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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 computationSat, 11 Dec 2010 13:04:54 +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/Dec/11/t12920725970yydwyyqw37zr42.htm/, Retrieved Mon, 06 May 2024 19:28:21 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=108116, Retrieved Mon, 06 May 2024 19:28:21 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact116
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
F     [Central Tendency] [Time needed to su...] [2010-09-25 09:42:08] [b98453cac15ba1066b407e146608df68]
-    D    [Central Tendency] [Central tendency ...] [2010-12-11 13:04:54] [de8ccb310fbbdc3d90ae577a3e011cf9] [Current]
-    D      [Central Tendency] [Central tendency ...] [2010-12-11 13:36:47] [04d4386fa51dbd2ef12d0f1f80644886]
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Dataseries X:
1606
1634
2013
1654
1003
1029
1052
1653
1918
1926
1862
1816
1712
1646
1555
1402
1047
891
940
1372
2012
1879
1667
1856
1771
1721
1773
1507
1033
1011
1111
1736
1865
2078
1947
1428
1500
1950
1591
1613
1077
880
1128
1320
1692
1575
1478
1500
1368
1563
1424
1274
1047
1049
1069
981
1540
1559
1459
1559




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=108116&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=108116&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=108116&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 Mean1488.743.244465372007234.4252145839605
Geometric Mean1448.76874694900
Harmonic Mean1406.54934315307
Quadratic Mean1525.30738978520
Winsorized Mean ( 1 / 20 )1487.842.96363460305834.6292862264987
Winsorized Mean ( 2 / 20 )1489.442.585807030652634.974093573663
Winsorized Mean ( 3 / 20 )1488.3541.534546406548635.8340256188602
Winsorized Mean ( 4 / 20 )1489.6166666666741.198232996957136.1572950659484
Winsorized Mean ( 5 / 20 )1488.5333333333340.741353570691936.5361776886112
Winsorized Mean ( 6 / 20 )1489.5333333333340.242979993965737.0134948643635
Winsorized Mean ( 7 / 20 )1485.4539.355854595732737.7440666772122
Winsorized Mean ( 8 / 20 )1485.4538.68122236016938.4023541492216
Winsorized Mean ( 9 / 20 )148538.606562481871738.4649630667662
Winsorized Mean ( 10 / 20 )1484.3333333333338.377640814684538.6770343831395
Winsorized Mean ( 11 / 20 )1477.5537.101954697466839.8240473324949
Winsorized Mean ( 12 / 20 )1472.3535.15154298997841.8857857938065
Winsorized Mean ( 13 / 20 )1473.6534.752497166707842.4041470439059
Winsorized Mean ( 14 / 20 )1473.4166666666732.065005404070845.9509252563422
Winsorized Mean ( 15 / 20 )1473.9166666666730.736728720978847.9529451571296
Winsorized Mean ( 16 / 20 )1510.4523.285205712742764.8673676596902
Winsorized Mean ( 17 / 20 )1517.8166666666720.252955307355374.9429722049224
Winsorized Mean ( 18 / 20 )1524.7166666666716.835177920975090.5673034062215
Winsorized Mean ( 19 / 20 )1521.8666666666716.052851739308594.8035085217966
Winsorized Mean ( 20 / 20 )1531.5333333333314.4535583300185105.962372611906
Trimmed Mean ( 1 / 20 )1489.0344827586242.253161807237035.2407824425480
Trimmed Mean ( 2 / 20 )1490.3571428571441.364772864567936.0296223005191
Trimmed Mean ( 3 / 20 )1490.8888888888940.502596017830236.8097118572983
Trimmed Mean ( 4 / 20 )1491.8653846153839.910240814922337.3805157311298
Trimmed Mean ( 5 / 20 )1492.5439.268923268837938.0081722583011
Trimmed Mean ( 6 / 20 )1493.5416666666738.581921665120938.7109195760166
Trimmed Mean ( 7 / 20 )1494.4130434782637.828772324025439.5046667303328
Trimmed Mean ( 8 / 20 )1496.1590909090937.079281142495340.3502723032674
Trimmed Mean ( 9 / 20 )1498.0714285714336.254030059246541.3215144943410
Trimmed Mean ( 10 / 20 )1500.2535.148216389805842.6835314589426
Trimmed Mean ( 11 / 20 )1502.7631578947433.700155421097944.592172917812
Trimmed Mean ( 12 / 20 )1506.5833333333332.058537109283446.9947623685256
Trimmed Mean ( 13 / 20 )1511.6176470588230.32277385809249.85090262959
Trimmed Mean ( 14 / 20 )1517.0937527.942097365651254.2941973949651
Trimmed Mean ( 15 / 20 )1523.3333333333325.382468985517760.0151756002339
Trimmed Mean ( 16 / 20 )1530.3928571428621.935411398982969.7681401687235
Trimmed Mean ( 17 / 20 )1533.2692307692320.184728247808375.961846597351
Trimmed Mean ( 18 / 20 )1535.5416666666718.748041363078281.9041113111002
Trimmed Mean ( 19 / 20 )1537.1818181818217.935144869434585.7078004873838
Trimmed Mean ( 20 / 20 )1539.616.824387061643691.510020208106
Median1557
Midrange1479
Midmean - Weighted Average at Xnp1510.03225806452
Midmean - Weighted Average at X(n+1)p1523.33333333333
Midmean - Empirical Distribution Function1510.03225806452
Midmean - Empirical Distribution Function - Averaging1523.33333333333
Midmean - Empirical Distribution Function - Interpolation1523.33333333333
Midmean - Closest Observation1510.03225806452
Midmean - True Basic - Statistics Graphics Toolkit1523.33333333333
