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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 computationThu, 22 Oct 2009 09:25:32 -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/22/t1256225207uhge80nu062bwue.htm/, Retrieved Thu, 02 May 2024 18:08:22 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=49758, Retrieved Thu, 02 May 2024 18:08:22 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact119
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Univariate Data Series] [workshop 2] [2009-10-12 16:55:02] [3af9fa3d2c04a43d660a9a466bdfbaa0]
- RMPD    [Central Tendency] [] [2009-10-22 15:25:32] [82bf023f1e4d9556a54030fcde33aa09] [Current]
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Dataseries X:
32905
32481
30946
31924
31899
30889
30334
29438
28549
28749
32858
34780
32145
31682
29736
30629
28593
28753
27538
28325
27873
27836
30777
31189
29923
26950
25327
25190
25443
23883
22545
21650
20923
20882
25011
25335
22251
21293
20292
21561
21262
20242
20205
19631
18357
19011
22883
23170
21538
21194
20915
23212
24414
24980
25453
25159
24708
25956
29371
30068




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

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=49758&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=49758&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=49758&T=0

As an alternative you can also use a QR Code:  

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

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







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean26183.6562.30046665662646.5651400854861
Geometric Mean25821.4584429103
Harmonic Mean25456.9510206701
Quadratic Mean26537.4383849183
Winsorized Mean ( 1 / 20 )26163.25552.53100872923447.3516410602418
Winsorized Mean ( 2 / 20 )26182.35547.84496282338947.7915318689176
Winsorized Mean ( 3 / 20 )26192.2538.41694867590248.6466855555216
Winsorized Mean ( 4 / 20 )26172.2666666667533.60972633345549.0475817345044
Winsorized Mean ( 5 / 20 )26158.0166666667529.37894296007849.4126504548923
Winsorized Mean ( 6 / 20 )26214.5166666667518.22615010307950.5850904309873
Winsorized Mean ( 7 / 20 )26193.05512.90494456674651.0680395606742
Winsorized Mean ( 8 / 20 )26128.3833333333501.12715217862552.1392289756033
Winsorized Mean ( 9 / 20 )26132.5833333333487.89266978192153.5621560885802
Winsorized Mean ( 10 / 20 )26134.4166666667484.36974326167653.9555102898898
Winsorized Mean ( 11 / 20 )26119.5666666667480.00434694751754.4152710965398
Winsorized Mean ( 12 / 20 )26138.9666666667466.88894744543355.9854046870999
Winsorized Mean ( 13 / 20 )26080.0333333333455.78757935609957.219710484821
Winsorized Mean ( 14 / 20 )26038.7333333333442.59824972443558.8315325457008
Winsorized Mean ( 15 / 20 )26152.7333333333412.29666234130263.4318337306449
Winsorized Mean ( 16 / 20 )26181.2666666667392.14903763911166.7635622014733
Winsorized Mean ( 17 / 20 )26192.6364.38317449232971.8820237418821
Winsorized Mean ( 18 / 20 )26258.6348.24144101892675.4034325241979
Winsorized Mean ( 19 / 20 )26076.2317.37630162971982.1617741025383
Winsorized Mean ( 20 / 20 )26298.5333333333283.89537886228492.634594612724
Trimmed Mean ( 1 / 20 )26170.3275862069545.59769441854247.966345631459
Trimmed Mean ( 2 / 20 )26177.9107142857536.79684981558848.7668858773648
Trimmed Mean ( 3 / 20 )26175.4444444444528.70723013481949.508391322301
Trimmed Mean ( 4 / 20 )26169522.71563059427650.0635497933139
Trimmed Mean ( 5 / 20 )26168.02516.5696629947750.6572915031306
Trimmed Mean ( 6 / 20 )26170.5208333333509.70593401996351.3443518833123
Trimmed Mean ( 7 / 20 )26160.9565217391503.7640828460551.9309681109876
Trimmed Mean ( 8 / 20 )26154.7045454545496.98737183001452.6264972269764
Trimmed Mean ( 9 / 20 )26159.4047619048490.68056279343353.3124944118021
Trimmed Mean ( 10 / 20 )26163.875485.05481475531053.9400377114051
Trimmed Mean ( 11 / 20 )26168.5263157895477.57533010743954.7945521178877
Trimmed Mean ( 12 / 20 )26175.9444444444467.74295604283555.962241881516
Trimmed Mean ( 13 / 20 )26181.3823529412456.99742568753857.2899996396087
Trimmed Mean ( 14 / 20 )26196444.19069893023358.9746702555662
Trimmed Mean ( 15 / 20 )26218.4666666667428.91642605104161.1272151734908
Trimmed Mean ( 16 / 20 )26227.8571428571415.61209947926263.106577444976
Trimmed Mean ( 17 / 20 )26234.5769230769401.37223533993465.3622114665159
Trimmed Mean ( 18 / 20 )26240.75388.27676821036367.5825909465258
Trimmed Mean ( 19 / 20 )26238.0454545455372.16679496999370.5007695720435
Trimmed Mean ( 20 / 20 )26263.6357.23994884759473.5180936082952
Median25448
Midrange26568.5
Midmean - Weighted Average at Xnp26071.0967741935
Midmean - Weighted Average at X(n+1)p26218.4666666667
Midmean - Empirical Distribution Function26071.0967741935
Midmean - Empirical Distribution Function - Averaging26218.4666666667
Midmean - Empirical Distribution Function - Interpolation26218.4666666667
