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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 computationWed, 28 Oct 2009 12:03:33 -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/28/t1256753103lvybul1uniu8nta.htm/, Retrieved Mon, 06 May 2024 09:08:21 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=51677, Retrieved Mon, 06 May 2024 09:08:21 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsSHWWS4V9
Estimated Impact82
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [] [2009-10-28 18:03:33] [71596e6a53ccce532e52aaf6113616ef] [Current]
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Dataseries X:
3816,277331
3596,008286
3132,274475
570,3993676
418,7931843
21,08056068
152,1902178
386,3244507
238,5739419
290,877733
17,11096272
95,16271786
36,55216903
387,4218724
262,1916862
66,80996187
206,8435961
35,68552302
71,64669479
227,4979491
295,5763546
30,96295983
292,4658588
19,29259955
18,79710598
147,72363
527,7476604
19,42751797
223,7246361
14,59416717
41,33886036
27,25081481
15,19726355
739,0418721
51,09573985
246,1468466
93,69792212
0,002316344
99,89250115
8,080218672
122,1438655
7,758032977
27,93465584
123,2970983
164,1786501
333,4703525
232,6195868
77,53465333
38,50669611
81,09680389
1173,827812
525,5086053
361,2043316
741,6511858
982,3568537
1432,764182
2539,058148
2799,221102
1934,220055
2272,473678




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'George Udny Yule' @ 72.249.76.132

\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 & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=51677&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]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=51677&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=51677&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'George Udny Yule' @ 72.249.76.132







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean548.543431262883119.2447958815854.60014566847521
Geometric Mean139.226035113915
Harmonic Mean0.138637875132398
Quadratic Mean1067.63282795504
Winsorized Mean ( 1 / 20 )545.001542456767117.5745388717084.63537044403337
Winsorized Mean ( 2 / 20 )529.554488279933111.0960073201374.76663834330206
Winsorized Mean ( 3 / 20 )513.227517054833104.6750155584544.90305651560403
Winsorized Mean ( 4 / 20 )495.92352654683398.40508162924355.03961297868033
Winsorized Mean ( 5 / 20 )473.86762897766790.74408420450225.22202227430883
Winsorized Mean ( 6 / 20 )440.21088100366779.65102543506045.5267446790446
Winsorized Mean ( 7 / 20 )381.765503403561.80566660308956.17686895693827
Winsorized Mean ( 8 / 20 )347.25864319283352.16358233875376.65710880318213
Winsorized Mean ( 9 / 20 )318.78595585433344.64330045398957.14073450243407
Winsorized Mean ( 10 / 20 )279.69672022634.90162469408858.01385960331452
Winsorized Mean ( 11 / 20 )279.34371690316734.77901603552728.0319614740628
Winsorized Mean ( 12 / 20 )246.22087680116727.50765421160788.95099505421533
Winsorized Mean ( 13 / 20 )238.00289559925.55914694790399.3118481647338
Winsorized Mean ( 14 / 20 )237.68266681133325.43172840686019.34591086413218
Winsorized Mean ( 15 / 20 )211.49244333133320.488681323930410.3224038671691
Winsorized Mean ( 16 / 20 )203.88200395818.975596664255810.7444317860134
Winsorized Mean ( 17 / 20 )206.335516998518.527484793704911.1367257507402
Winsorized Mean ( 18 / 20 )203.513747874516.637577019062612.2321746514726
Winsorized Mean ( 19 / 20 )196.26295325083315.037559239361513.0515165477857
Winsorized Mean ( 20 / 20 )185.59427346416712.863407935428914.4280795879135
Trimmed Mean ( 1 / 20 )501.660797041879108.9324710838664.60524572747142
Trimmed Mean ( 2 / 20 )455.22428409735797.51831419383744.66809017219583
Trimmed Mean ( 3 / 20 )413.92972621814887.33901435116864.7393450600878
Trimmed Mean ( 4 / 20 )375.73826820403877.44676960003574.85156798849704
Trimmed Mean ( 5 / 20 )339.682690701267.10259788260615.06213919311237
Trimmed Mean ( 6 / 20 )306.13645613208356.2495404279895.44247035269561
Trimmed Mean ( 7 / 20 )276.98984202956545.9242713070566.03144773223668
Trimmed Mean ( 8 / 20 )256.57899890477339.45424059099116.50320460009968
Trimmed Mean ( 9 / 20 )240.38620528190534.38997595710116.99000794829773
Trimmed Mean ( 10 / 20 )227.319580186530.28829036723037.50519680808537
Trimmed Mean ( 11 / 20 )219.04950544342128.27358396310177.74749694730214
Trimmed Mean ( 12 / 20 )209.91401885861125.41760326457888.25860788971952
Trimmed Mean ( 13 / 20 )204.57477504352924.08922652116498.49237624395243
Trimmed Mean ( 14 / 20 )199.75341150187522.83748169084428.7467354853735
Trimmed Mean ( 15 / 20 )194.33494645766721.00208749027939.25312526898164
Trimmed Mean ( 16 / 20 )191.88387547571420.21426625634149.49249767675927
Trimmed Mean ( 17 / 20 )190.15337617538519.53054213405259.73620572691849
Trimmed Mean ( 18 / 20 )187.7736495837518.551793848785810.1215899181652
Trimmed Mean ( 19 / 20 )185.38878620636417.724794709437510.4592910239832
Trimmed Mean ( 20 / 20 )183.671812462517.031040000438210.7845329737805
Median185.5111231
Midrange1908.139823672
Midmean - Weighted Average at Xnp189.245179443871
