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Description of Statistical Computation

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, 14 Dec 2017 11:04:29 +0100
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2017/Dec/14/t1513245950vr5dwmxz1ejrnwa.htm/, Retrieved Tue, 14 May 2024 08:18:42 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=309432, Retrieved Tue, 14 May 2024 08:18:42 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact76

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [] [2017-12-14 10:04:29] [f1ade19563a25eb31edff11eb9af1158] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
6477000000.00
114700000000.00
23740000000.00
38430000000.00
55070000000.00
23360000000.00
32280000000.00
23570000000.00
365000000000.00
2260000000.00
82720000000.00
3098000000000.00
46180000000.00
708200000.00
23200000000.00
3022000000.00
146080000000.00
185300000000.00
6162000000.00
359700000000.00
116400000000.00
133700000000.00
45360000000.00
107300000000.00
136000000000.00
4935000000.00
1217000000000.00
7601000000.00
1184000000.00
94500000000.00
178400000000.00
25370000000.00
2081000000.00
4630000000.00
8506000000.00
36130000000.00
25840000000.00
22050000000.00
61810000000.00
80690000000.00
114400000000.00
25130000000.00
40000000000.00
377700000000.00
535800000000.00
47230000000.00
371100000000.00
63140000000.00
6019000000.00
168300000.00
59390000000.00
679300000000.00
439000000000.00
4067000000.00
171900000000.00
106100000000.00
3034000000.00
15540000000.00
135000000000.00
117300000000.00
14000000000.00
10990000000.00
36910000000.00
592600000.00

Tables (Output of Computation)





Summary of computational transaction
Raw Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R ServerBig Analytics Cloud Computing Center

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input view raw input (R code)  \tabularnewline
Raw Outputview raw output of R engine  \tabularnewline
Computing time2 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=309432&T=0

[TABLE]
[ROW]
Summary of computational transaction[/C][/ROW] [ROW]Raw Input[/C] view raw input (R code) [/C][/ROW] [ROW]Raw Output[/C]view raw output of R engine [/C][/ROW] [ROW]Computing time[/C]2 seconds[/C][/ROW] [ROW]R Server[/C]Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=309432&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=309432&T=0

As an alternative you can also use a QR Code:  
QR Code


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

Summary of computational transaction
Raw Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R ServerBig Analytics Cloud Computing Center






Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean1.61238e+11527103000003.05895
Geometric Mean35895200000
Harmonic Mean4621970000
Quadratic Mean4.4837e+11
Winsorized Mean ( 1 / 21 )1.31854e+11300343000004.39013
Winsorized Mean ( 2 / 21 )1.15055e+112.1497e+105.35213
Winsorized Mean ( 3 / 21 )1.08351e+11188722000005.74128
Winsorized Mean ( 4 / 21 )1.02357e+11168107000006.08879
Winsorized Mean ( 5 / 21 )97581600000153516000006.35645
Winsorized Mean ( 6 / 21 )97034300000151662000006.39806
Winsorized Mean ( 7 / 21 )96368400000149754000006.43512
Winsorized Mean ( 8 / 21 )9.5835e+10147744000006.48656
Winsorized Mean ( 9 / 21 )7138920000084274100008.47107
Winsorized Mean ( 10 / 21 )7035880000081928600008.58781
Winsorized Mean ( 11 / 21 )6942790000079378200008.74647
Winsorized Mean ( 12 / 21 )6461340000069873000009.24727
Winsorized Mean ( 13 / 21 )6262990000066086100009.47702
Winsorized Mean ( 14 / 21 )6.2657e+1065371000009.58483
Winsorized Mean ( 15 / 21 )6256450000064554200009.69177
Winsorized Mean ( 16 / 21 )59085500000567869000010.4048
Winsorized Mean ( 17 / 21 )59645900000553368000010.7787
Winsorized Mean ( 18 / 21 )59600900000539962000011.038
Winsorized Mean ( 19 / 21 )61444500000514228000011.9489
Winsorized Mean ( 20 / 21 )59585200000473976000012.5713
Winsorized Mean ( 21 / 21 )59243900000467055000012.6846
Trimmed Mean ( 1 / 21 )1.16469e+11253356000004.59705
Trimmed Mean ( 2 / 21 )1.00058e+11183106000005.46449
Trimmed Mean ( 3 / 21 )91784300000159165000005.7666
Trimmed Mean ( 4 / 21 )85473300000143013000005.97663
Trimmed Mean ( 5 / 21 )80470800000131732000006.10867
Trimmed Mean ( 6 / 21 )76258900000123007000006.19955
Trimmed Mean ( 7 / 21 )71826800000112121000006.4062
Trimmed Mean ( 8 / 21 )6715220000097908000006.85871
Trimmed Mean ( 9 / 21 )6216390000077879800007.98203
Trimmed Mean ( 10 / 21 )6.0673e+1075195500008.0687
Trimmed Mean ( 11 / 21 )5.9197e+1072263300008.19185
Trimmed Mean ( 12 / 21 )5770890000069015100008.36178
Trimmed Mean ( 13 / 21 )5673980000067363400008.42294
Trimmed Mean ( 14 / 21 )5593440000066050700008.46839
Trimmed Mean ( 15 / 21 )5503050000064276300008.56155
Trimmed Mean ( 16 / 21 )5402590000061867000008.73259
Trimmed Mean ( 17 / 21 )5335130000060742300008.78323
Trimmed Mean ( 18 / 21 )5.2505e+1059268000008.85891
Trimmed Mean ( 19 / 21 )5153460000057240200009.00322
Trimmed Mean ( 20 / 21 )5014380000054555300009.19137
Trimmed Mean ( 21 / 21 )4877050000051796200009.41584
Median4.268e+10
Midrange1.54908e+12
Midmean - Weighted Average at Xnp52646500000
Midmean - Weighted Average at X(n+1)p54025900000
Midmean - Empirical Distribution Function52646500000
Midmean - Empirical Distribution Function - Averaging54025900000
Midmean - Empirical Distribution Function - Interpolation54025900000
Midmean - Closest Observation52646500000
Midmean - True Basic - Statistics Graphics Toolkit54025900000
Midmean - MS Excel (old versions)55030500000
Number of observations64

