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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 computationFri, 25 Dec 2009 11:16:51 -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/2009/Dec/25/t12617650543rzlxq0oxmd5gg3.htm/, Retrieved Sat, 04 May 2024 09:55:20 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=70722, Retrieved Sat, 04 May 2024 09:55:20 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact154
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Univariate Data Series] [Paper: aantal nie...] [2009-12-24 09:31:37] [005293453b571dbccb80b45226e44173]
- RM      [Central Tendency] [central tendency ...] [2009-12-25 18:16:51] [a315839f8c359622c3a1e6ed387dd5cd] [Current]
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Dataseries X:
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
11509
25447
24090
27786
26195
20516
22759
19028
16971




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 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 & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=70722&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=70722&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=70722&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 time2 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean22765.7743.20908400151630.631622365845
Geometric Mean21970.2709614870
Harmonic Mean21072.4065342179
Quadratic Mean23470.5415638413
Winsorized Mean ( 1 / 20 )22745.3833333333726.4299971296331.311184041419
Winsorized Mean ( 2 / 20 )22771.6833333333718.88224933807631.676513579659
Winsorized Mean ( 3 / 20 )22814.7333333333699.27071609495232.6264675585748
Winsorized Mean ( 4 / 20 )22856.5333333333676.29651900596533.7966153765339
Winsorized Mean ( 5 / 20 )22964.2636.969426400936.0522798240973
Winsorized Mean ( 6 / 20 )23050.1600.240944418138.4014123234225
Winsorized Mean ( 7 / 20 )23081.0166666667591.09206529635439.0480908504407
Winsorized Mean ( 8 / 20 )23051.4166666667582.66178194745639.5622595832885
Winsorized Mean ( 9 / 20 )23076.9166666667565.90718344776140.7786247314829
Winsorized Mean ( 10 / 20 )23038.75548.17333933494742.0282205405155
Winsorized Mean ( 11 / 20 )22832.8666666667500.01256903222745.664585414042
Winsorized Mean ( 12 / 20 )22718.2666666667478.25711938355447.5022027815273
Winsorized Mean ( 13 / 20 )22751.4166666667464.76474778779548.9525437868508
Winsorized Mean ( 14 / 20 )22751.4166666667449.65865477548750.5970838658190
Winsorized Mean ( 15 / 20 )22737.1666666667444.25905760451751.1799732103774
Winsorized Mean ( 16 / 20 )22767.3424.76466684905653.5997971980342
Winsorized Mean ( 17 / 20 )22787.7415.89049467296354.7925482594142
Winsorized Mean ( 18 / 20 )22856.1380.68164086926460.0399324427872
Winsorized Mean ( 19 / 20 )22781.6833333333360.56002775004263.1841623584706
Winsorized Mean ( 20 / 20 )22780.35357.61008010493163.7016439618137
Trimmed Mean ( 1 / 20 )22794.2931034483703.87963519344832.3837939950965
Trimmed Mean ( 2 / 20 )22846.6964285714676.0118202492133.7962972602299
Trimmed Mean ( 3 / 20 )22888.3703703704646.53002527517435.4018676249857
Trimmed Mean ( 4 / 20 )22916.6923076923619.54895500347636.9893163770468
Trimmed Mean ( 5 / 20 )22934.74595.07619392779638.5408460866489
Trimmed Mean ( 6 / 20 )22927.375578.05241119909339.6631422269137
Trimmed Mean ( 7 / 20 )22900.6956521739567.52474748191440.3518890652494
Trimmed Mean ( 8 / 20 )22865.5681818182556.02366160061441.123372548563
Trimmed Mean ( 9 / 20 )22832.3809523810542.8878388024642.0572709875878
Trimmed Mean ( 10 / 20 )22791.625529.5625452606643.038589499908
Trimmed Mean ( 11 / 20 )22752.6052631579516.05094130798444.0898435443003
Trimmed Mean ( 12 / 20 )22740.4444444444510.18972575015944.5725252718642
Trimmed Mean ( 13 / 20 )22743.7058823529506.48430939901844.9050552214343
Trimmed Mean ( 14 / 20 )22742.59375503.15765594156645.1997370634091
Trimmed Mean ( 15 / 20 )22741.3333333333500.52239224044745.4351966782908
Trimmed Mean ( 16 / 20 )22741.9285714286495.891255596645.8607170720686
Trimmed Mean ( 17 / 20 )22738.2692307692492.40994977666046.1775178204309
Trimmed Mean ( 18 / 20 )22731486.87007239232246.6880206628993
Trimmed Mean ( 19 / 20 )22712.0454545455486.96434208716446.6400586071662
Trimmed Mean ( 20 / 20 )22701.05489.58278948831346.3681536349061
Median22638.5
Midrange21936.5
Midmean - Weighted Average at Xnp22610.5806451613
Midmean - Weighted Average at X(n+1)p22741.3333333333
Midmean - Empirical Distribution Function22610.5806451613
Midmean - Empirical Distribution Function - Averaging22741.3333333333
Midmean - Empirical Distribution Function - Interpolation22741.3333333333
Midmean - Closest Observation22610.5806451613
Midmean - True Basic - Statistics Graphics Toolkit22741.3333333333
Midmean - MS Excel (old versions)22742.59375
