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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, 16 Oct 2009 04:14:51 -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/16/t1255688472dx1g4e9o27yt2uz.htm/, Retrieved Tue, 30 Apr 2024 06:20:43 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=46943, Retrieved Tue, 30 Apr 2024 06:20:43 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsW3
Estimated Impact146
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Univariate Data Series] [Workshop 2 ] [2009-10-08 16:59:47] [315ba876df544ad397193b5931d5f354]
- RMPD    [Central Tendency] [w3] [2009-10-16 10:14:51] [950726a732ba3ca782ecb1a5307d0f6f] [Current]
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Dataseries X:
1129,7
2140,4
2665,1
2318,1
1292,8
2135,9
1846,3
2217,5
2349,8
1790,8
2222,6
2525,7
1425,4
1903,5
2434,1
1444,6
207,9
1552,3
1420,7
1543,5
1724,8
2180,9
3136,5
1926,9
1202,5
2211,2
2510
1746,6
1544,8
2686,8
2170
2294,6
2378,3
2588,9
3072,9
2468,1
1971
2565,9
2348,6
1945,2
286,7
2394,4
2211,9
1979,7
2131,6
2393,3
2196,6
2498,5
1597,3
2674,8
2427,6
1243,7
1155,3
2119,2
2009,4
1755,2
1828,7
1915,8
1826,3
2066,7




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=46943&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=46943&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=46943&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 Mean1999.2316666666772.353323573670827.6315111444885
Geometric Mean1868.89822301977
Harmonic Mean1574.52842688787
Quadratic Mean2075.04035129440
Winsorized Mean ( 1 / 20 )1999.48571.535199933457727.9510646766896
Winsorized Mean ( 2 / 20 )2014.71559.154643633598934.0584420130912
Winsorized Mean ( 3 / 20 )2015.39558.718576903630534.3229537614252
Winsorized Mean ( 4 / 20 )2017.89557.828978641877434.8941836323342
Winsorized Mean ( 5 / 20 )2014.9783333333355.860832325418436.0713983206522
Winsorized Mean ( 6 / 20 )2017.5883333333354.333979551025237.1330859621392
Winsorized Mean ( 7 / 20 )2027.8250.320627505451240.2979871381836
Winsorized Mean ( 8 / 20 )2026.3533333333349.844851802609540.6532121182322
Winsorized Mean ( 9 / 20 )2027.5083333333348.977645038448341.3966072019531
Winsorized Mean ( 10 / 20 )2038.92544.947125410054045.3627452567617
Winsorized Mean ( 11 / 20 )2032.9343.915205228741546.2921666746417
Winsorized Mean ( 12 / 20 )2033.1343.432471990019646.8112890389291
Winsorized Mean ( 13 / 20 )2035.6866666666740.529574154777550.2271911096975
Winsorized Mean ( 14 / 20 )2065.1835.312537009630158.4829121577077
Winsorized Mean ( 15 / 20 )2066.8833.842273467459761.0739110653237
Winsorized Mean ( 16 / 20 )2061.5733333333332.306327576909663.8132987547246
Winsorized Mean ( 17 / 20 )2071.3230.661121962511467.555257845181
Winsorized Mean ( 18 / 20 )2072.8227.639249787459174.9955232482652
Winsorized Mean ( 19 / 20 )2066.1383333333326.418574518961878.2077901989139
Winsorized Mean ( 20 / 20 )2048.00522.143161373694392.4892776346286
Trimmed Mean ( 1 / 20 )2010.5086206896665.126541410974530.8708028575100
Trimmed Mean ( 2 / 20 )2022.3196428571456.735557371523435.644659831476
Trimmed Mean ( 3 / 20 )2026.5444444444455.055452870286936.8091503891371
Trimmed Mean ( 4 / 20 )2030.8326923076953.16086636642838.2016477743146
Trimmed Mean ( 5 / 20 )2034.71451.132380412144439.7930623139293
Trimmed Mean ( 6 / 20 )2039.6479166666749.247804068622341.4160175309462
Trimmed Mean ( 7 / 20 )2044.4434782608747.323534876011843.2014109600506
Trimmed Mean ( 8 / 20 )2047.6818181818246.064315878846244.4526696883424
Trimmed Mean ( 9 / 20 )2051.4904761904844.520238361940446.0799526613554
Trimmed Mean ( 10 / 20 )2055.487542.699909053452148.1379830909458
Trimmed Mean ( 11 / 20 )2058.1026315789541.415908476327349.6935285810603
Trimmed Mean ( 12 / 20 )2061.9166666666739.903681952087251.6723411424146
Trimmed Mean ( 13 / 20 )2066.1537.907148792675254.5055501615369
Trimmed Mean ( 14 / 20 )2070.5437535.978178853002457.5499876872509
Trimmed Mean ( 15 / 20 )2071.3134.911151052580559.3308996566843
Trimmed Mean ( 16 / 20 )2071.9428571428633.740672012362261.407871674391
Trimmed Mean ( 17 / 20 )2073.4384615384632.417149344099263.9611595556869
Trimmed Mean ( 18 / 20 )2073.7530.912036842290667.0855178705958
Trimmed Mean ( 19 / 20 )2073.8909090909129.663588469924369.9136893432031
Trimmed Mean ( 20 / 20 )2075.11527.988056921893674.1428747908807
Median2125.4
Midrange1672.2
Midmean - Weighted Average at Xnp2060.13225806452
Midmean - Weighted Average at X(n+1)p2071.31
Midmean - Empirical Distribution Function2060.13225806452
Midmean - Empirical Distribution Function - Averaging2071.31
Midmean - Empirical Distribution Function - Interpolation2071.31
Midmean - Closest Observation2060.13225806452
Midmean - True Basic - Statistics Graphics Toolkit2071.31