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 1.61238e+11 & 52710300000 & 3.05895 \tabularnewline
Geometric Mean & 35895200000 &  &  \tabularnewline
Harmonic Mean & 4621970000 &  &  \tabularnewline
Quadratic Mean & 4.4837e+11 &  &  \tabularnewline
Winsorized Mean ( 1 / 21 ) & 1.31854e+11 & 30034300000 & 4.39013 \tabularnewline
Winsorized Mean ( 2 / 21 ) & 1.15055e+11 & 2.1497e+10 & 5.35213 \tabularnewline
Winsorized Mean ( 3 / 21 ) & 1.08351e+11 & 18872200000 & 5.74128 \tabularnewline
Winsorized Mean ( 4 / 21 ) & 1.02357e+11 & 16810700000 & 6.08879 \tabularnewline
Winsorized Mean ( 5 / 21 ) & 97581600000 & 15351600000 & 6.35645 \tabularnewline
Winsorized Mean ( 6 / 21 ) & 97034300000 & 15166200000 & 6.39806 \tabularnewline
Winsorized Mean ( 7 / 21 ) & 96368400000 & 14975400000 & 6.43512 \tabularnewline
Winsorized Mean ( 8 / 21 ) & 9.5835e+10 & 14774400000 & 6.48656 \tabularnewline
Winsorized Mean ( 9 / 21 ) & 71389200000 & 8427410000 & 8.47107 \tabularnewline
Winsorized Mean ( 10 / 21 ) & 70358800000 & 8192860000 & 8.58781 \tabularnewline
Winsorized Mean ( 11 / 21 ) & 69427900000 & 7937820000 & 8.74647 \tabularnewline
Winsorized Mean ( 12 / 21 ) & 64613400000 & 6987300000 & 9.24727 \tabularnewline
Winsorized Mean ( 13 / 21 ) & 62629900000 & 6608610000 & 9.47702 \tabularnewline
Winsorized Mean ( 14 / 21 ) & 6.2657e+10 & 6537100000 & 9.58483 \tabularnewline
Winsorized Mean ( 15 / 21 ) & 62564500000 & 6455420000 & 9.69177 \tabularnewline
Winsorized Mean ( 16 / 21 ) & 59085500000 & 5678690000 & 10.4048 \tabularnewline
Winsorized Mean ( 17 / 21 ) & 59645900000 & 5533680000 & 10.7787 \tabularnewline
Winsorized Mean ( 18 / 21 ) & 59600900000 & 5399620000 & 11.038 \tabularnewline
Winsorized Mean ( 19 / 21 ) & 61444500000 & 5142280000 & 11.9489 \tabularnewline
Winsorized Mean ( 20 / 21 ) & 59585200000 & 4739760000 & 12.5713 \tabularnewline
Winsorized Mean ( 21 / 21 ) & 59243900000 & 4670550000 & 12.6846 \tabularnewline
Trimmed Mean ( 1 / 21 ) & 1.16469e+11 & 25335600000 & 4.59705 \tabularnewline
Trimmed Mean ( 2 / 21 ) & 1.00058e+11 & 18310600000 & 5.46449 \tabularnewline
Trimmed Mean ( 3 / 21 ) & 91784300000 & 15916500000 & 5.7666 \tabularnewline
Trimmed Mean ( 4 / 21 ) & 85473300000 & 14301300000 & 5.97663 \tabularnewline
Trimmed Mean ( 5 / 21 ) & 80470800000 & 13173200000 & 6.10867 \tabularnewline
Trimmed Mean ( 6 / 21 ) & 76258900000 & 12300700000 & 6.19955 \tabularnewline
Trimmed Mean ( 7 / 21 ) & 71826800000 & 11212100000 & 6.4062 \tabularnewline
Trimmed Mean ( 8 / 21 ) & 67152200000 & 9790800000 & 6.85871 \tabularnewline
Trimmed Mean ( 9 / 21 ) & 62163900000 & 7787980000 & 7.98203 \tabularnewline
Trimmed Mean ( 10 / 21 ) & 6.0673e+10 & 7519550000 & 8.0687 \tabularnewline
Trimmed Mean ( 11 / 21 ) & 5.9197e+10 & 7226330000 & 8.19185 \tabularnewline
Trimmed Mean ( 12 / 21 ) & 57708900000 & 6901510000 & 8.36178 \tabularnewline
Trimmed Mean ( 13 / 21 ) & 56739800000 & 6736340000 & 8.42294 \tabularnewline
Trimmed Mean ( 14 / 21 ) & 55934400000 & 6605070000 & 8.46839 \tabularnewline
Trimmed Mean ( 15 / 21 ) & 55030500000 & 6427630000 & 8.56155 \tabularnewline
Trimmed Mean ( 16 / 21 ) & 54025900000 & 6186700000 & 8.73259 \tabularnewline
Trimmed Mean ( 17 / 21 ) & 53351300000 & 6074230000 & 8.78323 \tabularnewline
Trimmed Mean ( 18 / 21 ) & 5.2505e+10 & 5926800000 & 8.85891 \tabularnewline
Trimmed Mean ( 19 / 21 ) & 51534600000 & 5724020000 & 9.00322 \tabularnewline
Trimmed Mean ( 20 / 21 ) & 50143800000 & 5455530000 & 9.19137 \tabularnewline
Trimmed Mean ( 21 / 21 ) & 48770500000 & 5179620000 & 9.41584 \tabularnewline
Median & 4.268e+10 &  &  \tabularnewline
Midrange & 1.54908e+12 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 52646500000 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 54025900000 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 52646500000 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 54025900000 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 54025900000 &  &  \tabularnewline
Midmean - Closest Observation & 52646500000 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 54025900000 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 55030500000 &  &  \tabularnewline
Number of observations & 64 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=309432&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]1.61238e+11[/C][C]52710300000[/C][C]3.05895[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]35895200000[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]4621970000[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]4.4837e+11[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 21 )[/C][C]1.31854e+11[/C][C]30034300000[/C][C]4.39013[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 21 )[/C][C]1.15055e+11[/C][C]2.1497e+10[/C][C]5.35213[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 21 )[/C][C]1.08351e+11[/C][C]18872200000[/C][C]5.74128[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 21 )[/C][C]1.02357e+11[/C][C]16810700000[/C][C]6.08879[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 21 )[/C][C]97581600000[/C][C]15351600000[/C][C]6.35645[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 21 )[/C][C]97034300000[/C][C]15166200000[/C][C]6.39806[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 21 )[/C][C]96368400000[/C][C]14975400000[/C][C]6.43512[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 21 )[/C][C]9.5835e+10[/C][C]14774400000[/C][C]6.48656[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 21 )[/C][C]71389200000[/C][C]8427410000[/C][C]8.47107[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 21 )[/C][C]70358800000[/C][C]8192860000[/C][C]8.58781[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 21 )[/C][C]69427900000[/C][C]7937820000[/C][C]8.74647[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 21 )[/C][C]64613400000[/C][C]6987300000[/C][C]9.24727[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 21 )[/C][C]62629900000[/C][C]6608610000[/C][C]9.47702[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 21 )[/C][C]6.2657e+10[/C][C]6537100000[/C][C]9.58483[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 21 )[/C][C]62564500000[/C][C]6455420000[/C][C]9.69177[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 21 )[/C][C]59085500000[/C][C]5678690000[/C][C]10.4048[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 21 )[/C][C]59645900000[/C][C]5533680000[/C][C]10.7787[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 21 )[/C][C]59600900000[/C][C]5399620000[/C][C]11.038[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 21 )[/C][C]61444500000[/C][C]5142280000[/C][C]11.9489[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 21 )[/C][C]59585200000[/C][C]4739760000[/C][C]12.5713[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 21 )[/C][C]59243900000[/C][C]4670550000[/C][C]12.6846[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 21 )[/C][C]1.16469e+11[/C][C]25335600000[/C][C]4.59705[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 21 )[/C][C]1.00058e+11[/C][C]18310600000[/C][C]5.46449[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 21 )[/C][C]91784300000[/C][C]15916500000[/C][C]5.7666[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 21 )[/C][C]85473300000[/C][C]14301300000[/C][C]5.97663[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 21 )[/C][C]80470800000[/C][C]13173200000[/C][C]6.10867[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 21 )[/C][C]76258900000[/C][C]12300700000[/C][C]6.19955[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 21 )[/C][C]71826800000[/C][C]11212100000[/C][C]6.4062[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 21 )[/C][C]67152200000[/C][C]9790800000[/C][C]6.85871[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 21 )[/C][C]62163900000[/C][C]7787980000[/C][C]7.98203[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 21 )[/C][C]6.0673e+10[/C][C]7519550000[/C][C]8.0687[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 21 )[/C][C]5.9197e+10[/C][C]7226330000[/C][C]8.19185[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 21 )[/C][C]57708900000[/C][C]6901510000[/C][C]8.36178[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 21 )[/C][C]56739800000[/C][C]6736340000[/C][C]8.42294[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 21 )[/C][C]55934400000[/C][C]6605070000[/C][C]8.46839[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 21 )[/C][C]55030500000[/C][C]6427630000[/C][C]8.56155[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 21 )[/C][C]54025900000[/C][C]6186700000[/C][C]8.73259[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 21 )[/C][C]53351300000[/C][C]6074230000[/C][C]8.78323[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 21 )[/C][C]5.2505e+10[/C][C]5926800000[/C][C]8.85891[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 21 )[/C][C]51534600000[/C][C]5724020000[/C][C]9.00322[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 21 )[/C][C]50143800000[/C][C]5455530000[/C][C]9.19137[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 21 )[/C][C]48770500000[/C][C]5179620000[/C][C]9.41584[/C][/ROW]
[ROW][C]Median[/C][C]4.268e+10[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]1.54908e+12[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]52646500000[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]54025900000[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]52646500000[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]54025900000[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]54025900000[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]52646500000[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]54025900000[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]55030500000[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]64[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=309432&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=309432&T=1

