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of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationWed, 20 Oct 2010 10:54:19 +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/Oct/20/t1287572039xqmwnvorthap1gy.htm/, Retrieved Sat, 04 May 2024 00:32:32 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=87153, Retrieved Sat, 04 May 2024 00:32:32 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDGP1W52
Estimated Impact119
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [] [opgave 5 grafiek 1] [1970-01-01 00:00:00] [cdbe0c453eb9effe5ed0ab336cdc30fc]
- RM D    [Central Tendency] [opgave 5 oefening 2] [2010-10-20 10:54:19] [49c40d716750d950b45a50638ed38982] [Current]
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Dataseries X:
1590
1798
1935
1887
2027
2080
1556
1682
1785
1869
1781
2082
2571
1862
1938
1505
1767
1607
1578
1495
1615
1700
1337
1531
1623
1543
1640
1524
1429
1827
1603
1351
1267
1742
1384
1392
1649
1665
1526
1717
1391
1790
1472
1350
1704
1391
1190
1351
1160
1236
1444
1257
1193
1701
1428
1611
1431
1472
1240
1276




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=87153&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=87153&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=87153&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 Mean1592.4666666666733.945065846038746.9130528097798
Geometric Mean1572.27472235764
Harmonic Mean1552.99906068468
Quadratic Mean1613.67092886582
Winsorized Mean ( 1 / 20 )1584.8166666666730.682366636401251.6523606359119
Winsorized Mean ( 2 / 20 )1584.8530.642340127258251.7209192711161
Winsorized Mean ( 3 / 20 )1584.3529.493356764199353.7188768530809
Winsorized Mean ( 4 / 20 )1578.6833333333328.037530252084256.3060768598184
Winsorized Mean ( 5 / 20 )1579.8527.698220638764457.03795996877
Winsorized Mean ( 6 / 20 )1576.0526.500756038676959.4718881868809
Winsorized Mean ( 7 / 20 )157525.883135883502360.8504319990027
Winsorized Mean ( 8 / 20 )1582.224.20413187866965.369004264697
Winsorized Mean ( 9 / 20 )1578.922.873487724393269.0275142568747
Winsorized Mean ( 10 / 20 )1574.2333333333321.983254626930671.6105672271482
Winsorized Mean ( 11 / 20 )1572.7666666666721.732481959685672.3693993895495
Winsorized Mean ( 12 / 20 )1578.3666666666720.458887625247977.1482152684994
Winsorized Mean ( 13 / 20 )1579.0166666666720.068237991484578.6823769648678
Winsorized Mean ( 14 / 20 )1575.7519.518246207798780.7321509947135
Winsorized Mean ( 15 / 20 )1569.7518.464007207182685.0167562428894
Winsorized Mean ( 16 / 20 )1572.6833333333315.896087207619498.9352482024323
Winsorized Mean ( 17 / 20 )1569.2833333333315.2936989289812102.609796401810
Winsorized Mean ( 18 / 20 )1568.9833333333315.0664721438870104.137406444542
Winsorized Mean ( 19 / 20 )1572.7833333333314.3872803927571109.317625735932
Winsorized Mean ( 20 / 20 )1576.1166666666712.1014798475617130.241647015116
Trimmed Mean ( 1 / 20 )1583.0517241379329.766843741590053.1817124408829
Trimmed Mean ( 2 / 20 )1581.1607142857128.636161146102155.215526488296
Trimmed Mean ( 3 / 20 )1579.1111111111127.254753163396557.9389254286801
Trimmed Mean ( 4 / 20 )1577.0961538461526.106107588173160.4110033837687
Trimmed Mean ( 5 / 20 )1576.6225.262037179312762.410643639267
Trimmed Mean ( 6 / 20 )1575.812524.306820108104064.8300556383603
Trimmed Mean ( 7 / 20 )1575.7608695652223.474627782957867.1261280108217
Trimmed Mean ( 8 / 20 )1575.9090909090922.582285948725369.7851889081248
Trimmed Mean ( 9 / 20 )1574.7857142857121.899690431954371.9090399555562
Trimmed Mean ( 10 / 20 )1574.121.359343118680873.6960865909446
Trimmed Mean ( 11 / 20 )1574.0789473684220.859905990240975.4595417690203
Trimmed Mean ( 12 / 20 )1574.2777777777820.225185113486177.83749661347
Trimmed Mean ( 13 / 20 )1573.6764705882419.685391879639279.9413331576043
Trimmed Mean ( 14 / 20 )1572.9062519.008134897677582.7491102344913
Trimmed Mean ( 15 / 20 )1572.518.183341498359986.4802544758804
Trimmed Mean ( 16 / 20 )1572.8928571428617.302807314638290.9039110556462
Trimmed Mean ( 17 / 20 )1572.9230769230816.851196997147993.341919698007
Trimmed Mean ( 18 / 20 )1573.4583333333316.300726751677496.5268823472194
Trimmed Mean ( 19 / 20 )1574.1363636363615.4375288287998101.96815702133
Trimmed Mean ( 20 / 20 )1574.3514.2648399183004110.365767090051
Median1584
Midrange1865.5
Midmean - Weighted Average at Xnp1561.15625
Midmean - Weighted Average at X(n+1)p1572.5
Midmean - Empirical Distribution Function1561.15625
Midmean - Empirical Distribution Function - Averaging1572.5
Midmean - Empirical Distribution Function - Interpolation1572.5
Midmean - Closest Observation1561.15625
Midmean - True Basic - Statistics Graphics Toolkit1572.5
Midmean - MS Excel (old versions)1567.39393939394