Midmean - Weighted Average at X(n+1)p194.334946457667
Midmean - Empirical Distribution Function189.245179443871
Midmean - Empirical Distribution Function - Averaging194.334946457667
Midmean - Empirical Distribution Function - Interpolation194.334946457667
Midmean - Closest Observation189.245179443871
Midmean - True Basic - Statistics Graphics Toolkit194.334946457667
Midmean - MS Excel (old versions)199.753411501875
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 548.543431262883 & 119.244795881585 & 4.60014566847521 \tabularnewline
Geometric Mean & 139.226035113915 &  &  \tabularnewline
Harmonic Mean & 0.138637875132398 &  &  \tabularnewline
Quadratic Mean & 1067.63282795504 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 545.001542456767 & 117.574538871708 & 4.63537044403337 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 529.554488279933 & 111.096007320137 & 4.76663834330206 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 513.227517054833 & 104.675015558454 & 4.90305651560403 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 495.923526546833 & 98.4050816292435 & 5.03961297868033 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 473.867628977667 & 90.7440842045022 & 5.22202227430883 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 440.210881003667 & 79.6510254350604 & 5.5267446790446 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 381.7655034035 & 61.8056666030895 & 6.17686895693827 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 347.258643192833 & 52.1635823387537 & 6.65710880318213 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 318.785955854333 & 44.6433004539895 & 7.14073450243407 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 279.696720226 & 34.9016246940885 & 8.01385960331452 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 279.343716903167 & 34.7790160355272 & 8.0319614740628 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 246.220876801167 & 27.5076542116078 & 8.95099505421533 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 238.002895599 & 25.5591469479039 & 9.3118481647338 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 237.682666811333 & 25.4317284068601 & 9.34591086413218 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 211.492443331333 & 20.4886813239304 & 10.3224038671691 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 203.882003958 & 18.9755966642558 & 10.7444317860134 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 206.3355169985 & 18.5274847937049 & 11.1367257507402 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 203.5137478745 & 16.6375770190626 & 12.2321746514726 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 196.262953250833 & 15.0375592393615 & 13.0515165477857 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 185.594273464167 & 12.8634079354289 & 14.4280795879135 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 501.660797041879 & 108.932471083866 & 4.60524572747142 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 455.224284097357 & 97.5183141938374 & 4.66809017219583 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 413.929726218148 & 87.3390143511686 & 4.7393450600878 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 375.738268204038 & 77.4467696000357 & 4.85156798849704 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 339.6826907012 & 67.1025978826061 & 5.06213919311237 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 306.136456132083 & 56.249540427989 & 5.44247035269561 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 276.989842029565 & 45.924271307056 & 6.03144773223668 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 256.578998904773 & 39.4542405909911 & 6.50320460009968 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 240.386205281905 & 34.3899759571011 & 6.99000794829773 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 227.3195801865 & 30.2882903672303 & 7.50519680808537 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 219.049505443421 & 28.2735839631017 & 7.74749694730214 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 209.914018858611 & 25.4176032645788 & 8.25860788971952 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 204.574775043529 & 24.0892265211649 & 8.49237624395243 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 199.753411501875 & 22.8374816908442 & 8.7467354853735 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 194.334946457667 & 21.0020874902793 & 9.25312526898164 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 191.883875475714 & 20.2142662563414 & 9.49249767675927 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 190.153376175385 & 19.5305421340525 & 9.73620572691849 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 187.77364958375 & 18.5517938487858 & 10.1215899181652 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 185.388786206364 & 17.7247947094375 & 10.4592910239832 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 183.6718124625 & 17.0310400004382 & 10.7845329737805 \tabularnewline
Median & 185.5111231 &  &  \tabularnewline
