0.787079514381215	113.347294273655
Trimmed Mean ( 11 / 26 )	89.248275862069	0.769504367396108	115.981506595047
Trimmed Mean ( 12 / 26 )	89.2821428571429	0.74875700956265	119.240476839466
Trimmed Mean ( 13 / 26 )	89.3018518518519	0.728795233894387	122.533528896256
Trimmed Mean ( 14 / 26 )	89.3115384615385	0.709170982910799	125.937948130588
Trimmed Mean ( 15 / 26 )	89.326	0.685439290096624	130.319345988188
Trimmed Mean ( 16 / 26 )	89.3458333333333	0.66137053013601	135.091948102011
Trimmed Mean ( 17 / 26 )	89.3369565217391	0.642258685641279	139.098090098289
Trimmed Mean ( 18 / 26 )	89.325	0.619333722674846	144.227573486897
Trimmed Mean ( 19 / 26 )	89.2952380952381	0.597079150510127	149.553435283993
Trimmed Mean ( 20 / 26 )	89.26	0.572912039608355	155.800531022212
Trimmed Mean ( 21 / 26 )	89.2447368421053	0.555416844836415	160.680644945852
Trimmed Mean ( 22 / 26 )	89.2555555555556	0.5433938681505	164.255728279280
Trimmed Mean ( 23 / 26 )	89.2588235294118	0.534064521846200	167.131160895793
Trimmed Mean ( 24 / 26 )	89.259375	0.520755874616485	171.403491253432
Trimmed Mean ( 25 / 26 )	89.26	0.500588159815158	178.310250152459
Trimmed Mean ( 26 / 26 )	89.2714285714286	0.489272679701249	182.457415414934
Median	89.15
Midrange	91.4
Midmean - Weighted Average at Xnp	89.1048780487805
Midmean - Weighted Average at X(n+1)p	89.26
Midmean - Empirical Distribution Function	89.1048780487805
Midmean - Empirical Distribution Function - Averaging	89.26
Midmean - Empirical Distribution Function - Interpolation	89.26
Midmean - Closest Observation	89.1048780487805
Midmean - True Basic - Statistics Graphics Toolkit	89.26
Midmean - MS Excel (old versions)	89.2952380952381
Number of observations	80

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