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 1592.46666666667 & 33.9450658460387 & 46.9130528097798 \tabularnewline
Geometric Mean & 1572.27472235764 &  &  \tabularnewline
Harmonic Mean & 1552.99906068468 &  &  \tabularnewline
Quadratic Mean & 1613.67092886582 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 1584.81666666667 & 30.6823666364012 & 51.6523606359119 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 1584.85 & 30.6423401272582 & 51.7209192711161 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 1584.35 & 29.4933567641993 & 53.7188768530809 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 1578.68333333333 & 28.0375302520842 & 56.3060768598184 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 1579.85 & 27.6982206387644 & 57.03795996877 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 1576.05 & 26.5007560386769 & 59.4718881868809 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 1575 & 25.8831358835023 & 60.8504319990027 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 1582.2 & 24.204131878669 & 65.369004264697 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 1578.9 & 22.8734877243932 & 69.0275142568747 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 1574.23333333333 & 21.9832546269306 & 71.6105672271482 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 1572.76666666667 & 21.7324819596856 & 72.3693993895495 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 1578.36666666667 & 20.4588876252479 & 77.1482152684994 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 1579.01666666667 & 20.0682379914845 & 78.6823769648678 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 1575.75 & 19.5182462077987 & 80.7321509947135 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 1569.75 & 18.4640072071826 & 85.0167562428894 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 1572.68333333333 & 15.8960872076194 & 98.9352482024323 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 1569.28333333333 & 15.2936989289812 & 102.609796401810 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 1568.98333333333 & 15.0664721438870 & 104.137406444542 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 1572.78333333333 & 14.3872803927571 & 109.317625735932 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 1576.11666666667 & 12.1014798475617 & 130.241647015116 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 1583.05172413793 & 29.7668437415900 & 53.1817124408829 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 1581.16071428571 & 28.6361611461021 & 55.215526488296 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 1579.11111111111 & 27.2547531633965 & 57.9389254286801 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 1577.09615384615 & 26.1061075881731 & 60.4110033837687 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 1576.62 & 25.2620371793127 & 62.410643639267 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 1575.8125 & 24.3068201081040 & 64.8300556383603 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 1575.76086956522 & 23.4746277829578 & 67.1261280108217 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 1575.90909090909 & 22.5822859487253 & 69.7851889081248 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 1574.78571428571 & 21.8996904319543 & 71.9090399555562 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 1574.1 & 21.3593431186808 & 73.6960865909446 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 1574.07894736842 & 20.8599059902409 & 75.4595417690203 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 1574.27777777778 & 20.2251851134861 & 77.83749661347 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 1573.67647058824 & 19.6853918796392 & 79.9413331576043 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 1572.90625 & 19.0081348976775 & 82.7491102344913 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 1572.5 & 18.1833414983599 & 86.4802544758804 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 1572.89285714286 & 17.3028073146382 & 90.9039110556462 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 1572.92307692308 & 16.8511969971479 & 93.341919698007 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 1573.45833333333 & 16.3007267516774 & 96.5268823472194 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 1574.13636363636 & 15.4375288287998 & 101.96815702133 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 1574.35 & 14.2648399183004 & 110.365767090051 \tabularnewline
Median & 1584 &  &  \tabularnewline
Midrange & 1865.5 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 1561.15625 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 1572.5 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 1561.15625 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 1572.5 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 1572.5 &  &  \tabularnewline