Midmean - MS Excel (old versions)2070.54375
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 1999.23166666667 & 72.3533235736708 & 27.6315111444885 \tabularnewline
Geometric Mean & 1868.89822301977 &  &  \tabularnewline
Harmonic Mean & 1574.52842688787 &  &  \tabularnewline
Quadratic Mean & 2075.04035129440 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 1999.485 & 71.5351999334577 & 27.9510646766896 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 2014.715 & 59.1546436335989 & 34.0584420130912 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 2015.395 & 58.7185769036305 & 34.3229537614252 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 2017.895 & 57.8289786418774 & 34.8941836323342 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 2014.97833333333 & 55.8608323254184 & 36.0713983206522 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 2017.58833333333 & 54.3339795510252 & 37.1330859621392 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 2027.82 & 50.3206275054512 & 40.2979871381836 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 2026.35333333333 & 49.8448518026095 & 40.6532121182322 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 2027.50833333333 & 48.9776450384483 & 41.3966072019531 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 2038.925 & 44.9471254100540 & 45.3627452567617 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 2032.93 & 43.9152052287415 & 46.2921666746417 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 2033.13 & 43.4324719900196 & 46.8112890389291 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 2035.68666666667 & 40.5295741547775 & 50.2271911096975 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 2065.18 & 35.3125370096301 & 58.4829121577077 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 2066.88 & 33.8422734674597 & 61.0739110653237 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 2061.57333333333 & 32.3063275769096 & 63.8132987547246 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 2071.32 & 30.6611219625114 & 67.555257845181 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 2072.82 & 27.6392497874591 & 74.9955232482652 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 2066.13833333333 & 26.4185745189618 & 78.2077901989139 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 2048.005 & 22.1431613736943 & 92.4892776346286 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 2010.50862068966 & 65.1265414109745 & 30.8708028575100 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 2022.31964285714 & 56.7355573715234 & 35.644659831476 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 2026.54444444444 & 55.0554528702869 & 36.8091503891371 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 2030.83269230769 & 53.160866366428 & 38.2016477743146 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 2034.714 & 51.1323804121444 & 39.7930623139293 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 2039.64791666667 & 49.2478040686223 & 41.4160175309462 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 2044.44347826087 & 47.3235348760118 & 43.2014109600506 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 2047.68181818182 & 46.0643158788462 & 44.4526696883424 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 2051.49047619048 & 44.5202383619404 & 46.0799526613554 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 2055.4875 & 42.6999090534521 & 48.1379830909458 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 2058.10263157895 & 41.4159084763273 & 49.6935285810603 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 2061.91666666667 & 39.9036819520872 & 51.6723411424146 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 2066.15 & 37.9071487926752 & 54.5055501615369 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 2070.54375 & 35.9781788530024 & 57.5499876872509 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 2071.31 & 34.9111510525805 & 59.3308996566843 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 2071.94285714286 & 33.7406720123622 & 61.407871674391 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 2073.43846153846 & 32.4171493440992 & 63.9611595556869 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 2073.75 & 30.9120368422906 & 67.0855178705958 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 2073.89090909091 & 29.6635884699243 & 69.9136893432031 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 2075.115 & 27.9880569218936 & 74.1428747908807 \tabularnewline
Median & 2125.4 &  &  \tabularnewline
Midrange & 1672.2 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 2060.13225806452 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 2071.31 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 2060.13225806452 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 2071.31 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 2071.31 &  &  \tabularnewline
