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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 computationTue, 15 Nov 2011 16:00:08 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2011/Nov/15/t1321390818fulf2mwv83dmh57.htm/, Retrieved Fri, 29 Mar 2024 06:06:12 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=143543, Retrieved Fri, 29 Mar 2024 06:06:12 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact111
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Central Tendency] [Arabica Price in ...] [2008-01-06 21:28:17] [74be16979710d4c4e7c6647856088456]
- RM D  [Central Tendency] [US car sales] [2010-11-06 13:18:47] [97ad38b1c3b35a5feca8b85f7bc7b3ff]
- R P       [Central Tendency] [] [2011-11-15 21:00:08] [542c32830549043c4555f1bd78aefedb] [Current]
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Dataseries X:
26862
28261
31761
32624
32950
34711
34124
31860
32404
33027
28944
29702
29144
29715
35710
37324
37687
39071
38986
37702
36444
36423
35266
35461
33073
35721
44670
43461
42998
45039
41555
43850
42253
42036
39552
38572
36862
37883
47264
43698
48335
50368
45633
48708
44588
44021
41601
39761
40848
45488
51253
49495
53348
50286
50191
50596
46689
49249
43597
41862




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net

\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 & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=143543&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]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=143543&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=143543&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'Gwilym Jenkins' @ jenkins.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean40009.45879.56239197117645.4879044002044
Geometric Mean39426.4869532331
Harmonic Mean38834.3112164706
Quadratic Mean40575.8580856072
Winsorized Mean ( 1 / 20 )39997.85865.58710483655146.2089254524567
Winsorized Mean ( 2 / 20 )39998.7166666667855.7657373527746.7402642110899
Winsorized Mean ( 3 / 20 )39997.3166666667851.21697211175946.9883918872512
Winsorized Mean ( 4 / 20 )40029.05842.20227498595947.5290214582564
Winsorized Mean ( 5 / 20 )40022.2166666667840.34817377033347.6257555092929
Winsorized Mean ( 6 / 20 )40157.2166666667786.32958368363851.0691922317691
Winsorized Mean ( 7 / 20 )40140.0666666667778.5090791797851.5601779608754
Winsorized Mean ( 8 / 20 )40140.4666666667751.51498718912353.4127294211434
Winsorized Mean ( 9 / 20 )40117.5166666667735.07754289128554.5758975425534
Winsorized Mean ( 10 / 20 )39993.35692.8879923606957.7197908477841
Winsorized Mean ( 11 / 20 )39902.05672.04652886781359.3739395800799
Winsorized Mean ( 12 / 20 )39700.05635.61638949164662.4591351896249
Winsorized Mean ( 13 / 20 )39896.35591.62042525993467.4357211086333
Winsorized Mean ( 14 / 20 )39928.55552.71894372147972.2402415433049
Winsorized Mean ( 15 / 20 )39975.05516.54871157186577.3887323779308
Winsorized Mean ( 16 / 20 )40005.1833333333505.20158335638779.1865755201172
Winsorized Mean ( 17 / 20 )39915.0833333333470.22144037638584.8857153374028
Winsorized Mean ( 18 / 20 )39867.0833333333462.17738131933986.2592695893688
Winsorized Mean ( 19 / 20 )40041.25422.04373727413294.8746455962498
Winsorized Mean ( 20 / 20 )40014.5833333333416.09756046605396.1663492775943
Trimmed Mean ( 1 / 20 )40006.1551724138849.87405522283747.0730397363691
Trimmed Mean ( 2 / 20 )40015.0535714286830.31690766574948.1925072246475
Trimmed Mean ( 3 / 20 )40024.1296296296812.40029052059249.2665131913996
Trimmed Mean ( 4 / 20 )40034.4423076923792.00498926884550.5482198346388
Trimmed Mean ( 5 / 20 )40036.06769.7524534019852.0116042801261
Trimmed Mean ( 6 / 20 )40039.5208333333741.98539728083653.9626803708897
Trimmed Mean ( 7 / 20 )40013.9347826087723.66932315627655.293120078779
Trimmed Mean ( 8 / 20 )39989.3636363636701.95052249920156.9689206783219
Trimmed Mean ( 9 / 20 )39962.380952381681.0317043213258.6791785151989
Trimmed Mean ( 10 / 20 )39936.525657.64316759273860.7267390098268
Trimmed Mean ( 11 / 20 )39927.5526315789637.93373965014862.5888711474577
Trimmed Mean ( 12 / 20 )39931.4166666667616.47336787054464.773952530342
Trimmed Mean ( 13 / 20 )39965.4411764706596.5321413856966.9962914045746
Trimmed Mean ( 14 / 20 )39975.40625580.80875527177968.8271412700972
Trimmed Mean ( 15 / 20 )39982.1568.60870805287870.3156659997579
Trimmed Mean ( 16 / 20 )39983.1071428571559.98248115852771.4006392845319
Trimmed Mean ( 17 / 20 )39979.9230769231548.30088854450972.9160282469206
Trimmed Mean ( 18 / 20 )39989.4583333333539.80552717705174.0812317029447
Trimmed Mean ( 19 / 20 )40008525.7775153722376.0930219156973
Trimmed Mean ( 20 / 20 )40002.75516.17858433012677.4978877744683
Median39656.5
Midrange40105
Midmean - Weighted Average at Xnp39812.064516129
Midmean - Weighted Average at X(n+1)p39982.1
Midmean - Empirical Distribution Function39812.064516129