Midmean - Closest Observation & 1561.15625 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 1572.5 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 1567.39393939394 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=87153&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]1592.46666666667[/C][C]33.9450658460387[/C][C]46.9130528097798[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]1572.27472235764[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]1552.99906068468[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]1613.67092886582[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]1584.81666666667[/C][C]30.6823666364012[/C][C]51.6523606359119[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]1584.85[/C][C]30.6423401272582[/C][C]51.7209192711161[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]1584.35[/C][C]29.4933567641993[/C][C]53.7188768530809[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]1578.68333333333[/C][C]28.0375302520842[/C][C]56.3060768598184[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]1579.85[/C][C]27.6982206387644[/C][C]57.03795996877[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]1576.05[/C][C]26.5007560386769[/C][C]59.4718881868809[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]1575[/C][C]25.8831358835023[/C][C]60.8504319990027[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]1582.2[/C][C]24.204131878669[/C][C]65.369004264697[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]1578.9[/C][C]22.8734877243932[/C][C]69.0275142568747[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]1574.23333333333[/C][C]21.9832546269306[/C][C]71.6105672271482[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]1572.76666666667[/C][C]21.7324819596856[/C][C]72.3693993895495[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]1578.36666666667[/C][C]20.4588876252479[/C][C]77.1482152684994[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]1579.01666666667[/C][C]20.0682379914845[/C][C]78.6823769648678[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]1575.75[/C][C]19.5182462077987[/C][C]80.7321509947135[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]1569.75[/C][C]18.4640072071826[/C][C]85.0167562428894[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]1572.68333333333[/C][C]15.8960872076194[/C][C]98.9352482024323[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]1569.28333333333[/C][C]15.2936989289812[/C][C]102.609796401810[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]1568.98333333333[/C][C]15.0664721438870[/C][C]104.137406444542[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]1572.78333333333[/C][C]14.3872803927571[/C][C]109.317625735932[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]1576.11666666667[/C][C]12.1014798475617[/C][C]130.241647015116[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]1583.05172413793[/C][C]29.7668437415900[/C][C]53.1817124408829[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]1581.16071428571[/C][C]28.6361611461021[/C][C]55.215526488296[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]1579.11111111111[/C][C]27.2547531633965[/C][C]57.9389254286801[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]1577.09615384615[/C][C]26.1061075881731[/C][C]60.4110033837687[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]1576.62[/C][C]25.2620371793127[/C][C]62.410643639267[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]1575.8125[/C][C]24.3068201081040[/C][C]64.8300556383603[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]1575.76086956522[/C][C]23.4746277829578[/C][C]67.1261280108217[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]1575.90909090909[/C][C]22.5822859487253[/C][C]69.7851889081248[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]1574.78571428571[/C][C]21.8996904319543[/C][C]71.9090399555562[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]1574.1[/C][C]21.3593431186808[/C][C]73.6960865909446[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]1574.07894736842[/C][C]20.8599059902409[/C][C]75.4595417690203[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]1574.27777777778[/C][C]20.2251851134861[/C][C]77.83749661347[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]1573.67647058824[/C][C]19.6853918796392[/C][C]79.9413331576043[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]1572.90625[/C][C]19.0081348976775[/C][C]82.7491102344913[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]1572.5[/C][C]18.1833414983599[/C][C]86.4802544758804[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]1572.89285714286[/C][C]17.3028073146382[/C][C]90.9039110556462[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]1572.92307692308[/C][C]16.8511969971479[/C][C]93.341919698007[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]1573.45833333333[/C][C]16.3007267516774[/C][C]96.5268823472194[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]1574.13636363636[/C][C]15.4375288287998[/C][C]101.96815702133[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]1574.35[/C][C]14.2648399183004[/C][C]110.365767090051[/C][/ROW]