Midmean - MS Excel (old versions)1517.09375
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 1488.7 & 43.2444653720072 & 34.4252145839605 \tabularnewline
Geometric Mean & 1448.76874694900 &  &  \tabularnewline
Harmonic Mean & 1406.54934315307 &  &  \tabularnewline
Quadratic Mean & 1525.30738978520 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 1487.8 & 42.963634603058 & 34.6292862264987 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 1489.4 & 42.5858070306526 & 34.974093573663 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 1488.35 & 41.5345464065486 & 35.8340256188602 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 1489.61666666667 & 41.1982329969571 & 36.1572950659484 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 1488.53333333333 & 40.7413535706919 & 36.5361776886112 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 1489.53333333333 & 40.2429799939657 & 37.0134948643635 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 1485.45 & 39.3558545957327 & 37.7440666772122 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 1485.45 & 38.681222360169 & 38.4023541492216 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 1485 & 38.6065624818717 & 38.4649630667662 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 1484.33333333333 & 38.3776408146845 & 38.6770343831395 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 1477.55 & 37.1019546974668 & 39.8240473324949 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 1472.35 & 35.151542989978 & 41.8857857938065 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 1473.65 & 34.7524971667078 & 42.4041470439059 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 1473.41666666667 & 32.0650054040708 & 45.9509252563422 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 1473.91666666667 & 30.7367287209788 & 47.9529451571296 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 1510.45 & 23.2852057127427 & 64.8673676596902 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 1517.81666666667 & 20.2529553073553 & 74.9429722049224 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 1524.71666666667 & 16.8351779209750 & 90.5673034062215 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 1521.86666666667 & 16.0528517393085 & 94.8035085217966 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 1531.53333333333 & 14.4535583300185 & 105.962372611906 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 1489.03448275862 & 42.2531618072370 & 35.2407824425480 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 1490.35714285714 & 41.3647728645679 & 36.0296223005191 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 1490.88888888889 & 40.5025960178302 & 36.8097118572983 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 1491.86538461538 & 39.9102408149223 & 37.3805157311298 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 1492.54 & 39.2689232688379 & 38.0081722583011 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 1493.54166666667 & 38.5819216651209 & 38.7109195760166 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 1494.41304347826 & 37.8287723240254 & 39.5046667303328 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 1496.15909090909 & 37.0792811424953 & 40.3502723032674 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 1498.07142857143 & 36.2540300592465 & 41.3215144943410 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 1500.25 & 35.1482163898058 & 42.6835314589426 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 1502.76315789474 & 33.7001554210979 & 44.592172917812 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 1506.58333333333 & 32.0585371092834 & 46.9947623685256 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 1511.61764705882 & 30.322773858092 & 49.85090262959 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 1517.09375 & 27.9420973656512 & 54.2941973949651 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 1523.33333333333 & 25.3824689855177 & 60.0151756002339 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 1530.39285714286 & 21.9354113989829 & 69.7681401687235 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 1533.26923076923 & 20.1847282478083 & 75.961846597351 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 1535.54166666667 & 18.7480413630782 & 81.9041113111002 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 1537.18181818182 & 17.9351448694345 & 85.7078004873838 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 1539.6 & 16.8243870616436 & 91.510020208106 \tabularnewline
Median & 1557 &  &  \tabularnewline
Midrange & 1479 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 1510.03225806452 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 1523.33333333333 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 1510.03225806452 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 1523.33333333333 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 1523.33333333333 &  &  \tabularnewline