Midmean - Empirical Distribution Function - Averaging39982.1
Midmean - Empirical Distribution Function - Interpolation39982.1
Midmean - Closest Observation39812.064516129
Midmean - True Basic - Statistics Graphics Toolkit39982.1
Midmean - MS Excel (old versions)39975.40625
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 40009.45 & 879.562391971176 & 45.4879044002044 \tabularnewline
Geometric Mean & 39426.4869532331 &  &  \tabularnewline
Harmonic Mean & 38834.3112164706 &  &  \tabularnewline
Quadratic Mean & 40575.8580856072 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 39997.85 & 865.587104836551 & 46.2089254524567 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 39998.7166666667 & 855.76573735277 & 46.7402642110899 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 39997.3166666667 & 851.216972111759 & 46.9883918872512 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 40029.05 & 842.202274985959 & 47.5290214582564 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 40022.2166666667 & 840.348173770333 & 47.6257555092929 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 40157.2166666667 & 786.329583683638 & 51.0691922317691 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 40140.0666666667 & 778.50907917978 & 51.5601779608754 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 40140.4666666667 & 751.514987189123 & 53.4127294211434 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 40117.5166666667 & 735.077542891285 & 54.5758975425534 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 39993.35 & 692.88799236069 & 57.7197908477841 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 39902.05 & 672.046528867813 & 59.3739395800799 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 39700.05 & 635.616389491646 & 62.4591351896249 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 39896.35 & 591.620425259934 & 67.4357211086333 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 39928.55 & 552.718943721479 & 72.2402415433049 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 39975.05 & 516.548711571865 & 77.3887323779308 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 40005.1833333333 & 505.201583356387 & 79.1865755201172 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 39915.0833333333 & 470.221440376385 & 84.8857153374028 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 39867.0833333333 & 462.177381319339 & 86.2592695893688 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 40041.25 & 422.043737274132 & 94.8746455962498 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 40014.5833333333 & 416.097560466053 & 96.1663492775943 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 40006.1551724138 & 849.874055222837 & 47.0730397363691 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 40015.0535714286 & 830.316907665749 & 48.1925072246475 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 40024.1296296296 & 812.400290520592 & 49.2665131913996 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 40034.4423076923 & 792.004989268845 & 50.5482198346388 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 40036.06 & 769.75245340198 & 52.0116042801261 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 40039.5208333333 & 741.985397280836 & 53.9626803708897 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 40013.9347826087 & 723.669323156276 & 55.293120078779 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 39989.3636363636 & 701.950522499201 & 56.9689206783219 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 39962.380952381 & 681.03170432132 & 58.6791785151989 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 39936.525 & 657.643167592738 & 60.7267390098268 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 39927.5526315789 & 637.933739650148 & 62.5888711474577 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 39931.4166666667 & 616.473367870544 & 64.773952530342 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 39965.4411764706 & 596.53214138569 & 66.9962914045746 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 39975.40625 & 580.808755271779 & 68.8271412700972 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 39982.1 & 568.608708052878 & 70.3156659997579 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 39983.1071428571 & 559.982481158527 & 71.4006392845319 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 39979.9230769231 & 548.300888544509 & 72.9160282469206 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 39989.4583333333 & 539.805527177051 & 74.0812317029447 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 40008 & 525.77751537223 & 76.0930219156973 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 40002.75 & 516.178584330126 & 77.4978877744683 \tabularnewline
Median & 39656.5 &  &  \tabularnewline