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 22765.7 & 743.209084001516 & 30.631622365845 \tabularnewline
Geometric Mean & 21970.2709614870 &  &  \tabularnewline
Harmonic Mean & 21072.4065342179 &  &  \tabularnewline
Quadratic Mean & 23470.5415638413 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 22745.3833333333 & 726.42999712963 & 31.311184041419 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 22771.6833333333 & 718.882249338076 & 31.676513579659 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 22814.7333333333 & 699.270716094952 & 32.6264675585748 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 22856.5333333333 & 676.296519005965 & 33.7966153765339 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 22964.2 & 636.9694264009 & 36.0522798240973 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 23050.1 & 600.2409444181 & 38.4014123234225 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 23081.0166666667 & 591.092065296354 & 39.0480908504407 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 23051.4166666667 & 582.661781947456 & 39.5622595832885 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 23076.9166666667 & 565.907183447761 & 40.7786247314829 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 23038.75 & 548.173339334947 & 42.0282205405155 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 22832.8666666667 & 500.012569032227 & 45.664585414042 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 22718.2666666667 & 478.257119383554 & 47.5022027815273 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 22751.4166666667 & 464.764747787795 & 48.9525437868508 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 22751.4166666667 & 449.658654775487 & 50.5970838658190 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 22737.1666666667 & 444.259057604517 & 51.1799732103774 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 22767.3 & 424.764666849056 & 53.5997971980342 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 22787.7 & 415.890494672963 & 54.7925482594142 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 22856.1 & 380.681640869264 & 60.0399324427872 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 22781.6833333333 & 360.560027750042 & 63.1841623584706 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 22780.35 & 357.610080104931 & 63.7016439618137 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 22794.2931034483 & 703.879635193448 & 32.3837939950965 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 22846.6964285714 & 676.01182024921 & 33.7962972602299 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 22888.3703703704 & 646.530025275174 & 35.4018676249857 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 22916.6923076923 & 619.548955003476 & 36.9893163770468 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 22934.74 & 595.076193927796 & 38.5408460866489 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 22927.375 & 578.052411199093 & 39.6631422269137 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 22900.6956521739 & 567.524747481914 & 40.3518890652494 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 22865.5681818182 & 556.023661600614 & 41.123372548563 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 22832.3809523810 & 542.88783880246 & 42.0572709875878 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 22791.625 & 529.56254526066 & 43.038589499908 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 22752.6052631579 & 516.050941307984 & 44.0898435443003 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 22740.4444444444 & 510.189725750159 & 44.5725252718642 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 22743.7058823529 & 506.484309399018 & 44.9050552214343 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 22742.59375 & 503.157655941566 & 45.1997370634091 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 22741.3333333333 & 500.522392240447 & 45.4351966782908 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 22741.9285714286 & 495.8912555966 & 45.8607170720686 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 22738.2692307692 & 492.409949776660 & 46.1775178204309 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 22731 & 486.870072392322 & 46.6880206628993 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 22712.0454545455 & 486.964342087164 & 46.6400586071662 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 22701.05 & 489.582789488313 & 46.3681536349061 \tabularnewline
Median & 22638.5 &  &  \tabularnewline
Midrange & 21936.5 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 22610.5806451613 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 22741.3333333333 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 22610.5806451613 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 22741.3333333333 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 22741.3333333333 &  &  \tabularnewline