Midrange & 1908.139823672 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 189.245179443871 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 194.334946457667 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 189.245179443871 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 194.334946457667 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 194.334946457667 &  &  \tabularnewline
Midmean - Closest Observation & 189.245179443871 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 194.334946457667 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 199.753411501875 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=51677&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]548.543431262883[/C][C]119.244795881585[/C][C]4.60014566847521[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]139.226035113915[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]0.138637875132398[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]1067.63282795504[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]545.001542456767[/C][C]117.574538871708[/C][C]4.63537044403337[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]529.554488279933[/C][C]111.096007320137[/C][C]4.76663834330206[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]513.227517054833[/C][C]104.675015558454[/C][C]4.90305651560403[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]495.923526546833[/C][C]98.4050816292435[/C][C]5.03961297868033[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]473.867628977667[/C][C]90.7440842045022[/C][C]5.22202227430883[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]440.210881003667[/C][C]79.6510254350604[/C][C]5.5267446790446[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]381.7655034035[/C][C]61.8056666030895[/C][C]6.17686895693827[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]347.258643192833[/C][C]52.1635823387537[/C][C]6.65710880318213[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]318.785955854333[/C][C]44.6433004539895[/C][C]7.14073450243407[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]279.696720226[/C][C]34.9016246940885[/C][C]8.01385960331452[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]279.343716903167[/C][C]34.7790160355272[/C][C]8.0319614740628[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]246.220876801167[/C][C]27.5076542116078[/C][C]8.95099505421533[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]238.002895599[/C][C]25.5591469479039[/C][C]9.3118481647338[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]237.682666811333[/C][C]25.4317284068601[/C][C]9.34591086413218[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]211.492443331333[/C][C]20.4886813239304[/C][C]10.3224038671691[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]203.882003958[/C][C]18.9755966642558[/C][C]10.7444317860134[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]206.3355169985[/C][C]18.5274847937049[/C][C]11.1367257507402[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]203.5137478745[/C][C]16.6375770190626[/C][C]12.2321746514726[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]196.262953250833[/C][C]15.0375592393615[/C][C]13.0515165477857[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]185.594273464167[/C][C]12.8634079354289[/C][C]14.4280795879135[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]501.660797041879[/C][C]108.932471083866[/C][C]4.60524572747142[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]455.224284097357[/C][C]97.5183141938374[/C][C]4.66809017219583[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]413.929726218148[/C][C]87.3390143511686[/C][C]4.7393450600878[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]375.738268204038[/C][C]77.4467696000357[/C][C]4.85156798849704[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]339.6826907012[/C][C]67.1025978826061[/C][C]5.06213919311237[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]306.136456132083[/C][C]56.249540427989[/C][C]5.44247035269561[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]276.989842029565[/C][C]45.924271307056[/C][C]6.03144773223668[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]256.578998904773[/C][C]39.4542405909911[/C][C]6.50320460009968[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]240.386205281905[/C][C]34.3899759571011[/C][C]6.99000794829773[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]227.3195801865[/C][C]30.2882903672303[/C][C]7.50519680808537[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]219.049505443421[/C][C]28.2735839631017[/C][C]7.74749694730214[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]209.914018858611[/C][C]25.4176032645788[/C][C]8.25860788971952[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]204.574775043529[/C][C]24.0892265211649[/C][C]8.49237624395243[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]199.753411501875[/C][C]22.8374816908442[/C][C]8.7467354853735[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]194.334946457667[/C][C]21.0020874902793[/C][C]9.25312526898164[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]191.883875475714[/C][C]20.2142662563414[/C][C]9.49249767675927[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]190.153376175385[/C][C]19.5305421340525[/C][C]9.73620572691849[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]187.77364958375[/C][C]18.5517938487858[/C][C]10.1215899181652[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]185.388786206364[/C][C]17.7247947094375[/C][C]10.4592910239832[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]183.6718124625[/C][C]17.0310400004382[/C][C]10.7845329737805[/C][/ROW]