As an alternative you can also use a QR Code:  
QR Code


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

Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean1.61238e+11527103000003.05895
Geometric Mean35895200000
Harmonic Mean4621970000
Quadratic Mean4.4837e+11
Winsorized Mean ( 1 / 21 )1.31854e+11300343000004.39013
Winsorized Mean ( 2 / 21 )1.15055e+112.1497e+105.35213
Winsorized Mean ( 3 / 21 )1.08351e+11188722000005.74128
Winsorized Mean ( 4 / 21 )1.02357e+11168107000006.08879
Winsorized Mean ( 5 / 21 )97581600000153516000006.35645
Winsorized Mean ( 6 / 21 )97034300000151662000006.39806
Winsorized Mean ( 7 / 21 )96368400000149754000006.43512
Winsorized Mean ( 8 / 21 )9.5835e+10147744000006.48656
Winsorized Mean ( 9 / 21 )7138920000084274100008.47107
Winsorized Mean ( 10 / 21 )7035880000081928600008.58781
Winsorized Mean ( 11 / 21 )6942790000079378200008.74647
Winsorized Mean ( 12 / 21 )6461340000069873000009.24727
Winsorized Mean ( 13 / 21 )6262990000066086100009.47702
Winsorized Mean ( 14 / 21 )6.2657e+1065371000009.58483
Winsorized Mean ( 15 / 21 )6256450000064554200009.69177
Winsorized Mean ( 16 / 21 )59085500000567869000010.4048
Winsorized Mean ( 17 / 21 )59645900000553368000010.7787
Winsorized Mean ( 18 / 21 )59600900000539962000011.038
Winsorized Mean ( 19 / 21 )61444500000514228000011.9489
Winsorized Mean ( 20 / 21 )59585200000473976000012.5713
Winsorized Mean ( 21 / 21 )59243900000467055000012.6846
Trimmed Mean ( 1 / 21 )1.16469e+11253356000004.59705
Trimmed Mean ( 2 / 21 )1.00058e+11183106000005.46449
Trimmed Mean ( 3 / 21 )91784300000159165000005.7666
Trimmed Mean ( 4 / 21 )85473300000143013000005.97663
Trimmed Mean ( 5 / 21 )80470800000131732000006.10867
Trimmed Mean ( 6 / 21 )76258900000123007000006.19955
Trimmed Mean ( 7 / 21 )71826800000112121000006.4062
Trimmed Mean ( 8 / 21 )6715220000097908000006.85871
Trimmed Mean ( 9 / 21 )6216390000077879800007.98203
Trimmed Mean ( 10 / 21 )6.0673e+1075195500008.0687
Trimmed Mean ( 11 / 21 )5.9197e+1072263300008.19185
Trimmed Mean ( 12 / 21 )5770890000069015100008.36178
Trimmed Mean ( 13 / 21 )5673980000067363400008.42294
Trimmed Mean ( 14 / 21 )5593440000066050700008.46839
Trimmed Mean ( 15 / 21 )5503050000064276300008.56155
Trimmed Mean ( 16 / 21 )5402590000061867000008.73259
Trimmed Mean ( 17 / 21 )5335130000060742300008.78323
Trimmed Mean ( 18 / 21 )5.2505e+1059268000008.85891
Trimmed Mean ( 19 / 21 )5153460000057240200009.00322
Trimmed Mean ( 20 / 21 )5014380000054555300009.19137
Trimmed Mean ( 21 / 21 )4877050000051796200009.41584
Median4.268e+10
Midrange1.54908e+12
Midmean - Weighted Average at Xnp52646500000
Midmean - Weighted Average at X(n+1)p54025900000
Midmean - Empirical Distribution Function52646500000
Midmean - Empirical Distribution Function - Averaging54025900000
Midmean - Empirical Distribution Function - Interpolation54025900000
Midmean - Closest Observation52646500000
Midmean - True Basic - Statistics Graphics Toolkit54025900000
Midmean - MS Excel (old versions)55030500000
