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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 computationSun, 28 Nov 2010 19:58:23 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2010/Nov/28/t1290974332rd2gwel03r9a8ei.htm/, Retrieved Mon, 29 Apr 2024 09:59:06 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=102719, Retrieved Mon, 29 Apr 2024 09:59:06 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact145
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
F     [Univariate Data Series] [HPC Retail Sales] [2008-03-02 15:42:48] [74be16979710d4c4e7c6647856088456]
- RMPD  [Central Tendency] [Workshop 8, Robus...] [2010-11-28 19:41:12] [d946de7cca328fbcf207448a112523ab]
-    D      [Central Tendency] [Workshop 8, Centr...] [2010-11-28 19:58:23] [23a9b79f355c69a75648521a893cf584] [Current]
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Dataseries X:
9 911
8 915
9 452
9 112
8 472
8 230
8 384
8 625
8 221
8 649
8 625
10 443
10 357
8 586
8 892
8 329
8 101
7 922
8 120
7 838
7 735
8 406
8 209
9 451
10 041
9 411
10 405
8 467
8 464
8 102
7 627
7 513
7 510
8 291
8 064
9 383
9 706
8 579
9 474
8 318
8 213
8 059
9 111
7 708
7 680
8 014
8 007
8 718
9 486
9 113
9 025
8 476
7 952
7 759
7 835
7 600
7 651
8 319
8 812
8 630




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'George Udny Yule' @ 72.249.76.132

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 2 seconds \tabularnewline
R Server & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=102719&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=102719&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=102719&T=0

As an alternative you can also use a QR Code:  

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

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'George Udny Yule' @ 72.249.76.132







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean8575.1333333333397.473361467925587.9741213824359
Geometric Mean8543.67550118091
Harmonic Mean8513.4183895635
Quadratic Mean8607.75661830654
Winsorized Mean ( 1 / 20 )8574.5597.260240989836888.160896094181
Winsorized Mean ( 2 / 20 )8575.8596.236528369717189.1122128497164
Winsorized Mean ( 3 / 20 )8561.491.348467342784293.7224263202297
Winsorized Mean ( 4 / 20 )8554.3333333333388.758542730946696.377577528104
Winsorized Mean ( 5 / 20 )8539.6666666666784.1150163161618101.523687929498
Winsorized Mean ( 6 / 20 )8520.4666666666778.7467279085858108.200897903437
Winsorized Mean ( 7 / 20 )8522.2166666666777.9111332516569109.383810900805
Winsorized Mean ( 8 / 20 )8522.4833333333376.762656041356111.023820342301
Winsorized Mean ( 9 / 20 )8533.7333333333374.868418913846113.983084685593
Winsorized Mean ( 10 / 20 )8527.5666666666773.4169324465969116.152587454802
Winsorized Mean ( 11 / 20 )8537.8333333333369.9922601316942121.982535172731
Winsorized Mean ( 12 / 20 )8489.8333333333358.631869656013144.798952909779
Winsorized Mean ( 13 / 20 )8501.5333333333356.7860115795352149.711752892277
Winsorized Mean ( 14 / 20 )8502.9333333333356.5031515878513150.486001123547
Winsorized Mean ( 15 / 20 )8492.6833333333351.0011769647434166.519359723879
Winsorized Mean ( 16 / 20 )8464.6833333333345.7572228355217184.991195024234
Winsorized Mean ( 17 / 20 )8468.6543.1358897656662196.324917510814
Winsorized Mean ( 18 / 20 )8444.9539.1863894926405215.50722353704
Winsorized Mean ( 19 / 20 )8420.8833333333333.738510006205249.592626698233
Winsorized Mean ( 20 / 20 )8427.5525.9797990297677324.388575536851
Trimmed Mean ( 1 / 20 )8561.2931034482893.657279645650291.410866681583
Trimmed Mean ( 2 / 20 )8547.0892857142989.169549854697795.8521075820368
Trimmed Mean ( 3 / 20 )8531.1111111111184.226204803423101.288086421821
Trimmed Mean ( 4 / 20 )8519.4615384615480.5311902024843105.790831068566
Trimmed Mean ( 5 / 20 )850976.9385283382594110.594785002779
Trimmed Mean ( 6 / 20 )8501.3333333333374.078244366454114.761539046181
Trimmed Mean ( 7 / 20 )8497.1739130434872.1654453446062117.745742057955
Trimmed Mean ( 8 / 20 )8492.2954545454569.8991540230261121.493536985411
Trimmed Mean ( 9 / 20 )8486.9047619047667.2339321851518126.229486898567
Trimmed Mean ( 10 / 20 )8479.164.1874039084992132.099126677365
Trimmed Mean ( 11 / 20 )8471.4473684210560.495602480205140.034102002588
Trimmed Mean ( 12 / 20 )8461.3888888888956.4076753442517150.004211966717
Trimmed Mean ( 13 / 20 )8457.2058823529454.4329999031134155.369094068049
Trimmed Mean ( 14 / 20 )8450.812552.0902101642878162.234179385088
Trimmed Mean ( 15 / 20 )8443.3666666666748.6999606630475173.375225599993
Trimmed Mean ( 16 / 20 )8436.3214285714345.6571955643656184.775287318694
Trimmed Mean ( 17 / 20 )8432.2307692307743.1054273824363195.618771956929
Trimmed Mean ( 18 / 20 )8426.87540.062465379035210.343395501812
Trimmed Mean ( 19 / 20 )8424.1363636363636.9839848020445227.777953314827
Trimmed Mean ( 20 / 20 )8424.6534.5295658972515243.98366388587
Median8435
Midrange8976.5
Midmean - Weighted Average at Xnp8429.51612903226