Midrange & 40105 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 39812.064516129 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 39982.1 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 39812.064516129 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 39982.1 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 39982.1 &  &  \tabularnewline
Midmean - Closest Observation & 39812.064516129 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 39982.1 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 39975.40625 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=143543&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]40009.45[/C][C]879.562391971176[/C][C]45.4879044002044[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]39426.4869532331[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]38834.3112164706[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]40575.8580856072[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]39997.85[/C][C]865.587104836551[/C][C]46.2089254524567[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]39998.7166666667[/C][C]855.76573735277[/C][C]46.7402642110899[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]39997.3166666667[/C][C]851.216972111759[/C][C]46.9883918872512[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]40029.05[/C][C]842.202274985959[/C][C]47.5290214582564[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]40022.2166666667[/C][C]840.348173770333[/C][C]47.6257555092929[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]40157.2166666667[/C][C]786.329583683638[/C][C]51.0691922317691[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]40140.0666666667[/C][C]778.50907917978[/C][C]51.5601779608754[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]40140.4666666667[/C][C]751.514987189123[/C][C]53.4127294211434[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]40117.5166666667[/C][C]735.077542891285[/C][C]54.5758975425534[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]39993.35[/C][C]692.88799236069[/C][C]57.7197908477841[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]39902.05[/C][C]672.046528867813[/C][C]59.3739395800799[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]39700.05[/C][C]635.616389491646[/C][C]62.4591351896249[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]39896.35[/C][C]591.620425259934[/C][C]67.4357211086333[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]39928.55[/C][C]552.718943721479[/C][C]72.2402415433049[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]39975.05[/C][C]516.548711571865[/C][C]77.3887323779308[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]40005.1833333333[/C][C]505.201583356387[/C][C]79.1865755201172[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]39915.0833333333[/C][C]470.221440376385[/C][C]84.8857153374028[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]39867.0833333333[/C][C]462.177381319339[/C][C]86.2592695893688[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]40041.25[/C][C]422.043737274132[/C][C]94.8746455962498[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]40014.5833333333[/C][C]416.097560466053[/C][C]96.1663492775943[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]40006.1551724138[/C][C]849.874055222837[/C][C]47.0730397363691[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]40015.0535714286[/C][C]830.316907665749[/C][C]48.1925072246475[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]40024.1296296296[/C][C]812.400290520592[/C][C]49.2665131913996[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]40034.4423076923[/C][C]792.004989268845[/C][C]50.5482198346388[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]40036.06[/C][C]769.75245340198[/C][C]52.0116042801261[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]40039.5208333333[/C][C]741.985397280836[/C][C]53.9626803708897[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]40013.9347826087[/C][C]723.669323156276[/C][C]55.293120078779[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]39989.3636363636[/C][C]701.950522499201[/C][C]56.9689206783219[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]39962.380952381[/C][C]681.03170432132[/C][C]58.6791785151989[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]39936.525[/C][C]657.643167592738[/C][C]60.7267390098268[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]39927.5526315789[/C][C]637.933739650148[/C][C]62.5888711474577[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]39931.4166666667[/C][C]616.473367870544[/C][C]64.773952530342[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]39965.4411764706[/C][C]596.53214138569[/C][C]66.9962914045746[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]39975.40625[/C][C]580.808755271779[/C][C]68.8271412700972[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]39982.1[/C][C]568.608708052878[/C][C]70.3156659997579[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]39983.1071428571[/C][C]559.982481158527[/C][C]71.4006392845319[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]39979.9230769231[/C][C]548.300888544509[/C][C]72.9160282469206[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]39989.4583333333[/C][C]539.805527177051[/C][C]74.0812317029447[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]40008[/C][C]525.77751537223[/C][C]76.0930219156973[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]40002.75[/C][C]516.178584330126[/C][C]77.4978877744683[/C][/ROW]
