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Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationMon, 26 Oct 2009 16:16:38 -0600
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2009/Oct/26/t1256595487z39dh6o619eo72q.htm/, Retrieved Thu, 02 May 2024 14:08:51 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=50778, Retrieved Thu, 02 May 2024 14:08:51 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact114
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [Workshop3/part2(2)] [2009-10-26 22:16:38] [f94f05f163a3ee3ab544c4fef41db0eb] [Current]
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Dataseries X:
184.7926685
206.6394558
173.6951794
124.9389196
268.8268257
230.6534475
261.7017449
238.1689001
200.5998747
242.1128021
160.6903335
167.5762727
176.1747069
176.6360146
165.1975684
95.4837558
285.6785267
263.3523742
338.9254494
267.056626
262.6842209
232.1736574
177.3837436
168.9547582
177.2811374
204.2911355
169.003403
91.03012634
302.9984424
258.3033369
297.8717201
251.2778156
243.0051312
249.4242864
198.2907643
181.3488598
197.9453382
240.0542583
191.773132
123.2988094
304.6911197
290.4224537
289.2839934
307.5900597
248.6616599
258.2771896
194.9724983
171.6256633
197.8784957
216.9991327
149.8172022
110.6315486
244.6121311
230.9905072
266.2769526
250.2627305
195.8942041
217.04177
182.8736185
162.9476716




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\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 & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=50778&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]1 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=50778&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=50778&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 Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean215.6507687647.1655827394385830.0953567358984
Geometric Mean207.890572110914
Harmonic Mean199.180338832809
Quadratic Mean222.563795466048
Winsorized Mean ( 1 / 20 )215.2027394266677.0092208845568830.7028046299431
Winsorized Mean ( 2 / 20 )215.611034526.8490130854692731.4805990044662
Winsorized Mean ( 3 / 20 )216.1597636956.6732914742120832.3917761617811
Winsorized Mean ( 4 / 20 )215.9273228883336.5737629273834432.8468375378847
Winsorized Mean ( 5 / 20 )217.3797409056.0010298995561836.2237390153775
Winsorized Mean ( 6 / 20 )218.3532080055.7815885217860137.7669920960663
Winsorized Mean ( 7 / 20 )218.1959263355.6511907381527438.6106108332
Winsorized Mean ( 8 / 20 )216.2490191083335.1791139479001341.7540570228255
Winsorized Mean ( 9 / 20 )216.3402947983335.0749094404859942.6293902059493
Winsorized Mean ( 10 / 20 )216.4400968155.0158192886285443.1514941747792
Winsorized Mean ( 11 / 20 )215.9128423216674.9254602610350943.8360743725283
Winsorized Mean ( 12 / 20 )216.3036637216674.8201183372731544.8751770364282
Winsorized Mean ( 13 / 20 )216.5391890766674.7157286348474645.9185007967853
Winsorized Mean ( 14 / 20 )216.3247836266674.5003415296517148.0685259554975
Winsorized Mean ( 15 / 20 )216.4335737266674.4819096135769748.2904815998582
Winsorized Mean ( 16 / 20 )214.739106744.1692421867647451.5055487593619
Winsorized Mean ( 17 / 20 )214.4805710516674.12229322643352.0294310158173
Winsorized Mean ( 18 / 20 )215.4185726816673.906525907934655.1432597040063
Winsorized Mean ( 19 / 20 )215.6599145453.7999392713661656.7535160811834
Winsorized Mean ( 20 / 20 )214.9497549453.5104739531812761.2309784410187
Trimmed Mean ( 1 / 20 )215.6739750017246.7591070599206331.9086490404335
Trimmed Mean ( 2 / 20 )216.1788702607146.4498018063693233.5171338206444
Trimmed Mean ( 3 / 20 )216.4943345611116.1755077459525935.0569286716547
Trimmed Mean ( 4 / 20 )216.6230156634625.9211309761676136.5847363511065
Trimmed Mean ( 5 / 20 )216.8317234965.6412860413346238.4365766790123
Trimmed Mean ( 6 / 20 )216.694719143755.4926458927161539.4517912452924
Trimmed Mean ( 7 / 20 )216.3341780869575.3680909534528540.3000209874996
Trimmed Mean ( 8 / 20 )215.9714998568185.2417963530831441.2018104689983
Trimmed Mean ( 9 / 20 )215.9219428476195.2028326371014641.5008434651304
Trimmed Mean ( 10 / 20 )215.85221752255.1677853735355541.7688046078478
Trimmed Mean ( 11 / 20 )215.7593944763165.124274630649442.1053534456979
Trimmed Mean ( 12 / 20 )215.7361448027785.0762270321920342.4993097106648
Trimmed Mean ( 13 / 20 )215.6526861382355.0238015183159942.9261955019519
Trimmed Mean ( 14 / 20 )215.52482513754.9631928832738243.4246321282069
Trimmed Mean ( 15 / 20 )215.4105453533334.9197458884260143.7848926018922
Trimmed Mean ( 16 / 20 )215.2643984428574.8408235864009544.4685485022811
Trimmed Mean ( 17 / 20 )215.3401616692314.7999900011830644.8626271338389
Trimmed Mean ( 18 / 20 )215.4665720541674.7233766882166445.6170630201248
Trimmed Mean ( 19 / 20 )215.4738446863644.6519866803720746.3186718903352
Trimmed Mean ( 20 / 20 )215.4444652354.5404352055647647.4501794389558
Median211.81929425
Midrange214.97778787
Midmean - Weighted Average at Xnp214.144873145161
Midmean - Weighted Average at X(n+1)p215.410545353333
Midmean - Empirical Distribution Function214.144873145161
Midmean - Empirical Distribution Function - Averaging215.410545353333
Midmean - Empirical Distribution Function - Interpolation215.410545353333
Midmean - Closest Observation214.144873145161
Midmean - True Basic - Statistics Graphics Toolkit215.410545353333
Midmean - MS Excel (old versions)215.5248251375
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 215.650768764 & 7.16558273943858 & 30.0953567358984 \tabularnewline
