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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 computationSun, 21 Dec 2008 06:10:01 -0700
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2008/Dec/21/t12298655238yg29w4a764amdi.htm/, Retrieved Sun, 19 May 2024 12:16:02 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=35559, Retrieved Sun, 19 May 2024 12:16:02 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact147
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [central tendency ...] [2008-12-21 13:10:01] [00a0a665d7a07edd2e460056b0c0c354] [Current]
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Dataseries X:
17704
15548
28029
29383
36438
32034
22679
24319
18004
17537
20366
22782
19169
13807
29743
25591
29096
26482
22405
27044
17970
18730
19684
19785
18479
10698
31956
29506
34506
27165
26736
23691
18157
17328
18205
20995
17382
9367
31124
26551
30651
25859
25100
25778
20418
18688
20424
24776
19814
12738
31566
30111
30019
31934
25826
26835
20205
17789
20520
22518
15572




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24

\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 & 3 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=35559&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]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=35559&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=35559&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 time3 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean23169.1147540984774.36198913536829.9202634932642
Geometric Mean22332.1243025103
Harmonic Mean21416.6089441899
Quadratic Mean23932.9494191928
Winsorized Mean ( 1 / 20 )23159.2622950820759.66551738703230.4861307575751
Winsorized Mean ( 2 / 20 )23145.0983606557724.06104703868231.965672584261
Winsorized Mean ( 3 / 20 )23193.8360655738711.19045245375832.6126932463029
Winsorized Mean ( 4 / 20 )23306.5573770492687.56865549875533.8970620470516
Winsorized Mean ( 5 / 20 )23278.3606557377680.98447300722934.1833941571978
Winsorized Mean ( 6 / 20 )23407.6065573771642.22891722461636.4474503243061
Winsorized Mean ( 7 / 20 )23359.5245901639630.58381423847237.0442819221013
Winsorized Mean ( 8 / 20 )23309.0327868852614.01981997843237.9613687188534
Winsorized Mean ( 9 / 20 )23320.0983606557607.6918980932338.3748712691873
Winsorized Mean ( 10 / 20 )23288.7868852459597.31829260927438.9889062052883
Winsorized Mean ( 11 / 20 )23278.6885245902584.7020288922439.8129087540423
Winsorized Mean ( 12 / 20 )23261.1803278689579.41219060052740.146170041331
Winsorized Mean ( 13 / 20 )23232.6229508197563.81335959798541.2062299612503
Winsorized Mean ( 14 / 20 )22998.7540983607521.16404634227944.1295869501636
Winsorized Mean ( 15 / 20 )22853.6721311475477.74251628839747.8367977560355
Winsorized Mean ( 16 / 20 )22876.7540983607464.6816118142949.2310294118187
Winsorized Mean ( 17 / 20 )22830.2131147541454.28938871229150.2547796228911
Winsorized Mean ( 18 / 20 )22930.5409836066430.81608514613253.2258236732933
Winsorized Mean ( 19 / 20 )23033.3278688525399.4478735365257.6629127223194
Winsorized Mean ( 20 / 20 )23043.8196721311391.52111759597958.8571564507809
Trimmed Mean ( 1 / 20 )23178.1525423729730.90399173060931.7116239678654
Trimmed Mean ( 2 / 20 )23198.3684210526695.4933287390633.3552709457496
Trimmed Mean ( 3 / 20 )23227.9090909091675.81344639261934.3702973281989
Trimmed Mean ( 4 / 20 )23240.9811320755657.52526012311935.3461418770797
Trimmed Mean ( 5 / 20 )23221.3725490196643.75047776005736.0720082567066
Trimmed Mean ( 6 / 20 )23207.1836734694628.34203584357836.9339982837734
Trimmed Mean ( 7 / 20 )23163.8297872340620.07457350383737.3565225491232
Trimmed Mean ( 8 / 20 )23125.9333333333612.05104543838737.784321268121
Trimmed Mean ( 9 / 20 )23093.4651162791605.27771679662838.1535028887218
Trimmed Mean ( 10 / 20 )23056597.036000058538.6174368006969
Trimmed Mean ( 11 / 20 )23019.5897435897587.81618271922239.1612045063165
Trimmed Mean ( 12 / 20 )22980.7567567568577.63927822115139.7839233293248
Trimmed Mean ( 13 / 20 )22940.0285714286564.07114171633240.6686796662343
Trimmed Mean ( 14 / 20 )22898.4242424242548.58571094621341.7408324451771
Trimmed Mean ( 15 / 20 )22884.3225806452538.25891237065942.5154550248978
Trimmed Mean ( 16 / 20 )22888.6206896552534.18884322963742.8474330374883
Trimmed Mean ( 17 / 20 )22890.2962962963529.47052199385143.2324281436807
Trimmed Mean ( 18 / 20 )22898.92522.6971555308143.8091536517846
Trimmed Mean ( 19 / 20 )22894.2608695652517.08250508481544.2758373072590
Trimmed Mean ( 20 / 20 )22873515.48496814257644.3718079353842
Median22679
Midrange22902.5
Midmean - Weighted Average at Xnp22741.6333333333
Midmean - Weighted Average at X(n+1)p22884.3225806452
Midmean - Empirical Distribution Function22884.3225806452
Midmean - Empirical Distribution Function - Averaging22884.3225806452
Midmean - Empirical Distribution Function - Interpolation22884.3225806452
Midmean - Closest Observation22738.09375
Midmean - True Basic - Statistics Graphics Toolkit22884.3225806452