Midmean - Closest Observation & 22610.5806451613 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 22741.3333333333 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 22742.59375 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=70722&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]22765.7[/C][C]743.209084001516[/C][C]30.631622365845[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]21970.2709614870[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]21072.4065342179[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]23470.5415638413[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]22745.3833333333[/C][C]726.42999712963[/C][C]31.311184041419[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]22771.6833333333[/C][C]718.882249338076[/C][C]31.676513579659[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]22814.7333333333[/C][C]699.270716094952[/C][C]32.6264675585748[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]22856.5333333333[/C][C]676.296519005965[/C][C]33.7966153765339[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]22964.2[/C][C]636.9694264009[/C][C]36.0522798240973[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]23050.1[/C][C]600.2409444181[/C][C]38.4014123234225[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]23081.0166666667[/C][C]591.092065296354[/C][C]39.0480908504407[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]23051.4166666667[/C][C]582.661781947456[/C][C]39.5622595832885[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]23076.9166666667[/C][C]565.907183447761[/C][C]40.7786247314829[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]23038.75[/C][C]548.173339334947[/C][C]42.0282205405155[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]22832.8666666667[/C][C]500.012569032227[/C][C]45.664585414042[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]22718.2666666667[/C][C]478.257119383554[/C][C]47.5022027815273[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]22751.4166666667[/C][C]464.764747787795[/C][C]48.9525437868508[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]22751.4166666667[/C][C]449.658654775487[/C][C]50.5970838658190[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]22737.1666666667[/C][C]444.259057604517[/C][C]51.1799732103774[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]22767.3[/C][C]424.764666849056[/C][C]53.5997971980342[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]22787.7[/C][C]415.890494672963[/C][C]54.7925482594142[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]22856.1[/C][C]380.681640869264[/C][C]60.0399324427872[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]22781.6833333333[/C][C]360.560027750042[/C][C]63.1841623584706[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]22780.35[/C][C]357.610080104931[/C][C]63.7016439618137[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]22794.2931034483[/C][C]703.879635193448[/C][C]32.3837939950965[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]22846.6964285714[/C][C]676.01182024921[/C][C]33.7962972602299[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]22888.3703703704[/C][C]646.530025275174[/C][C]35.4018676249857[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]22916.6923076923[/C][C]619.548955003476[/C][C]36.9893163770468[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]22934.74[/C][C]595.076193927796[/C][C]38.5408460866489[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]22927.375[/C][C]578.052411199093[/C][C]39.6631422269137[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]22900.6956521739[/C][C]567.524747481914[/C][C]40.3518890652494[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]22865.5681818182[/C][C]556.023661600614[/C][C]41.123372548563[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]22832.3809523810[/C][C]542.88783880246[/C][C]42.0572709875878[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]22791.625[/C][C]529.56254526066[/C][C]43.038589499908[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]22752.6052631579[/C][C]516.050941307984[/C][C]44.0898435443003[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]22740.4444444444[/C][C]510.189725750159[/C][C]44.5725252718642[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]22743.7058823529[/C][C]506.484309399018[/C][C]44.9050552214343[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]22742.59375[/C][C]503.157655941566[/C][C]45.1997370634091[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]22741.3333333333[/C][C]500.522392240447[/C][C]45.4351966782908[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]22741.9285714286[/C][C]495.8912555966[/C][C]45.8607170720686[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]22738.2692307692[/C][C]492.409949776660[/C][C]46.1775178204309[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]22731[/C][C]486.870072392322[/C][C]46.6880206628993[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]22712.0454545455[/C][C]486.964342087164[/C][C]46.6400586071662[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]22701.05[/C][C]489.582789488313[/C][C]46.3681536349061[/C][/ROW]