Midmean - Closest Observation26071.0967741935
Midmean - True Basic - Statistics Graphics Toolkit26218.4666666667
Midmean - MS Excel (old versions)26196
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 26183.6 & 562.300466656626 & 46.5651400854861 \tabularnewline
Geometric Mean & 25821.4584429103 &  &  \tabularnewline
Harmonic Mean & 25456.9510206701 &  &  \tabularnewline
Quadratic Mean & 26537.4383849183 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 26163.25 & 552.531008729234 & 47.3516410602418 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 26182.35 & 547.844962823389 & 47.7915318689176 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 26192.2 & 538.416948675902 & 48.6466855555216 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 26172.2666666667 & 533.609726333455 & 49.0475817345044 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 26158.0166666667 & 529.378942960078 & 49.4126504548923 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 26214.5166666667 & 518.226150103079 & 50.5850904309873 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 26193.05 & 512.904944566746 & 51.0680395606742 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 26128.3833333333 & 501.127152178625 & 52.1392289756033 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 26132.5833333333 & 487.892669781921 & 53.5621560885802 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 26134.4166666667 & 484.369743261676 & 53.9555102898898 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 26119.5666666667 & 480.004346947517 & 54.4152710965398 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 26138.9666666667 & 466.888947445433 & 55.9854046870999 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 26080.0333333333 & 455.787579356099 & 57.219710484821 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 26038.7333333333 & 442.598249724435 & 58.8315325457008 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 26152.7333333333 & 412.296662341302 & 63.4318337306449 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 26181.2666666667 & 392.149037639111 & 66.7635622014733 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 26192.6 & 364.383174492329 & 71.8820237418821 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 26258.6 & 348.241441018926 & 75.4034325241979 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 26076.2 & 317.376301629719 & 82.1617741025383 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 26298.5333333333 & 283.895378862284 & 92.634594612724 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 26170.3275862069 & 545.597694418542 & 47.966345631459 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 26177.9107142857 & 536.796849815588 & 48.7668858773648 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 26175.4444444444 & 528.707230134819 & 49.508391322301 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 26169 & 522.715630594276 & 50.0635497933139 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 26168.02 & 516.56966299477 & 50.6572915031306 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 26170.5208333333 & 509.705934019963 & 51.3443518833123 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 26160.9565217391 & 503.76408284605 & 51.9309681109876 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 26154.7045454545 & 496.987371830014 & 52.6264972269764 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 26159.4047619048 & 490.680562793433 & 53.3124944118021 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 26163.875 & 485.054814755310 & 53.9400377114051 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 26168.5263157895 & 477.575330107439 & 54.7945521178877 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 26175.9444444444 & 467.742956042835 & 55.962241881516 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 26181.3823529412 & 456.997425687538 & 57.2899996396087 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 26196 & 444.190698930233 & 58.9746702555662 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 26218.4666666667 & 428.916426051041 & 61.1272151734908 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 26227.8571428571 & 415.612099479262 & 63.106577444976 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 26234.5769230769 & 401.372235339934 & 65.3622114665159 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 26240.75 & 388.276768210363 & 67.5825909465258 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 26238.0454545455 & 372.166794969993 & 70.5007695720435 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 26263.6 & 357.239948847594 & 73.5180936082952 \tabularnewline
Median & 25448 &  &  \tabularnewline