Midmean - Weighted Average at X(n+1)p8443.36666666667
Midmean - Empirical Distribution Function8429.51612903226
Midmean - Empirical Distribution Function - Averaging8443.36666666667
Midmean - Empirical Distribution Function - Interpolation8443.36666666667
Midmean - Closest Observation8429.51612903226
Midmean - True Basic - Statistics Graphics Toolkit8443.36666666667
Midmean - MS Excel (old versions)8450.8125
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 8575.13333333333 & 97.4733614679255 & 87.9741213824359 \tabularnewline
Geometric Mean & 8543.67550118091 &  &  \tabularnewline
Harmonic Mean & 8513.4183895635 &  &  \tabularnewline
Quadratic Mean & 8607.75661830654 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 8574.55 & 97.2602409898368 & 88.160896094181 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 8575.85 & 96.2365283697171 & 89.1122128497164 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 8561.4 & 91.3484673427842 & 93.7224263202297 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 8554.33333333333 & 88.7585427309466 & 96.377577528104 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 8539.66666666667 & 84.1150163161618 & 101.523687929498 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 8520.46666666667 & 78.7467279085858 & 108.200897903437 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 8522.21666666667 & 77.9111332516569 & 109.383810900805 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 8522.48333333333 & 76.762656041356 & 111.023820342301 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 8533.73333333333 & 74.868418913846 & 113.983084685593 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 8527.56666666667 & 73.4169324465969 & 116.152587454802 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 8537.83333333333 & 69.9922601316942 & 121.982535172731 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 8489.83333333333 & 58.631869656013 & 144.798952909779 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 8501.53333333333 & 56.7860115795352 & 149.711752892277 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 8502.93333333333 & 56.5031515878513 & 150.486001123547 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 8492.68333333333 & 51.0011769647434 & 166.519359723879 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 8464.68333333333 & 45.7572228355217 & 184.991195024234 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 8468.65 & 43.1358897656662 & 196.324917510814 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 8444.95 & 39.1863894926405 & 215.50722353704 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 8420.88333333333 & 33.738510006205 & 249.592626698233 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 8427.55 & 25.9797990297677 & 324.388575536851 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 8561.29310344828 & 93.6572796456502 & 91.410866681583 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 8547.08928571429 & 89.1695498546977 & 95.8521075820368 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 8531.11111111111 & 84.226204803423 & 101.288086421821 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 8519.46153846154 & 80.5311902024843 & 105.790831068566 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 8509 & 76.9385283382594 & 110.594785002779 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 8501.33333333333 & 74.078244366454 & 114.761539046181 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 8497.17391304348 & 72.1654453446062 & 117.745742057955 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 8492.29545454545 & 69.8991540230261 & 121.493536985411 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 8486.90476190476 & 67.2339321851518 & 126.229486898567 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 8479.1 & 64.1874039084992 & 132.099126677365 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 8471.44736842105 & 60.495602480205 & 140.034102002588 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 8461.38888888889 & 56.4076753442517 & 150.004211966717 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 8457.20588235294 & 54.4329999031134 & 155.369094068049 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 8450.8125 & 52.0902101642878 & 162.234179385088 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 8443.36666666667 & 48.6999606630475 & 173.375225599993 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 8436.32142857143 & 45.6571955643656 & 184.775287318694 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 8432.23076923077 & 43.1054273824363 & 195.618771956929 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 8426.875 & 40.062465379035 & 210.343395501812 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 8424.13636363636 & 36.9839848020445 & 227.777953314827 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 8424.65 & 34.5295658972515 & 243.98366388587 \tabularnewline