Midmean - MS Excel (old versions)22884.3225806452
Number of observations61

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 23169.1147540984 & 774.361989135368 & 29.9202634932642 \tabularnewline
Geometric Mean & 22332.1243025103 &  &  \tabularnewline
Harmonic Mean & 21416.6089441899 &  &  \tabularnewline
Quadratic Mean & 23932.9494191928 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 23159.2622950820 & 759.665517387032 & 30.4861307575751 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 23145.0983606557 & 724.061047038682 & 31.965672584261 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 23193.8360655738 & 711.190452453758 & 32.6126932463029 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 23306.5573770492 & 687.568655498755 & 33.8970620470516 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 23278.3606557377 & 680.984473007229 & 34.1833941571978 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 23407.6065573771 & 642.228917224616 & 36.4474503243061 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 23359.5245901639 & 630.583814238472 & 37.0442819221013 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 23309.0327868852 & 614.019819978432 & 37.9613687188534 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 23320.0983606557 & 607.69189809323 & 38.3748712691873 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 23288.7868852459 & 597.318292609274 & 38.9889062052883 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 23278.6885245902 & 584.70202889224 & 39.8129087540423 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 23261.1803278689 & 579.412190600527 & 40.146170041331 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 23232.6229508197 & 563.813359597985 & 41.2062299612503 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 22998.7540983607 & 521.164046342279 & 44.1295869501636 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 22853.6721311475 & 477.742516288397 & 47.8367977560355 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 22876.7540983607 & 464.68161181429 & 49.2310294118187 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 22830.2131147541 & 454.289388712291 & 50.2547796228911 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 22930.5409836066 & 430.816085146132 & 53.2258236732933 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 23033.3278688525 & 399.44787353652 & 57.6629127223194 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 23043.8196721311 & 391.521117595979 & 58.8571564507809 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 23178.1525423729 & 730.903991730609 & 31.7116239678654 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 23198.3684210526 & 695.49332873906 & 33.3552709457496 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 23227.9090909091 & 675.813446392619 & 34.3702973281989 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 23240.9811320755 & 657.525260123119 & 35.3461418770797 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 23221.3725490196 & 643.750477760057 & 36.0720082567066 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 23207.1836734694 & 628.342035843578 & 36.9339982837734 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 23163.8297872340 & 620.074573503837 & 37.3565225491232 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 23125.9333333333 & 612.051045438387 & 37.784321268121 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 23093.4651162791 & 605.277716796628 & 38.1535028887218 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 23056 & 597.0360000585 & 38.6174368006969 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 23019.5897435897 & 587.816182719222 & 39.1612045063165 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 22980.7567567568 & 577.639278221151 & 39.7839233293248 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 22940.0285714286 & 564.071141716332 & 40.6686796662343 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 22898.4242424242 & 548.585710946213 & 41.7408324451771 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 22884.3225806452 & 538.258912370659 & 42.5154550248978 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 22888.6206896552 & 534.188843229637 & 42.8474330374883 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 22890.2962962963 & 529.470521993851 & 43.2324281436807 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 22898.92 & 522.69715553081 & 43.8091536517846 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 22894.2608695652 & 517.082505084815 & 44.2758373072590 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 22873 & 515.484968142576 & 44.3718079353842 \tabularnewline
Median & 22679 &  &  \tabularnewline
Midrange & 22902.5 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 22741.6333333333 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 22884.3225806452 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 22884.3225806452 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 22884.3225806452 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 22884.3225806452 &  &  \tabularnewline