Geometric Mean & 207.890572110914 &  &  \tabularnewline
Harmonic Mean & 199.180338832809 &  &  \tabularnewline
Quadratic Mean & 222.563795466048 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 215.202739426667 & 7.00922088455688 & 30.7028046299431 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 215.61103452 & 6.84901308546927 & 31.4805990044662 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 216.159763695 & 6.67329147421208 & 32.3917761617811 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 215.927322888333 & 6.57376292738344 & 32.8468375378847 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 217.379740905 & 6.00102989955618 & 36.2237390153775 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 218.353208005 & 5.78158852178601 & 37.7669920960663 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 218.195926335 & 5.65119073815274 & 38.6106108332 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 216.249019108333 & 5.17911394790013 & 41.7540570228255 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 216.340294798333 & 5.07490944048599 & 42.6293902059493 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 216.440096815 & 5.01581928862854 & 43.1514941747792 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 215.912842321667 & 4.92546026103509 & 43.8360743725283 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 216.303663721667 & 4.82011833727315 & 44.8751770364282 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 216.539189076667 & 4.71572863484746 & 45.9185007967853 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 216.324783626667 & 4.50034152965171 & 48.0685259554975 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 216.433573726667 & 4.48190961357697 & 48.2904815998582 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 214.73910674 & 4.16924218676474 & 51.5055487593619 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 214.480571051667 & 4.122293226433 & 52.0294310158173 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 215.418572681667 & 3.9065259079346 & 55.1432597040063 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 215.659914545 & 3.79993927136616 & 56.7535160811834 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 214.949754945 & 3.51047395318127 & 61.2309784410187 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 215.673975001724 & 6.75910705992063 & 31.9086490404335 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 216.178870260714 & 6.44980180636932 & 33.5171338206444 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 216.494334561111 & 6.17550774595259 & 35.0569286716547 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 216.623015663462 & 5.92113097616761 & 36.5847363511065 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 216.831723496 & 5.64128604133462 & 38.4365766790123 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 216.69471914375 & 5.49264589271615 & 39.4517912452924 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 216.334178086957 & 5.36809095345285 & 40.3000209874996 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 215.971499856818 & 5.24179635308314 & 41.2018104689983 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 215.921942847619 & 5.20283263710146 & 41.5008434651304 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 215.8522175225 & 5.16778537353555 & 41.7688046078478 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 215.759394476316 & 5.1242746306494 & 42.1053534456979 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 215.736144802778 & 5.07622703219203 & 42.4993097106648 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 215.652686138235 & 5.02380151831599 & 42.9261955019519 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 215.5248251375 & 4.96319288327382 & 43.4246321282069 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 215.410545353333 & 4.91974588842601 & 43.7848926018922 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 215.264398442857 & 4.84082358640095 & 44.4685485022811 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 215.340161669231 & 4.79999000118306 & 44.8626271338389 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 215.466572054167 & 4.72337668821664 & 45.6170630201248 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 215.473844686364 & 4.65198668037207 & 46.3186718903352 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 215.444465235 & 4.54043520556476 & 47.4501794389558 \tabularnewline
Median & 211.81929425 &  &  \tabularnewline
Midrange & 214.97778787 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 214.144873145161 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 215.410545353333 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 214.144873145161 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 215.410545353333 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 215.410545353333 &  &  \tabularnewline