[ROW][C]Median[/C][C]185.5111231[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]1908.139823672[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]189.245179443871[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]194.334946457667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]189.245179443871[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]194.334946457667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]194.334946457667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]189.245179443871[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]194.334946457667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]199.753411501875[/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=51677&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=51677&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 Mean548.543431262883119.2447958815854.60014566847521
Geometric Mean139.226035113915
Harmonic Mean0.138637875132398
Quadratic Mean1067.63282795504
Winsorized Mean ( 1 / 20 )545.001542456767117.5745388717084.63537044403337
Winsorized Mean ( 2 / 20 )529.554488279933111.0960073201374.76663834330206
Winsorized Mean ( 3 / 20 )513.227517054833104.6750155584544.90305651560403
Winsorized Mean ( 4 / 20 )495.92352654683398.40508162924355.03961297868033
Winsorized Mean ( 5 / 20 )473.86762897766790.74408420450225.22202227430883
Winsorized Mean ( 6 / 20 )440.21088100366779.65102543506045.5267446790446
Winsorized Mean ( 7 / 20 )381.765503403561.80566660308956.17686895693827
Winsorized Mean ( 8 / 20 )347.25864319283352.16358233875376.65710880318213
Winsorized Mean ( 9 / 20 )318.78595585433344.64330045398957.14073450243407
Winsorized Mean ( 10 / 20 )279.69672022634.90162469408858.01385960331452
Winsorized Mean ( 11 / 20 )279.34371690316734.77901603552728.0319614740628
Winsorized Mean ( 12 / 20 )246.22087680116727.50765421160788.95099505421533
Winsorized Mean ( 13 / 20 )238.00289559925.55914694790399.3118481647338
Winsorized Mean ( 14 / 20 )237.68266681133325.43172840686019.34591086413218
Winsorized Mean ( 15 / 20 )211.49244333133320.488681323930410.3224038671691
Winsorized Mean ( 16 / 20 )203.88200395818.975596664255810.7444317860134
Winsorized Mean ( 17 / 20 )206.335516998518.527484793704911.1367257507402
Winsorized Mean ( 18 / 20 )203.513747874516.637577019062612.2321746514726
Winsorized Mean ( 19 / 20 )196.26295325083315.037559239361513.0515165477857
Winsorized Mean ( 20 / 20 )185.59427346416712.863407935428914.4280795879135
Trimmed Mean ( 1 / 20 )501.660797041879108.9324710838664.60524572747142
Trimmed Mean ( 2 / 20 )455.22428409735797.51831419383744.66809017219583
Trimmed Mean ( 3 / 20 )413.92972621814887.33901435116864.7393450600878
Trimmed Mean ( 4 / 20 )375.73826820403877.44676960003574.85156798849704
Trimmed Mean ( 5 / 20 )339.682690701267.10259788260615.06213919311237
Trimmed Mean ( 6 / 20 )306.13645613208356.2495404279895.44247035269561
Trimmed Mean ( 7 / 20 )276.98984202956545.9242713070566.03144773223668
Trimmed Mean ( 8 / 20 )256.57899890477339.45424059099116.50320460009968
Trimmed Mean ( 9 / 20 )240.38620528190534.38997595710116.99000794829773
Trimmed Mean ( 10 / 20 )227.319580186530.28829036723037.50519680808537
Trimmed Mean ( 11 / 20 )219.04950544342128.27358396310177.74749694730214
Trimmed Mean ( 12 / 20 )209.91401885861125.41760326457888.25860788971952
Trimmed Mean ( 13 / 20 )204.57477504352924.08922652116498.49237624395243
Trimmed Mean ( 14 / 20 )199.75341150187522.83748169084428.7467354853735
Trimmed Mean ( 15 / 20 )194.33494645766721.00208749027939.25312526898164
Trimmed Mean ( 16 / 20 )191.88387547571420.21426625634149.49249767675927
Trimmed Mean ( 17 / 20 )190.15337617538519.53054213405259.73620572691849
Trimmed Mean ( 18 / 20 )187.7736495837518.551793848785810.1215899181652
Trimmed Mean ( 19 / 20 )185.38878620636417.724794709437510.4592910239832
Trimmed Mean ( 20 / 20 )183.671812462517.031040000438210.7845329737805
Median185.5111231
Midrange1908.139823672
Midmean - Weighted Average at Xnp189.245179443871
Midmean - Weighted Average at X(n+1)p194.334946457667
Midmean - Empirical Distribution Function189.245179443871
Midmean - Empirical Distribution Function - Averaging194.334946457667
Midmean - Empirical Distribution Function - Interpolation194.334946457667
Midmean - Closest Observation189.245179443871
Midmean - True Basic - Statistics Graphics Toolkit194.334946457667
Midmean - MS Excel (old versions)199.753411501875
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')