[ROW][C]Median[/C][C]39656.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]40105[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]39812.064516129[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]39982.1[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]39812.064516129[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]39982.1[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]39982.1[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]39812.064516129[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]39982.1[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]39975.40625[/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=143543&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=143543&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 Mean40009.45879.56239197117645.4879044002044
Geometric Mean39426.4869532331
Harmonic Mean38834.3112164706
Quadratic Mean40575.8580856072
Winsorized Mean ( 1 / 20 )39997.85865.58710483655146.2089254524567
Winsorized Mean ( 2 / 20 )39998.7166666667855.7657373527746.7402642110899
Winsorized Mean ( 3 / 20 )39997.3166666667851.21697211175946.9883918872512
Winsorized Mean ( 4 / 20 )40029.05842.20227498595947.5290214582564
Winsorized Mean ( 5 / 20 )40022.2166666667840.34817377033347.6257555092929
Winsorized Mean ( 6 / 20 )40157.2166666667786.32958368363851.0691922317691
Winsorized Mean ( 7 / 20 )40140.0666666667778.5090791797851.5601779608754
Winsorized Mean ( 8 / 20 )40140.4666666667751.51498718912353.4127294211434
Winsorized Mean ( 9 / 20 )40117.5166666667735.07754289128554.5758975425534
Winsorized Mean ( 10 / 20 )39993.35692.8879923606957.7197908477841
Winsorized Mean ( 11 / 20 )39902.05672.04652886781359.3739395800799
Winsorized Mean ( 12 / 20 )39700.05635.61638949164662.4591351896249
Winsorized Mean ( 13 / 20 )39896.35591.62042525993467.4357211086333
Winsorized Mean ( 14 / 20 )39928.55552.71894372147972.2402415433049
Winsorized Mean ( 15 / 20 )39975.05516.54871157186577.3887323779308
Winsorized Mean ( 16 / 20 )40005.1833333333505.20158335638779.1865755201172
Winsorized Mean ( 17 / 20 )39915.0833333333470.22144037638584.8857153374028
Winsorized Mean ( 18 / 20 )39867.0833333333462.17738131933986.2592695893688
Winsorized Mean ( 19 / 20 )40041.25422.04373727413294.8746455962498
Winsorized Mean ( 20 / 20 )40014.5833333333416.09756046605396.1663492775943
Trimmed Mean ( 1 / 20 )40006.1551724138849.87405522283747.0730397363691
Trimmed Mean ( 2 / 20 )40015.0535714286830.31690766574948.1925072246475
Trimmed Mean ( 3 / 20 )40024.1296296296812.40029052059249.2665131913996
Trimmed Mean ( 4 / 20 )40034.4423076923792.00498926884550.5482198346388
Trimmed Mean ( 5 / 20 )40036.06769.7524534019852.0116042801261
Trimmed Mean ( 6 / 20 )40039.5208333333741.98539728083653.9626803708897
Trimmed Mean ( 7 / 20 )40013.9347826087723.66932315627655.293120078779
Trimmed Mean ( 8 / 20 )39989.3636363636701.95052249920156.9689206783219
Trimmed Mean ( 9 / 20 )39962.380952381681.0317043213258.6791785151989
Trimmed Mean ( 10 / 20 )39936.525657.64316759273860.7267390098268
Trimmed Mean ( 11 / 20 )39927.5526315789637.93373965014862.5888711474577
Trimmed Mean ( 12 / 20 )39931.4166666667616.47336787054464.773952530342
Trimmed Mean ( 13 / 20 )39965.4411764706596.5321413856966.9962914045746
Trimmed Mean ( 14 / 20 )39975.40625580.80875527177968.8271412700972
Trimmed Mean ( 15 / 20 )39982.1568.60870805287870.3156659997579
Trimmed Mean ( 16 / 20 )39983.1071428571559.98248115852771.4006392845319
Trimmed Mean ( 17 / 20 )39979.9230769231548.30088854450972.9160282469206
Trimmed Mean ( 18 / 20 )39989.4583333333539.80552717705174.0812317029447
Trimmed Mean ( 19 / 20 )40008525.7775153722376.0930219156973
Trimmed Mean ( 20 / 20 )40002.75516.17858433012677.4978877744683
Median39656.5
Midrange40105
Midmean - Weighted Average at Xnp39812.064516129
Midmean - Weighted Average at X(n+1)p39982.1
Midmean - Empirical Distribution Function39812.064516129
Midmean - Empirical Distribution Function - Averaging39982.1
Midmean - Empirical Distribution Function - Interpolation39982.1
Midmean - Closest Observation39812.064516129
Midmean - True Basic - Statistics Graphics Toolkit39982.1
Midmean - MS Excel (old versions)39975.40625
Number of observations60



Parameters (Session):
par1 = 0.01 ; par2 = 0.99 ; par3 = 0.01 ;
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')