Midrange & 26568.5 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 26071.0967741935 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 26218.4666666667 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 26071.0967741935 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 26218.4666666667 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 26218.4666666667 &  &  \tabularnewline
Midmean - Closest Observation & 26071.0967741935 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 26218.4666666667 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 26196 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=49758&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]26183.6[/C][C]562.300466656626[/C][C]46.5651400854861[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]25821.4584429103[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]25456.9510206701[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]26537.4383849183[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]26163.25[/C][C]552.531008729234[/C][C]47.3516410602418[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]26182.35[/C][C]547.844962823389[/C][C]47.7915318689176[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]26192.2[/C][C]538.416948675902[/C][C]48.6466855555216[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]26172.2666666667[/C][C]533.609726333455[/C][C]49.0475817345044[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]26158.0166666667[/C][C]529.378942960078[/C][C]49.4126504548923[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]26214.5166666667[/C][C]518.226150103079[/C][C]50.5850904309873[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]26193.05[/C][C]512.904944566746[/C][C]51.0680395606742[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]26128.3833333333[/C][C]501.127152178625[/C][C]52.1392289756033[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]26132.5833333333[/C][C]487.892669781921[/C][C]53.5621560885802[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]26134.4166666667[/C][C]484.369743261676[/C][C]53.9555102898898[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]26119.5666666667[/C][C]480.004346947517[/C][C]54.4152710965398[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]26138.9666666667[/C][C]466.888947445433[/C][C]55.9854046870999[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]26080.0333333333[/C][C]455.787579356099[/C][C]57.219710484821[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]26038.7333333333[/C][C]442.598249724435[/C][C]58.8315325457008[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]26152.7333333333[/C][C]412.296662341302[/C][C]63.4318337306449[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]26181.2666666667[/C][C]392.149037639111[/C][C]66.7635622014733[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]26192.6[/C][C]364.383174492329[/C][C]71.8820237418821[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]26258.6[/C][C]348.241441018926[/C][C]75.4034325241979[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]26076.2[/C][C]317.376301629719[/C][C]82.1617741025383[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]26298.5333333333[/C][C]283.895378862284[/C][C]92.634594612724[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]26170.3275862069[/C][C]545.597694418542[/C][C]47.966345631459[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]26177.9107142857[/C][C]536.796849815588[/C][C]48.7668858773648[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]26175.4444444444[/C][C]528.707230134819[/C][C]49.508391322301[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]26169[/C][C]522.715630594276[/C][C]50.0635497933139[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]26168.02[/C][C]516.56966299477[/C][C]50.6572915031306[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]26170.5208333333[/C][C]509.705934019963[/C][C]51.3443518833123[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]26160.9565217391[/C][C]503.76408284605[/C][C]51.9309681109876[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]26154.7045454545[/C][C]496.987371830014[/C][C]52.6264972269764[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]26159.4047619048[/C][C]490.680562793433[/C][C]53.3124944118021[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]26163.875[/C][C]485.054814755310[/C][C]53.9400377114051[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]26168.5263157895[/C][C]477.575330107439[/C][C]54.7945521178877[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]26175.9444444444[/C][C]467.742956042835[/C][C]55.962241881516[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]26181.3823529412[/C][C]456.997425687538[/C][C]57.2899996396087[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]26196[/C][C]444.190698930233[/C][C]58.9746702555662[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]26218.4666666667[/C][C]428.916426051041[/C][C]61.1272151734908[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]26227.8571428571[/C][C]415.612099479262[/C][C]63.106577444976[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]26234.5769230769[/C][C]401.372235339934[/C][C]65.3622114665159[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]26240.75[/C][C]388.276768210363[/C][C]67.5825909465258[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]26238.0454545455[/C][C]372.166794969993[/C][C]70.5007695720435[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]26263.6[/C][C]357.239948847594[/C][C]73.5180936082952[/C][/ROW]