Midmean - Closest Observation & 2060.13225806452 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 2071.31 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 2070.54375 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=46943&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]1999.23166666667[/C][C]72.3533235736708[/C][C]27.6315111444885[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]1868.89822301977[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]1574.52842688787[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]2075.04035129440[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]1999.485[/C][C]71.5351999334577[/C][C]27.9510646766896[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]2014.715[/C][C]59.1546436335989[/C][C]34.0584420130912[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]2015.395[/C][C]58.7185769036305[/C][C]34.3229537614252[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]2017.895[/C][C]57.8289786418774[/C][C]34.8941836323342[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]2014.97833333333[/C][C]55.8608323254184[/C][C]36.0713983206522[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]2017.58833333333[/C][C]54.3339795510252[/C][C]37.1330859621392[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]2027.82[/C][C]50.3206275054512[/C][C]40.2979871381836[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]2026.35333333333[/C][C]49.8448518026095[/C][C]40.6532121182322[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]2027.50833333333[/C][C]48.9776450384483[/C][C]41.3966072019531[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]2038.925[/C][C]44.9471254100540[/C][C]45.3627452567617[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]2032.93[/C][C]43.9152052287415[/C][C]46.2921666746417[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]2033.13[/C][C]43.4324719900196[/C][C]46.8112890389291[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]2035.68666666667[/C][C]40.5295741547775[/C][C]50.2271911096975[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]2065.18[/C][C]35.3125370096301[/C][C]58.4829121577077[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]2066.88[/C][C]33.8422734674597[/C][C]61.0739110653237[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]2061.57333333333[/C][C]32.3063275769096[/C][C]63.8132987547246[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]2071.32[/C][C]30.6611219625114[/C][C]67.555257845181[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]2072.82[/C][C]27.6392497874591[/C][C]74.9955232482652[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]2066.13833333333[/C][C]26.4185745189618[/C][C]78.2077901989139[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]2048.005[/C][C]22.1431613736943[/C][C]92.4892776346286[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]2010.50862068966[/C][C]65.1265414109745[/C][C]30.8708028575100[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]2022.31964285714[/C][C]56.7355573715234[/C][C]35.644659831476[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]2026.54444444444[/C][C]55.0554528702869[/C][C]36.8091503891371[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]2030.83269230769[/C][C]53.160866366428[/C][C]38.2016477743146[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]2034.714[/C][C]51.1323804121444[/C][C]39.7930623139293[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]2039.64791666667[/C][C]49.2478040686223[/C][C]41.4160175309462[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]2044.44347826087[/C][C]47.3235348760118[/C][C]43.2014109600506[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]2047.68181818182[/C][C]46.0643158788462[/C][C]44.4526696883424[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]2051.49047619048[/C][C]44.5202383619404[/C][C]46.0799526613554[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]2055.4875[/C][C]42.6999090534521[/C][C]48.1379830909458[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]2058.10263157895[/C][C]41.4159084763273[/C][C]49.6935285810603[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]2061.91666666667[/C][C]39.9036819520872[/C][C]51.6723411424146[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]2066.15[/C][C]37.9071487926752[/C][C]54.5055501615369[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]2070.54375[/C][C]35.9781788530024[/C][C]57.5499876872509[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]2071.31[/C][C]34.9111510525805[/C][C]59.3308996566843[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]2071.94285714286[/C][C]33.7406720123622[/C][C]61.407871674391[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]2073.43846153846[/C][C]32.4171493440992[/C][C]63.9611595556869[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]2073.75[/C][C]30.9120368422906[/C][C]67.0855178705958[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]2073.89090909091[/C][C]29.6635884699243[/C][C]69.9136893432031[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]2075.115[/C][C]27.9880569218936[/C][C]74.1428747908807[/C][/ROW]