[ROW][C]Median[/C][C]1584[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]1865.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]1561.15625[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]1572.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]1561.15625[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]1572.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]1572.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]1561.15625[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]1572.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]1567.39393939394[/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=87153&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=87153&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 Mean1592.4666666666733.945065846038746.9130528097798
Geometric Mean1572.27472235764
Harmonic Mean1552.99906068468
Quadratic Mean1613.67092886582
Winsorized Mean ( 1 / 20 )1584.8166666666730.682366636401251.6523606359119
Winsorized Mean ( 2 / 20 )1584.8530.642340127258251.7209192711161
Winsorized Mean ( 3 / 20 )1584.3529.493356764199353.7188768530809
Winsorized Mean ( 4 / 20 )1578.6833333333328.037530252084256.3060768598184
Winsorized Mean ( 5 / 20 )1579.8527.698220638764457.03795996877
Winsorized Mean ( 6 / 20 )1576.0526.500756038676959.4718881868809
Winsorized Mean ( 7 / 20 )157525.883135883502360.8504319990027
Winsorized Mean ( 8 / 20 )1582.224.20413187866965.369004264697
Winsorized Mean ( 9 / 20 )1578.922.873487724393269.0275142568747
Winsorized Mean ( 10 / 20 )1574.2333333333321.983254626930671.6105672271482
Winsorized Mean ( 11 / 20 )1572.7666666666721.732481959685672.3693993895495
Winsorized Mean ( 12 / 20 )1578.3666666666720.458887625247977.1482152684994
Winsorized Mean ( 13 / 20 )1579.0166666666720.068237991484578.6823769648678
Winsorized Mean ( 14 / 20 )1575.7519.518246207798780.7321509947135
Winsorized Mean ( 15 / 20 )1569.7518.464007207182685.0167562428894
Winsorized Mean ( 16 / 20 )1572.6833333333315.896087207619498.9352482024323
Winsorized Mean ( 17 / 20 )1569.2833333333315.2936989289812102.609796401810
Winsorized Mean ( 18 / 20 )1568.9833333333315.0664721438870104.137406444542
Winsorized Mean ( 19 / 20 )1572.7833333333314.3872803927571109.317625735932
Winsorized Mean ( 20 / 20 )1576.1166666666712.1014798475617130.241647015116
Trimmed Mean ( 1 / 20 )1583.0517241379329.766843741590053.1817124408829
Trimmed Mean ( 2 / 20 )1581.1607142857128.636161146102155.215526488296
Trimmed Mean ( 3 / 20 )1579.1111111111127.254753163396557.9389254286801
Trimmed Mean ( 4 / 20 )1577.0961538461526.106107588173160.4110033837687
Trimmed Mean ( 5 / 20 )1576.6225.262037179312762.410643639267
Trimmed Mean ( 6 / 20 )1575.812524.306820108104064.8300556383603
Trimmed Mean ( 7 / 20 )1575.7608695652223.474627782957867.1261280108217
Trimmed Mean ( 8 / 20 )1575.9090909090922.582285948725369.7851889081248
Trimmed Mean ( 9 / 20 )1574.7857142857121.899690431954371.9090399555562
Trimmed Mean ( 10 / 20 )1574.121.359343118680873.6960865909446
Trimmed Mean ( 11 / 20 )1574.0789473684220.859905990240975.4595417690203
Trimmed Mean ( 12 / 20 )1574.2777777777820.225185113486177.83749661347
Trimmed Mean ( 13 / 20 )1573.6764705882419.685391879639279.9413331576043
Trimmed Mean ( 14 / 20 )1572.9062519.008134897677582.7491102344913
Trimmed Mean ( 15 / 20 )1572.518.183341498359986.4802544758804
Trimmed Mean ( 16 / 20 )1572.8928571428617.302807314638290.9039110556462
Trimmed Mean ( 17 / 20 )1572.9230769230816.851196997147993.341919698007
Trimmed Mean ( 18 / 20 )1573.4583333333316.300726751677496.5268823472194
Trimmed Mean ( 19 / 20 )1574.1363636363615.4375288287998101.96815702133
Trimmed Mean ( 20 / 20 )1574.3514.2648399183004110.365767090051
Median1584
Midrange1865.5
Midmean - Weighted Average at Xnp1561.15625
Midmean - Weighted Average at X(n+1)p1572.5
Midmean - Empirical Distribution Function1561.15625
Midmean - Empirical Distribution Function - Averaging1572.5
Midmean - Empirical Distribution Function - Interpolation1572.5
Midmean - Closest Observation1561.15625
Midmean - True Basic - Statistics Graphics Toolkit1572.5
Midmean - MS Excel (old versions)1567.39393939394
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')