Midmean - Closest Observation & 214.144873145161 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 215.410545353333 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 215.5248251375 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=50778&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]215.650768764[/C][C]7.16558273943858[/C][C]30.0953567358984[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]207.890572110914[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]199.180338832809[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]222.563795466048[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]215.202739426667[/C][C]7.00922088455688[/C][C]30.7028046299431[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]215.61103452[/C][C]6.84901308546927[/C][C]31.4805990044662[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]216.159763695[/C][C]6.67329147421208[/C][C]32.3917761617811[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]215.927322888333[/C][C]6.57376292738344[/C][C]32.8468375378847[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]217.379740905[/C][C]6.00102989955618[/C][C]36.2237390153775[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]218.353208005[/C][C]5.78158852178601[/C][C]37.7669920960663[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]218.195926335[/C][C]5.65119073815274[/C][C]38.6106108332[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]216.249019108333[/C][C]5.17911394790013[/C][C]41.7540570228255[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]216.340294798333[/C][C]5.07490944048599[/C][C]42.6293902059493[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]216.440096815[/C][C]5.01581928862854[/C][C]43.1514941747792[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]215.912842321667[/C][C]4.92546026103509[/C][C]43.8360743725283[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]216.303663721667[/C][C]4.82011833727315[/C][C]44.8751770364282[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]216.539189076667[/C][C]4.71572863484746[/C][C]45.9185007967853[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]216.324783626667[/C][C]4.50034152965171[/C][C]48.0685259554975[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]216.433573726667[/C][C]4.48190961357697[/C][C]48.2904815998582[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]214.73910674[/C][C]4.16924218676474[/C][C]51.5055487593619[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]214.480571051667[/C][C]4.122293226433[/C][C]52.0294310158173[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]215.418572681667[/C][C]3.9065259079346[/C][C]55.1432597040063[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]215.659914545[/C][C]3.79993927136616[/C][C]56.7535160811834[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]214.949754945[/C][C]3.51047395318127[/C][C]61.2309784410187[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]215.673975001724[/C][C]6.75910705992063[/C][C]31.9086490404335[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]216.178870260714[/C][C]6.44980180636932[/C][C]33.5171338206444[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]216.494334561111[/C][C]6.17550774595259[/C][C]35.0569286716547[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]216.623015663462[/C][C]5.92113097616761[/C][C]36.5847363511065[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]216.831723496[/C][C]5.64128604133462[/C][C]38.4365766790123[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]216.69471914375[/C][C]5.49264589271615[/C][C]39.4517912452924[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]216.334178086957[/C][C]5.36809095345285[/C][C]40.3000209874996[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]215.971499856818[/C][C]5.24179635308314[/C][C]41.2018104689983[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]215.921942847619[/C][C]5.20283263710146[/C][C]41.5008434651304[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]215.8522175225[/C][C]5.16778537353555[/C][C]41.7688046078478[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]215.759394476316[/C][C]5.1242746306494[/C][C]42.1053534456979[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]215.736144802778[/C][C]5.07622703219203[/C][C]42.4993097106648[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]215.652686138235[/C][C]5.02380151831599[/C][C]42.9261955019519[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]215.5248251375[/C][C]4.96319288327382[/C][C]43.4246321282069[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]215.410545353333[/C][C]4.91974588842601[/C][C]43.7848926018922[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]215.264398442857[/C][C]4.84082358640095[/C][C]44.4685485022811[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]215.340161669231[/C][C]4.79999000118306[/C][C]44.8626271338389[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]215.466572054167[/C][C]4.72337668821664[/C][C]45.6170630201248[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]215.473844686364[/C][C]4.65198668037207[/C][C]46.3186718903352[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]215.444465235[/C][C]4.54043520556476[/C][C]47.4501794389558[/C][/ROW]
[ROW][C]Median[/C][C]211.81929425[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]214.97778787[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]214.144873145161[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]215.410545353333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]214.144873145161[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]215.410545353333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]215.410545353333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]214.144873145161[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]215.410545353333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]215.5248251375[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]60[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=50778&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=50778&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
MeasureValueS.E.Value/S.E.