Median & 8435 &  &  \tabularnewline
Midrange & 8976.5 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 8429.51612903226 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 8443.36666666667 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 8429.51612903226 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 8443.36666666667 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 8443.36666666667 &  &  \tabularnewline
Midmean - Closest Observation & 8429.51612903226 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 8443.36666666667 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 8450.8125 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=102719&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]8575.13333333333[/C][C]97.4733614679255[/C][C]87.9741213824359[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]8543.67550118091[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]8513.4183895635[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]8607.75661830654[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]8574.55[/C][C]97.2602409898368[/C][C]88.160896094181[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]8575.85[/C][C]96.2365283697171[/C][C]89.1122128497164[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]8561.4[/C][C]91.3484673427842[/C][C]93.7224263202297[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]8554.33333333333[/C][C]88.7585427309466[/C][C]96.377577528104[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]8539.66666666667[/C][C]84.1150163161618[/C][C]101.523687929498[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]8520.46666666667[/C][C]78.7467279085858[/C][C]108.200897903437[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]8522.21666666667[/C][C]77.9111332516569[/C][C]109.383810900805[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]8522.48333333333[/C][C]76.762656041356[/C][C]111.023820342301[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]8533.73333333333[/C][C]74.868418913846[/C][C]113.983084685593[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]8527.56666666667[/C][C]73.4169324465969[/C][C]116.152587454802[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]8537.83333333333[/C][C]69.9922601316942[/C][C]121.982535172731[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]8489.83333333333[/C][C]58.631869656013[/C][C]144.798952909779[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]8501.53333333333[/C][C]56.7860115795352[/C][C]149.711752892277[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]8502.93333333333[/C][C]56.5031515878513[/C][C]150.486001123547[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]8492.68333333333[/C][C]51.0011769647434[/C][C]166.519359723879[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]8464.68333333333[/C][C]45.7572228355217[/C][C]184.991195024234[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]8468.65[/C][C]43.1358897656662[/C][C]196.324917510814[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]8444.95[/C][C]39.1863894926405[/C][C]215.50722353704[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]8420.88333333333[/C][C]33.738510006205[/C][C]249.592626698233[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]8427.55[/C][C]25.9797990297677[/C][C]324.388575536851[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]8561.29310344828[/C][C]93.6572796456502[/C][C]91.410866681583[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]8547.08928571429[/C][C]89.1695498546977[/C][C]95.8521075820368[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]8531.11111111111[/C][C]84.226204803423[/C][C]101.288086421821[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]8519.46153846154[/C][C]80.5311902024843[/C][C]105.790831068566[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]8509[/C][C]76.9385283382594[/C][C]110.594785002779[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]8501.33333333333[/C][C]74.078244366454[/C][C]114.761539046181[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]8497.17391304348[/C][C]72.1654453446062[/C][C]117.745742057955[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]8492.29545454545[/C][C]69.8991540230261[/C][C]121.493536985411[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]8486.90476190476[/C][C]67.2339321851518[/C][C]126.229486898567[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]8479.1[/C][C]64.1874039084992[/C][C]132.099126677365[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]8471.44736842105[/C][C]60.495602480205[/C][C]140.034102002588[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]8461.38888888889[/C][C]56.4076753442517[/C][C]150.004211966717[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]8457.20588235294[/C][C]54.4329999031134[/C][C]155.369094068049[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]8450.8125[/C][C]52.0902101642878[/C][C]162.234179385088[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]8443.36666666667[/C][C]48.6999606630475[/C][C]173.375225599993[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]8436.32142857143[/C][C]45.6571955643656[/C][C]184.775287318694[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]8432.23076923077[/C][C]43.1054273824363[/C][C]195.618771956929[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]8426.875[/C][C]40.062465379035[/C][C]210.343395501812[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]8424.13636363636[/C][C]36.9839848020445[/C][C]227.777953314827[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]8424.65[/C][C]34.5295658972515[/C][C]243.98366388587[/C][/ROW]