Midmean - Closest Observation & 22738.09375 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 22884.3225806452 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 22884.3225806452 &  &  \tabularnewline
Number of observations & 61 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=35559&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]23169.1147540984[/C][C]774.361989135368[/C][C]29.9202634932642[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]22332.1243025103[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]21416.6089441899[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]23932.9494191928[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]23159.2622950820[/C][C]759.665517387032[/C][C]30.4861307575751[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]23145.0983606557[/C][C]724.061047038682[/C][C]31.965672584261[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]23193.8360655738[/C][C]711.190452453758[/C][C]32.6126932463029[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]23306.5573770492[/C][C]687.568655498755[/C][C]33.8970620470516[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]23278.3606557377[/C][C]680.984473007229[/C][C]34.1833941571978[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]23407.6065573771[/C][C]642.228917224616[/C][C]36.4474503243061[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]23359.5245901639[/C][C]630.583814238472[/C][C]37.0442819221013[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]23309.0327868852[/C][C]614.019819978432[/C][C]37.9613687188534[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]23320.0983606557[/C][C]607.69189809323[/C][C]38.3748712691873[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]23288.7868852459[/C][C]597.318292609274[/C][C]38.9889062052883[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]23278.6885245902[/C][C]584.70202889224[/C][C]39.8129087540423[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]23261.1803278689[/C][C]579.412190600527[/C][C]40.146170041331[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]23232.6229508197[/C][C]563.813359597985[/C][C]41.2062299612503[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]22998.7540983607[/C][C]521.164046342279[/C][C]44.1295869501636[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]22853.6721311475[/C][C]477.742516288397[/C][C]47.8367977560355[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]22876.7540983607[/C][C]464.68161181429[/C][C]49.2310294118187[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]22830.2131147541[/C][C]454.289388712291[/C][C]50.2547796228911[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]22930.5409836066[/C][C]430.816085146132[/C][C]53.2258236732933[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]23033.3278688525[/C][C]399.44787353652[/C][C]57.6629127223194[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]23043.8196721311[/C][C]391.521117595979[/C][C]58.8571564507809[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]23178.1525423729[/C][C]730.903991730609[/C][C]31.7116239678654[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]23198.3684210526[/C][C]695.49332873906[/C][C]33.3552709457496[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]23227.9090909091[/C][C]675.813446392619[/C][C]34.3702973281989[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]23240.9811320755[/C][C]657.525260123119[/C][C]35.3461418770797[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]23221.3725490196[/C][C]643.750477760057[/C][C]36.0720082567066[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]23207.1836734694[/C][C]628.342035843578[/C][C]36.9339982837734[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]23163.8297872340[/C][C]620.074573503837[/C][C]37.3565225491232[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]23125.9333333333[/C][C]612.051045438387[/C][C]37.784321268121[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]23093.4651162791[/C][C]605.277716796628[/C][C]38.1535028887218[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]23056[/C][C]597.0360000585[/C][C]38.6174368006969[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]23019.5897435897[/C][C]587.816182719222[/C][C]39.1612045063165[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]22980.7567567568[/C][C]577.639278221151[/C][C]39.7839233293248[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]22940.0285714286[/C][C]564.071141716332[/C][C]40.6686796662343[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]22898.4242424242[/C][C]548.585710946213[/C][C]41.7408324451771[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]22884.3225806452[/C][C]538.258912370659[/C][C]42.5154550248978[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]22888.6206896552[/C][C]534.188843229637[/C][C]42.8474330374883[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]22890.2962962963[/C][C]529.470521993851[/C][C]43.2324281436807[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]22898.92[/C][C]522.69715553081[/C][C]43.8091536517846[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]22894.2608695652[/C][C]517.082505084815[/C][C]44.2758373072590[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]22873[/C][C]515.484968142576[/C][C]44.3718079353842[/C][/ROW]