Number of observations64


Figures (Output of Computation)

Input Parameters & R Code

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,'Arithmetic Mean',header=TRUE)
a<-table.element(a,signif(arm,6))
a<-table.element(a, signif(armse,6))
a<-table.element(a,signif(armose,6))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Geometric Mean',header=TRUE)
a<-table.element(a,signif(geo,6))
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Harmonic Mean',header=TRUE)
a<-table.element(a,signif(har,6))
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Quadratic Mean',header=TRUE)
a<-table.element(a,signif(qua,6))
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, mylabel,header=TRUE)
a<-table.element(a,signif(win[j,1],6))
a<-table.element(a,signif(win[j,2],6))
a<-table.element(a,signif(win[j,1]/win[j,2],6))
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, mylabel,header=TRUE)
a<-table.element(a,signif(tri[j,1],6))
a<-table.element(a,signif(tri[j,2],6))
a<-table.element(a,signif(tri[j,1]/tri[j,2],6))
a<-table.row.end(a)
}
a<-table.row.start(a)
a<-table.element(a, 'Median',header=TRUE)
a<-table.element(a,signif(median(x),6))
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Midrange',header=TRUE)
a<-table.element(a,signif(midr,6))
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <-  'Midmean'
mylabel <- paste(mymid,'Weighted Average at Xnp',sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,signif(midm[1],6))
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <-  'Midmean'
mylabel <- paste(mymid,'Weighted Average at X(n+1)p',sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,signif(midm[2],6))
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <-  'Midmean'
mylabel <- paste(mymid,'Empirical Distribution Function',sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,signif(midm[3],6))
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <-  'Midmean'
mylabel <- paste(mymid,'Empirical Distribution Function - Averaging',sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,signif(midm[4],6))
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <-  'Midmean'
mylabel <- paste(mymid,'Empirical Distribution Function - Interpolation',sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,signif(midm[5],6))
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <-  'Midmean'
mylabel <- paste(mymid,'Closest Observation',sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,signif(midm[6],6))
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <-  'Midmean'
mylabel <- paste(mymid,'True Basic - Statistics Graphics Toolkit',sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,signif(midm[7],6))
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <-  'Midmean'
mylabel <- paste(mymid,'MS Excel (old versions)',sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,signif(midm[8],6))
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,signif(length(x),6))
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')