[ROW][C]Median[/C][C]8435[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]8976.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]8429.51612903226[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]8443.36666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]8429.51612903226[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]8443.36666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]8443.36666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]8429.51612903226[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]8443.36666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]8450.8125[/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=102719&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=102719&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 Mean8575.1333333333397.473361467925587.9741213824359
Geometric Mean8543.67550118091
Harmonic Mean8513.4183895635
Quadratic Mean8607.75661830654
Winsorized Mean ( 1 / 20 )8574.5597.260240989836888.160896094181
Winsorized Mean ( 2 / 20 )8575.8596.236528369717189.1122128497164
Winsorized Mean ( 3 / 20 )8561.491.348467342784293.7224263202297
Winsorized Mean ( 4 / 20 )8554.3333333333388.758542730946696.377577528104
Winsorized Mean ( 5 / 20 )8539.6666666666784.1150163161618101.523687929498
Winsorized Mean ( 6 / 20 )8520.4666666666778.7467279085858108.200897903437
Winsorized Mean ( 7 / 20 )8522.2166666666777.9111332516569109.383810900805
Winsorized Mean ( 8 / 20 )8522.4833333333376.762656041356111.023820342301
Winsorized Mean ( 9 / 20 )8533.7333333333374.868418913846113.983084685593
Winsorized Mean ( 10 / 20 )8527.5666666666773.4169324465969116.152587454802
Winsorized Mean ( 11 / 20 )8537.8333333333369.9922601316942121.982535172731
Winsorized Mean ( 12 / 20 )8489.8333333333358.631869656013144.798952909779
Winsorized Mean ( 13 / 20 )8501.5333333333356.7860115795352149.711752892277
Winsorized Mean ( 14 / 20 )8502.9333333333356.5031515878513150.486001123547
Winsorized Mean ( 15 / 20 )8492.6833333333351.0011769647434166.519359723879
Winsorized Mean ( 16 / 20 )8464.6833333333345.7572228355217184.991195024234
Winsorized Mean ( 17 / 20 )8468.6543.1358897656662196.324917510814
Winsorized Mean ( 18 / 20 )8444.9539.1863894926405215.50722353704
Winsorized Mean ( 19 / 20 )8420.8833333333333.738510006205249.592626698233
Winsorized Mean ( 20 / 20 )8427.5525.9797990297677324.388575536851
Trimmed Mean ( 1 / 20 )8561.2931034482893.657279645650291.410866681583
Trimmed Mean ( 2 / 20 )8547.0892857142989.169549854697795.8521075820368
Trimmed Mean ( 3 / 20 )8531.1111111111184.226204803423101.288086421821
Trimmed Mean ( 4 / 20 )8519.4615384615480.5311902024843105.790831068566
Trimmed Mean ( 5 / 20 )850976.9385283382594110.594785002779
Trimmed Mean ( 6 / 20 )8501.3333333333374.078244366454114.761539046181
Trimmed Mean ( 7 / 20 )8497.1739130434872.1654453446062117.745742057955
Trimmed Mean ( 8 / 20 )8492.2954545454569.8991540230261121.493536985411
Trimmed Mean ( 9 / 20 )8486.9047619047667.2339321851518126.229486898567
Trimmed Mean ( 10 / 20 )8479.164.1874039084992132.099126677365
Trimmed Mean ( 11 / 20 )8471.4473684210560.495602480205140.034102002588
Trimmed Mean ( 12 / 20 )8461.3888888888956.4076753442517150.004211966717
Trimmed Mean ( 13 / 20 )8457.2058823529454.4329999031134155.369094068049
Trimmed Mean ( 14 / 20 )8450.812552.0902101642878162.234179385088
Trimmed Mean ( 15 / 20 )8443.3666666666748.6999606630475173.375225599993
Trimmed Mean ( 16 / 20 )8436.3214285714345.6571955643656184.775287318694
Trimmed Mean ( 17 / 20 )8432.2307692307743.1054273824363195.618771956929
Trimmed Mean ( 18 / 20 )8426.87540.062465379035210.343395501812
Trimmed Mean ( 19 / 20 )8424.1363636363636.9839848020445227.777953314827
Trimmed Mean ( 20 / 20 )8424.6534.5295658972515243.98366388587
Median8435
Midrange8976.5
Midmean - Weighted Average at Xnp8429.51612903226
Midmean - Weighted Average at X(n+1)p8443.36666666667
Midmean - Empirical Distribution Function8429.51612903226
Midmean - Empirical Distribution Function - Averaging8443.36666666667
Midmean - Empirical Distribution Function - Interpolation8443.36666666667
Midmean - Closest Observation8429.51612903226
Midmean - True Basic - Statistics Graphics Toolkit8443.36666666667
Midmean - MS Excel (old versions)8450.8125
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')