[ROW][C]Median[/C][C]22679[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]22902.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]22741.6333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]22884.3225806452[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]22884.3225806452[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]22884.3225806452[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]22884.3225806452[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]22738.09375[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]22884.3225806452[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]22884.3225806452[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]61[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=35559&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=35559&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 Mean23169.1147540984774.36198913536829.9202634932642
Geometric Mean22332.1243025103
Harmonic Mean21416.6089441899
Quadratic Mean23932.9494191928
Winsorized Mean ( 1 / 20 )23159.2622950820759.66551738703230.4861307575751
Winsorized Mean ( 2 / 20 )23145.0983606557724.06104703868231.965672584261
Winsorized Mean ( 3 / 20 )23193.8360655738711.19045245375832.6126932463029
Winsorized Mean ( 4 / 20 )23306.5573770492687.56865549875533.8970620470516
Winsorized Mean ( 5 / 20 )23278.3606557377680.98447300722934.1833941571978
Winsorized Mean ( 6 / 20 )23407.6065573771642.22891722461636.4474503243061
Winsorized Mean ( 7 / 20 )23359.5245901639630.58381423847237.0442819221013
Winsorized Mean ( 8 / 20 )23309.0327868852614.01981997843237.9613687188534
Winsorized Mean ( 9 / 20 )23320.0983606557607.6918980932338.3748712691873
Winsorized Mean ( 10 / 20 )23288.7868852459597.31829260927438.9889062052883
Winsorized Mean ( 11 / 20 )23278.6885245902584.7020288922439.8129087540423
Winsorized Mean ( 12 / 20 )23261.1803278689579.41219060052740.146170041331
Winsorized Mean ( 13 / 20 )23232.6229508197563.81335959798541.2062299612503
Winsorized Mean ( 14 / 20 )22998.7540983607521.16404634227944.1295869501636
Winsorized Mean ( 15 / 20 )22853.6721311475477.74251628839747.8367977560355
Winsorized Mean ( 16 / 20 )22876.7540983607464.6816118142949.2310294118187
Winsorized Mean ( 17 / 20 )22830.2131147541454.28938871229150.2547796228911
Winsorized Mean ( 18 / 20 )22930.5409836066430.81608514613253.2258236732933
Winsorized Mean ( 19 / 20 )23033.3278688525399.4478735365257.6629127223194
Winsorized Mean ( 20 / 20 )23043.8196721311391.52111759597958.8571564507809
Trimmed Mean ( 1 / 20 )23178.1525423729730.90399173060931.7116239678654
Trimmed Mean ( 2 / 20 )23198.3684210526695.4933287390633.3552709457496
Trimmed Mean ( 3 / 20 )23227.9090909091675.81344639261934.3702973281989
Trimmed Mean ( 4 / 20 )23240.9811320755657.52526012311935.3461418770797
Trimmed Mean ( 5 / 20 )23221.3725490196643.75047776005736.0720082567066
Trimmed Mean ( 6 / 20 )23207.1836734694628.34203584357836.9339982837734
Trimmed Mean ( 7 / 20 )23163.8297872340620.07457350383737.3565225491232
Trimmed Mean ( 8 / 20 )23125.9333333333612.05104543838737.784321268121
Trimmed Mean ( 9 / 20 )23093.4651162791605.27771679662838.1535028887218
Trimmed Mean ( 10 / 20 )23056597.036000058538.6174368006969
Trimmed Mean ( 11 / 20 )23019.5897435897587.81618271922239.1612045063165
Trimmed Mean ( 12 / 20 )22980.7567567568577.63927822115139.7839233293248
Trimmed Mean ( 13 / 20 )22940.0285714286564.07114171633240.6686796662343
Trimmed Mean ( 14 / 20 )22898.4242424242548.58571094621341.7408324451771
Trimmed Mean ( 15 / 20 )22884.3225806452538.25891237065942.5154550248978
Trimmed Mean ( 16 / 20 )22888.6206896552534.18884322963742.8474330374883
Trimmed Mean ( 17 / 20 )22890.2962962963529.47052199385143.2324281436807
Trimmed Mean ( 18 / 20 )22898.92522.6971555308143.8091536517846
Trimmed Mean ( 19 / 20 )22894.2608695652517.08250508481544.2758373072590
Trimmed Mean ( 20 / 20 )22873515.48496814257644.3718079353842
Median22679
Midrange22902.5
Midmean - Weighted Average at Xnp22741.6333333333
Midmean - Weighted Average at X(n+1)p22884.3225806452
Midmean - Empirical Distribution Function22884.3225806452
Midmean - Empirical Distribution Function - Averaging22884.3225806452
Midmean - Empirical Distribution Function - Interpolation22884.3225806452
Midmean - Closest Observation22738.09375
Midmean - True Basic - Statistics Graphics Toolkit22884.3225806452
Midmean - MS Excel (old versions)22884.3225806452
Number of observations61



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')