[ROW][C]Median[/C][C]25448[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]26568.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]26071.0967741935[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]26218.4666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]26071.0967741935[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]26218.4666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]26218.4666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]26071.0967741935[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]26218.4666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]26196[/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=49758&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=49758&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 Mean26183.6562.30046665662646.5651400854861
Geometric Mean25821.4584429103
Harmonic Mean25456.9510206701
Quadratic Mean26537.4383849183
Winsorized Mean ( 1 / 20 )26163.25552.53100872923447.3516410602418
Winsorized Mean ( 2 / 20 )26182.35547.84496282338947.7915318689176
Winsorized Mean ( 3 / 20 )26192.2538.41694867590248.6466855555216
Winsorized Mean ( 4 / 20 )26172.2666666667533.60972633345549.0475817345044
Winsorized Mean ( 5 / 20 )26158.0166666667529.37894296007849.4126504548923
Winsorized Mean ( 6 / 20 )26214.5166666667518.22615010307950.5850904309873
Winsorized Mean ( 7 / 20 )26193.05512.90494456674651.0680395606742
Winsorized Mean ( 8 / 20 )26128.3833333333501.12715217862552.1392289756033
Winsorized Mean ( 9 / 20 )26132.5833333333487.89266978192153.5621560885802
Winsorized Mean ( 10 / 20 )26134.4166666667484.36974326167653.9555102898898
Winsorized Mean ( 11 / 20 )26119.5666666667480.00434694751754.4152710965398
Winsorized Mean ( 12 / 20 )26138.9666666667466.88894744543355.9854046870999
Winsorized Mean ( 13 / 20 )26080.0333333333455.78757935609957.219710484821
Winsorized Mean ( 14 / 20 )26038.7333333333442.59824972443558.8315325457008
Winsorized Mean ( 15 / 20 )26152.7333333333412.29666234130263.4318337306449
Winsorized Mean ( 16 / 20 )26181.2666666667392.14903763911166.7635622014733
Winsorized Mean ( 17 / 20 )26192.6364.38317449232971.8820237418821
Winsorized Mean ( 18 / 20 )26258.6348.24144101892675.4034325241979
Winsorized Mean ( 19 / 20 )26076.2317.37630162971982.1617741025383
Winsorized Mean ( 20 / 20 )26298.5333333333283.89537886228492.634594612724
Trimmed Mean ( 1 / 20 )26170.3275862069545.59769441854247.966345631459
Trimmed Mean ( 2 / 20 )26177.9107142857536.79684981558848.7668858773648
Trimmed Mean ( 3 / 20 )26175.4444444444528.70723013481949.508391322301
Trimmed Mean ( 4 / 20 )26169522.71563059427650.0635497933139
Trimmed Mean ( 5 / 20 )26168.02516.5696629947750.6572915031306
Trimmed Mean ( 6 / 20 )26170.5208333333509.70593401996351.3443518833123
Trimmed Mean ( 7 / 20 )26160.9565217391503.7640828460551.9309681109876
Trimmed Mean ( 8 / 20 )26154.7045454545496.98737183001452.6264972269764
Trimmed Mean ( 9 / 20 )26159.4047619048490.68056279343353.3124944118021
Trimmed Mean ( 10 / 20 )26163.875485.05481475531053.9400377114051
Trimmed Mean ( 11 / 20 )26168.5263157895477.57533010743954.7945521178877
Trimmed Mean ( 12 / 20 )26175.9444444444467.74295604283555.962241881516
Trimmed Mean ( 13 / 20 )26181.3823529412456.99742568753857.2899996396087
Trimmed Mean ( 14 / 20 )26196444.19069893023358.9746702555662
Trimmed Mean ( 15 / 20 )26218.4666666667428.91642605104161.1272151734908
Trimmed Mean ( 16 / 20 )26227.8571428571415.61209947926263.106577444976
Trimmed Mean ( 17 / 20 )26234.5769230769401.37223533993465.3622114665159
Trimmed Mean ( 18 / 20 )26240.75388.27676821036367.5825909465258
Trimmed Mean ( 19 / 20 )26238.0454545455372.16679496999370.5007695720435
Trimmed Mean ( 20 / 20 )26263.6357.23994884759473.5180936082952
Median25448
Midrange26568.5
Midmean - Weighted Average at Xnp26071.0967741935
Midmean - Weighted Average at X(n+1)p26218.4666666667
Midmean - Empirical Distribution Function26071.0967741935
Midmean - Empirical Distribution Function - Averaging26218.4666666667
Midmean - Empirical Distribution Function - Interpolation26218.4666666667
Midmean - Closest Observation26071.0967741935
Midmean - True Basic - Statistics Graphics Toolkit26218.4666666667
Midmean - MS Excel (old versions)26196
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')