Arithmetic Mean215.6507687647.1655827394385830.0953567358984
Geometric Mean207.890572110914
Harmonic Mean199.180338832809
Quadratic Mean222.563795466048
Winsorized Mean ( 1 / 20 )215.2027394266677.0092208845568830.7028046299431
Winsorized Mean ( 2 / 20 )215.611034526.8490130854692731.4805990044662
Winsorized Mean ( 3 / 20 )216.1597636956.6732914742120832.3917761617811
Winsorized Mean ( 4 / 20 )215.9273228883336.5737629273834432.8468375378847
Winsorized Mean ( 5 / 20 )217.3797409056.0010298995561836.2237390153775
Winsorized Mean ( 6 / 20 )218.3532080055.7815885217860137.7669920960663
Winsorized Mean ( 7 / 20 )218.1959263355.6511907381527438.6106108332
Winsorized Mean ( 8 / 20 )216.2490191083335.1791139479001341.7540570228255
Winsorized Mean ( 9 / 20 )216.3402947983335.0749094404859942.6293902059493
Winsorized Mean ( 10 / 20 )216.4400968155.0158192886285443.1514941747792
Winsorized Mean ( 11 / 20 )215.9128423216674.9254602610350943.8360743725283
Winsorized Mean ( 12 / 20 )216.3036637216674.8201183372731544.8751770364282
Winsorized Mean ( 13 / 20 )216.5391890766674.7157286348474645.9185007967853
Winsorized Mean ( 14 / 20 )216.3247836266674.5003415296517148.0685259554975
Winsorized Mean ( 15 / 20 )216.4335737266674.4819096135769748.2904815998582
Winsorized Mean ( 16 / 20 )214.739106744.1692421867647451.5055487593619
Winsorized Mean ( 17 / 20 )214.4805710516674.12229322643352.0294310158173
Winsorized Mean ( 18 / 20 )215.4185726816673.906525907934655.1432597040063
Winsorized Mean ( 19 / 20 )215.6599145453.7999392713661656.7535160811834
Winsorized Mean ( 20 / 20 )214.9497549453.5104739531812761.2309784410187
Trimmed Mean ( 1 / 20 )215.6739750017246.7591070599206331.9086490404335
Trimmed Mean ( 2 / 20 )216.1788702607146.4498018063693233.5171338206444
Trimmed Mean ( 3 / 20 )216.4943345611116.1755077459525935.0569286716547
Trimmed Mean ( 4 / 20 )216.6230156634625.9211309761676136.5847363511065
Trimmed Mean ( 5 / 20 )216.8317234965.6412860413346238.4365766790123
Trimmed Mean ( 6 / 20 )216.694719143755.4926458927161539.4517912452924
Trimmed Mean ( 7 / 20 )216.3341780869575.3680909534528540.3000209874996
Trimmed Mean ( 8 / 20 )215.9714998568185.2417963530831441.2018104689983
Trimmed Mean ( 9 / 20 )215.9219428476195.2028326371014641.5008434651304
Trimmed Mean ( 10 / 20 )215.85221752255.1677853735355541.7688046078478
Trimmed Mean ( 11 / 20 )215.7593944763165.124274630649442.1053534456979
Trimmed Mean ( 12 / 20 )215.7361448027785.0762270321920342.4993097106648
Trimmed Mean ( 13 / 20 )215.6526861382355.0238015183159942.9261955019519
Trimmed Mean ( 14 / 20 )215.52482513754.9631928832738243.4246321282069
Trimmed Mean ( 15 / 20 )215.4105453533334.9197458884260143.7848926018922
Trimmed Mean ( 16 / 20 )215.2643984428574.8408235864009544.4685485022811
Trimmed Mean ( 17 / 20 )215.3401616692314.7999900011830644.8626271338389
Trimmed Mean ( 18 / 20 )215.4665720541674.7233766882166445.6170630201248
Trimmed Mean ( 19 / 20 )215.4738446863644.6519866803720746.3186718903352
Trimmed Mean ( 20 / 20 )215.4444652354.5404352055647647.4501794389558
Median211.81929425
Midrange214.97778787
Midmean - Weighted Average at Xnp214.144873145161
Midmean - Weighted Average at X(n+1)p215.410545353333
Midmean - Empirical Distribution Function214.144873145161
Midmean - Empirical Distribution Function - Averaging215.410545353333
Midmean - Empirical Distribution Function - Interpolation215.410545353333
Midmean - Closest Observation214.144873145161
Midmean - True Basic - Statistics Graphics Toolkit215.410545353333
Midmean - MS Excel (old versions)215.5248251375
Number of observations60



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')