[ROW][C]Median[/C][C]22638.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]21936.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]22610.5806451613[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]22741.3333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]22610.5806451613[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]22741.3333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]22741.3333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]22610.5806451613[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]22741.3333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]22742.59375[/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=70722&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=70722&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 Mean22765.7743.20908400151630.631622365845
Geometric Mean21970.2709614870
Harmonic Mean21072.4065342179
Quadratic Mean23470.5415638413
Winsorized Mean ( 1 / 20 )22745.3833333333726.4299971296331.311184041419
Winsorized Mean ( 2 / 20 )22771.6833333333718.88224933807631.676513579659
Winsorized Mean ( 3 / 20 )22814.7333333333699.27071609495232.6264675585748
Winsorized Mean ( 4 / 20 )22856.5333333333676.29651900596533.7966153765339
Winsorized Mean ( 5 / 20 )22964.2636.969426400936.0522798240973
Winsorized Mean ( 6 / 20 )23050.1600.240944418138.4014123234225
Winsorized Mean ( 7 / 20 )23081.0166666667591.09206529635439.0480908504407
Winsorized Mean ( 8 / 20 )23051.4166666667582.66178194745639.5622595832885
Winsorized Mean ( 9 / 20 )23076.9166666667565.90718344776140.7786247314829
Winsorized Mean ( 10 / 20 )23038.75548.17333933494742.0282205405155
Winsorized Mean ( 11 / 20 )22832.8666666667500.01256903222745.664585414042
Winsorized Mean ( 12 / 20 )22718.2666666667478.25711938355447.5022027815273
Winsorized Mean ( 13 / 20 )22751.4166666667464.76474778779548.9525437868508
Winsorized Mean ( 14 / 20 )22751.4166666667449.65865477548750.5970838658190
Winsorized Mean ( 15 / 20 )22737.1666666667444.25905760451751.1799732103774
Winsorized Mean ( 16 / 20 )22767.3424.76466684905653.5997971980342
Winsorized Mean ( 17 / 20 )22787.7415.89049467296354.7925482594142
Winsorized Mean ( 18 / 20 )22856.1380.68164086926460.0399324427872
Winsorized Mean ( 19 / 20 )22781.6833333333360.56002775004263.1841623584706
Winsorized Mean ( 20 / 20 )22780.35357.61008010493163.7016439618137
Trimmed Mean ( 1 / 20 )22794.2931034483703.87963519344832.3837939950965
Trimmed Mean ( 2 / 20 )22846.6964285714676.0118202492133.7962972602299
Trimmed Mean ( 3 / 20 )22888.3703703704646.53002527517435.4018676249857
Trimmed Mean ( 4 / 20 )22916.6923076923619.54895500347636.9893163770468
Trimmed Mean ( 5 / 20 )22934.74595.07619392779638.5408460866489
Trimmed Mean ( 6 / 20 )22927.375578.05241119909339.6631422269137
Trimmed Mean ( 7 / 20 )22900.6956521739567.52474748191440.3518890652494
Trimmed Mean ( 8 / 20 )22865.5681818182556.02366160061441.123372548563
Trimmed Mean ( 9 / 20 )22832.3809523810542.8878388024642.0572709875878
Trimmed Mean ( 10 / 20 )22791.625529.5625452606643.038589499908
Trimmed Mean ( 11 / 20 )22752.6052631579516.05094130798444.0898435443003
Trimmed Mean ( 12 / 20 )22740.4444444444510.18972575015944.5725252718642
Trimmed Mean ( 13 / 20 )22743.7058823529506.48430939901844.9050552214343
Trimmed Mean ( 14 / 20 )22742.59375503.15765594156645.1997370634091
Trimmed Mean ( 15 / 20 )22741.3333333333500.52239224044745.4351966782908
Trimmed Mean ( 16 / 20 )22741.9285714286495.891255596645.8607170720686
Trimmed Mean ( 17 / 20 )22738.2692307692492.40994977666046.1775178204309
Trimmed Mean ( 18 / 20 )22731486.87007239232246.6880206628993
Trimmed Mean ( 19 / 20 )22712.0454545455486.96434208716446.6400586071662
Trimmed Mean ( 20 / 20 )22701.05489.58278948831346.3681536349061
Median22638.5
Midrange21936.5
Midmean - Weighted Average at Xnp22610.5806451613
Midmean - Weighted Average at X(n+1)p22741.3333333333
Midmean - Empirical Distribution Function22610.5806451613
Midmean - Empirical Distribution Function - Averaging22741.3333333333
Midmean - Empirical Distribution Function - Interpolation22741.3333333333
Midmean - Closest Observation22610.5806451613
Midmean - True Basic - Statistics Graphics Toolkit22741.3333333333
Midmean - MS Excel (old versions)22742.59375
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')