Midmean - Closest Observation & 1510.03225806452 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 1523.33333333333 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 1517.09375 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=108116&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]1488.7[/C][C]43.2444653720072[/C][C]34.4252145839605[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]1448.76874694900[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]1406.54934315307[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]1525.30738978520[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]1487.8[/C][C]42.963634603058[/C][C]34.6292862264987[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]1489.4[/C][C]42.5858070306526[/C][C]34.974093573663[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]1488.35[/C][C]41.5345464065486[/C][C]35.8340256188602[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]1489.61666666667[/C][C]41.1982329969571[/C][C]36.1572950659484[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]1488.53333333333[/C][C]40.7413535706919[/C][C]36.5361776886112[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]1489.53333333333[/C][C]40.2429799939657[/C][C]37.0134948643635[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]1485.45[/C][C]39.3558545957327[/C][C]37.7440666772122[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]1485.45[/C][C]38.681222360169[/C][C]38.4023541492216[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]1485[/C][C]38.6065624818717[/C][C]38.4649630667662[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]1484.33333333333[/C][C]38.3776408146845[/C][C]38.6770343831395[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]1477.55[/C][C]37.1019546974668[/C][C]39.8240473324949[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]1472.35[/C][C]35.151542989978[/C][C]41.8857857938065[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]1473.65[/C][C]34.7524971667078[/C][C]42.4041470439059[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]1473.41666666667[/C][C]32.0650054040708[/C][C]45.9509252563422[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]1473.91666666667[/C][C]30.7367287209788[/C][C]47.9529451571296[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]1510.45[/C][C]23.2852057127427[/C][C]64.8673676596902[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]1517.81666666667[/C][C]20.2529553073553[/C][C]74.9429722049224[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]1524.71666666667[/C][C]16.8351779209750[/C][C]90.5673034062215[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]1521.86666666667[/C][C]16.0528517393085[/C][C]94.8035085217966[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]1531.53333333333[/C][C]14.4535583300185[/C][C]105.962372611906[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]1489.03448275862[/C][C]42.2531618072370[/C][C]35.2407824425480[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]1490.35714285714[/C][C]41.3647728645679[/C][C]36.0296223005191[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]1490.88888888889[/C][C]40.5025960178302[/C][C]36.8097118572983[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]1491.86538461538[/C][C]39.9102408149223[/C][C]37.3805157311298[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]1492.54[/C][C]39.2689232688379[/C][C]38.0081722583011[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]1493.54166666667[/C][C]38.5819216651209[/C][C]38.7109195760166[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]1494.41304347826[/C][C]37.8287723240254[/C][C]39.5046667303328[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]1496.15909090909[/C][C]37.0792811424953[/C][C]40.3502723032674[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]1498.07142857143[/C][C]36.2540300592465[/C][C]41.3215144943410[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]1500.25[/C][C]35.1482163898058[/C][C]42.6835314589426[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]1502.76315789474[/C][C]33.7001554210979[/C][C]44.592172917812[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]1506.58333333333[/C][C]32.0585371092834[/C][C]46.9947623685256[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]1511.61764705882[/C][C]30.322773858092[/C][C]49.85090262959[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]1517.09375[/C][C]27.9420973656512[/C][C]54.2941973949651[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]1523.33333333333[/C][C]25.3824689855177[/C][C]60.0151756002339[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]1530.39285714286[/C][C]21.9354113989829[/C][C]69.7681401687235[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]1533.26923076923[/C][C]20.1847282478083[/C][C]75.961846597351[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]1535.54166666667[/C][C]18.7480413630782[/C][C]81.9041113111002[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]1537.18181818182[/C][C]17.9351448694345[/C][C]85.7078004873838[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]1539.6[/C][C]16.8243870616436[/C][C]91.510020208106[/C][/ROW]