[ROW][C]Median[/C][C]2125.4[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]1672.2[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]2060.13225806452[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]2071.31[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]2060.13225806452[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]2071.31[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]2071.31[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]2060.13225806452[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]2071.31[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]2070.54375[/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=46943&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=46943&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 Mean1999.2316666666772.353323573670827.6315111444885
Geometric Mean1868.89822301977
Harmonic Mean1574.52842688787
Quadratic Mean2075.04035129440
Winsorized Mean ( 1 / 20 )1999.48571.535199933457727.9510646766896
Winsorized Mean ( 2 / 20 )2014.71559.154643633598934.0584420130912
Winsorized Mean ( 3 / 20 )2015.39558.718576903630534.3229537614252
Winsorized Mean ( 4 / 20 )2017.89557.828978641877434.8941836323342
Winsorized Mean ( 5 / 20 )2014.9783333333355.860832325418436.0713983206522
Winsorized Mean ( 6 / 20 )2017.5883333333354.333979551025237.1330859621392
Winsorized Mean ( 7 / 20 )2027.8250.320627505451240.2979871381836
Winsorized Mean ( 8 / 20 )2026.3533333333349.844851802609540.6532121182322
Winsorized Mean ( 9 / 20 )2027.5083333333348.977645038448341.3966072019531
Winsorized Mean ( 10 / 20 )2038.92544.947125410054045.3627452567617
Winsorized Mean ( 11 / 20 )2032.9343.915205228741546.2921666746417
Winsorized Mean ( 12 / 20 )2033.1343.432471990019646.8112890389291
Winsorized Mean ( 13 / 20 )2035.6866666666740.529574154777550.2271911096975
Winsorized Mean ( 14 / 20 )2065.1835.312537009630158.4829121577077
Winsorized Mean ( 15 / 20 )2066.8833.842273467459761.0739110653237
Winsorized Mean ( 16 / 20 )2061.5733333333332.306327576909663.8132987547246
Winsorized Mean ( 17 / 20 )2071.3230.661121962511467.555257845181
Winsorized Mean ( 18 / 20 )2072.8227.639249787459174.9955232482652
Winsorized Mean ( 19 / 20 )2066.1383333333326.418574518961878.2077901989139
Winsorized Mean ( 20 / 20 )2048.00522.143161373694392.4892776346286
Trimmed Mean ( 1 / 20 )2010.5086206896665.126541410974530.8708028575100
Trimmed Mean ( 2 / 20 )2022.3196428571456.735557371523435.644659831476
Trimmed Mean ( 3 / 20 )2026.5444444444455.055452870286936.8091503891371
Trimmed Mean ( 4 / 20 )2030.8326923076953.16086636642838.2016477743146
Trimmed Mean ( 5 / 20 )2034.71451.132380412144439.7930623139293
Trimmed Mean ( 6 / 20 )2039.6479166666749.247804068622341.4160175309462
Trimmed Mean ( 7 / 20 )2044.4434782608747.323534876011843.2014109600506
Trimmed Mean ( 8 / 20 )2047.6818181818246.064315878846244.4526696883424
Trimmed Mean ( 9 / 20 )2051.4904761904844.520238361940446.0799526613554
Trimmed Mean ( 10 / 20 )2055.487542.699909053452148.1379830909458
Trimmed Mean ( 11 / 20 )2058.1026315789541.415908476327349.6935285810603
Trimmed Mean ( 12 / 20 )2061.9166666666739.903681952087251.6723411424146
Trimmed Mean ( 13 / 20 )2066.1537.907148792675254.5055501615369
Trimmed Mean ( 14 / 20 )2070.5437535.978178853002457.5499876872509
Trimmed Mean ( 15 / 20 )2071.3134.911151052580559.3308996566843
Trimmed Mean ( 16 / 20 )2071.9428571428633.740672012362261.407871674391
Trimmed Mean ( 17 / 20 )2073.4384615384632.417149344099263.9611595556869
Trimmed Mean ( 18 / 20 )2073.7530.912036842290667.0855178705958
Trimmed Mean ( 19 / 20 )2073.8909090909129.663588469924369.9136893432031
Trimmed Mean ( 20 / 20 )2075.11527.988056921893674.1428747908807
Median2125.4
Midrange1672.2
Midmean - Weighted Average at Xnp2060.13225806452
Midmean - Weighted Average at X(n+1)p2071.31
Midmean - Empirical Distribution Function2060.13225806452
Midmean - Empirical Distribution Function - Averaging2071.31
Midmean - Empirical Distribution Function - Interpolation2071.31
Midmean - Closest Observation2060.13225806452
Midmean - True Basic - Statistics Graphics Toolkit2071.31
Midmean - MS Excel (old versions)2070.54375
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')