[ROW][C]Median[/C][C]1557[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]1479[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]1510.03225806452[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]1523.33333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]1510.03225806452[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]1523.33333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]1523.33333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]1510.03225806452[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]1523.33333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]1517.09375[/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=108116&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=108116&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 Mean1488.743.244465372007234.4252145839605
Geometric Mean1448.76874694900
Harmonic Mean1406.54934315307
Quadratic Mean1525.30738978520
Winsorized Mean ( 1 / 20 )1487.842.96363460305834.6292862264987
Winsorized Mean ( 2 / 20 )1489.442.585807030652634.974093573663
Winsorized Mean ( 3 / 20 )1488.3541.534546406548635.8340256188602
Winsorized Mean ( 4 / 20 )1489.6166666666741.198232996957136.1572950659484
Winsorized Mean ( 5 / 20 )1488.5333333333340.741353570691936.5361776886112
Winsorized Mean ( 6 / 20 )1489.5333333333340.242979993965737.0134948643635
Winsorized Mean ( 7 / 20 )1485.4539.355854595732737.7440666772122
Winsorized Mean ( 8 / 20 )1485.4538.68122236016938.4023541492216
Winsorized Mean ( 9 / 20 )148538.606562481871738.4649630667662
Winsorized Mean ( 10 / 20 )1484.3333333333338.377640814684538.6770343831395
Winsorized Mean ( 11 / 20 )1477.5537.101954697466839.8240473324949
Winsorized Mean ( 12 / 20 )1472.3535.15154298997841.8857857938065
Winsorized Mean ( 13 / 20 )1473.6534.752497166707842.4041470439059
Winsorized Mean ( 14 / 20 )1473.4166666666732.065005404070845.9509252563422
Winsorized Mean ( 15 / 20 )1473.9166666666730.736728720978847.9529451571296
Winsorized Mean ( 16 / 20 )1510.4523.285205712742764.8673676596902
Winsorized Mean ( 17 / 20 )1517.8166666666720.252955307355374.9429722049224
Winsorized Mean ( 18 / 20 )1524.7166666666716.835177920975090.5673034062215
Winsorized Mean ( 19 / 20 )1521.8666666666716.052851739308594.8035085217966
Winsorized Mean ( 20 / 20 )1531.5333333333314.4535583300185105.962372611906
Trimmed Mean ( 1 / 20 )1489.0344827586242.253161807237035.2407824425480
Trimmed Mean ( 2 / 20 )1490.3571428571441.364772864567936.0296223005191
Trimmed Mean ( 3 / 20 )1490.8888888888940.502596017830236.8097118572983
Trimmed Mean ( 4 / 20 )1491.8653846153839.910240814922337.3805157311298
Trimmed Mean ( 5 / 20 )1492.5439.268923268837938.0081722583011
Trimmed Mean ( 6 / 20 )1493.5416666666738.581921665120938.7109195760166
Trimmed Mean ( 7 / 20 )1494.4130434782637.828772324025439.5046667303328
Trimmed Mean ( 8 / 20 )1496.1590909090937.079281142495340.3502723032674
Trimmed Mean ( 9 / 20 )1498.0714285714336.254030059246541.3215144943410
Trimmed Mean ( 10 / 20 )1500.2535.148216389805842.6835314589426
Trimmed Mean ( 11 / 20 )1502.7631578947433.700155421097944.592172917812
Trimmed Mean ( 12 / 20 )1506.5833333333332.058537109283446.9947623685256
Trimmed Mean ( 13 / 20 )1511.6176470588230.32277385809249.85090262959
Trimmed Mean ( 14 / 20 )1517.0937527.942097365651254.2941973949651
Trimmed Mean ( 15 / 20 )1523.3333333333325.382468985517760.0151756002339
Trimmed Mean ( 16 / 20 )1530.3928571428621.935411398982969.7681401687235
Trimmed Mean ( 17 / 20 )1533.2692307692320.184728247808375.961846597351
Trimmed Mean ( 18 / 20 )1535.5416666666718.748041363078281.9041113111002
Trimmed Mean ( 19 / 20 )1537.1818181818217.935144869434585.7078004873838
Trimmed Mean ( 20 / 20 )1539.616.824387061643691.510020208106
Median1557
Midrange1479
Midmean - Weighted Average at Xnp1510.03225806452
Midmean - Weighted Average at X(n+1)p1523.33333333333
Midmean - Empirical Distribution Function1510.03225806452
Midmean - Empirical Distribution Function - Averaging1523.33333333333
Midmean - Empirical Distribution Function - Interpolation1523.33333333333
Midmean - Closest Observation1510.03225806452
Midmean - True Basic - Statistics Graphics Toolkit1523.33333333333
Midmean - MS Excel (old versions)1517.09375
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')