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Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationFri, 17 Oct 2008 07:35:45 -0600
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2008/Oct/17/t12242507823pkcjue8wk1lue4.htm/, Retrieved Wed, 15 May 2024 18:52:09 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=16450, Retrieved Wed, 15 May 2024 18:52:09 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact186
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
F     [Univariate Data Series] [uitvoer van belgi...] [2008-10-13 19:19:38] [1e1d8320a8a1170c475bf6e4ce119de6]
- RMP     [Central Tendency] [Central Tendency ...] [2008-10-17 13:35:45] [fdd69703d301fae09456f660b2f52997] [Current]
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Dataseries X:
1332.7
1343.8
1421.6
1329.8
1306.8
1412.8
1358.1
1163.9
1467.9
1433.7
1362.2
1299
1291.5
1452.7
1555.4
1402.5
1242.9
1514.6
1308.6
1239.3
1519.9
1659.4
1597.6
1340.6
1427.2
1438.1
1616.2
1392.8
1318.7
1420.9
1221
1310
1466.7
1299.3
1640
1506.3
1530.2
1661.9
1880.3
1230.8
1406.5
1523.5
1323.2
1319.2
1500.7
1483
1497
1219.8
1472.9
1423.9
1629.6
1353.4
1366.8
1527.1
1487.6
1478.6
1536.7
1682.1
1576.5
1280.5




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=16450&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=16450&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=16450&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 Mean1430.10517.819719196206280.2540704628203
Geometric Mean1423.71668733015
Harmonic Mean1417.47426104538
Quadratic Mean1436.64028628139
Winsorized Mean ( 1 / 20 )1427.7333333333316.450161104884386.7914498970724
Winsorized Mean ( 2 / 20 )1427.116.270971691144187.7083450877577
Winsorized Mean ( 3 / 20 )1427.46516.137245024396288.457788045107
Winsorized Mean ( 4 / 20 )1426.7383333333315.715038515579390.7880901417405
Winsorized Mean ( 5 / 20 )1426.1716666666715.458221093901792.2597534349729
Winsorized Mean ( 6 / 20 )1428.5916666666714.455380850954498.8276740264747
Winsorized Mean ( 7 / 20 )1427.70513.7704513391808103.678882037641
Winsorized Mean ( 8 / 20 )1425.8916666666713.0339290596727109.398452311545
Winsorized Mean ( 9 / 20 )1422.7716666666712.429737917538114.465138050834
Winsorized Mean ( 10 / 20 )1420.90511.6765599920776121.68866523737
Winsorized Mean ( 11 / 20 )1420.0433333333311.4243948934608124.299216420307
Winsorized Mean ( 12 / 20 )1419.7033333333311.2774613900867125.888556318296
Winsorized Mean ( 13 / 20 )1420.8083333333310.8460358275850130.997938409880
Winsorized Mean ( 14 / 20 )1420.08510.6935470337883132.798312432065
Winsorized Mean ( 15 / 20 )1419.7610.3263707726061137.488768441896
Winsorized Mean ( 16 / 20 )1419.306666666679.70886974828055146.186600857224
Winsorized Mean ( 17 / 20 )1418.541666666679.34190646159015151.847128045982
Winsorized Mean ( 18 / 20 )1419.801666666678.81155170533227161.129584680015
Winsorized Mean ( 19 / 20 )1417.838333333338.22174569132408172.449791876863
Winsorized Mean ( 20 / 20 )1419.5057.5188390230299188.793109634628
Trimmed Mean ( 1 / 20 )1426.9327586206916.034368031971288.9921421147065
Trimmed Mean ( 2 / 20 )1426.07515.520412459792491.8838338668146
Trimmed Mean ( 3 / 20 )1425.5055555555615.003302319151395.0127862008044
Trimmed Mean ( 4 / 20 )1424.7519230769214.421828208890998.7913531100431
Trimmed Mean ( 5 / 20 )1424.15613.8629628897156102.730997069647
Trimmed Mean ( 6 / 20 )1423.6520833333313.2450328537805107.485734391892
Trimmed Mean ( 7 / 20 )1422.5782608695712.7811727150303111.302639639370
Trimmed Mean ( 8 / 20 )1421.5795454545512.3867775354164114.765889787715
Trimmed Mean ( 9 / 20 )1420.8095238095212.0789802208968117.626612332017
Trimmed Mean ( 10 / 20 )1420.482511.8310596700662120.063843781802
Trimmed Mean ( 11 / 20 )1420.4157894736811.6836261435500121.573197569133
Trimmed Mean ( 12 / 20 )1420.4722222222211.5254567179491123.246501807608
Trimmed Mean ( 13 / 20 )1420.5852941176511.3209349181780125.483036903306
Trimmed Mean ( 14 / 20 )1420.55312511.1273529447011127.663167696723
Trimmed Mean ( 15 / 20 )1420.6210.8641056145731130.762719951322
Trimmed Mean ( 16 / 20 )1420.7428571428610.5635973066681134.494227288089
Trimmed Mean ( 17 / 20 )1420.9510.2859115747257138.145266919416
Trimmed Mean ( 18 / 20 )1421.304166666679.94722027875902142.884557377469
Trimmed Mean ( 19 / 20 )1421.531818181829.5770613084487148.430898831959
Trimmed Mean ( 20 / 20 )1422.1159.17098478038783155.066771350575
Median1422.75
Midrange1522.1
Midmean - Weighted Average at Xnp1417.34838709677
Midmean - Weighted Average at X(n+1)p1420.62
Midmean - Empirical Distribution Function1417.34838709677
Midmean - Empirical Distribution Function - Averaging1420.62
Midmean - Empirical Distribution Function - Interpolation1420.62
Midmean - Closest Observation1417.34838709677
Midmean - True Basic - Statistics Graphics Toolkit1420.62
Midmean - MS Excel (old versions)1420.553125
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 1430.105 & 17.8197191962062 & 80.2540704628203 \tabularnewline
Geometric Mean & 1423.71668733015 &  &  \tabularnewline
Harmonic Mean & 1417.47426104538 &  &  \tabularnewline
Quadratic Mean & 1436.64028628139 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 1427.73333333333 & 16.4501611048843 & 86.7914498970724 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 1427.1 & 16.2709716911441 & 87.7083450877577 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 1427.465 & 16.1372450243962 & 88.457788045107 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 1426.73833333333 & 15.7150385155793 & 90.7880901417405 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 1426.17166666667 & 15.4582210939017 & 92.2597534349729 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 1428.59166666667 & 14.4553808509544 & 98.8276740264747 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 1427.705 & 13.7704513391808 & 103.678882037641 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 1425.89166666667 & 13.0339290596727 & 109.398452311545 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 1422.77166666667 & 12.429737917538 & 114.465138050834 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 1420.905 & 11.6765599920776 & 121.68866523737 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 1420.04333333333 & 11.4243948934608 & 124.299216420307 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 1419.70333333333 & 11.2774613900867 & 125.888556318296 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 1420.80833333333 & 10.8460358275850 & 130.997938409880 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 1420.085 & 10.6935470337883 & 132.798312432065 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 1419.76 & 10.3263707726061 & 137.488768441896 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 1419.30666666667 & 9.70886974828055 & 146.186600857224 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 1418.54166666667 & 9.34190646159015 & 151.847128045982 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 1419.80166666667 & 8.81155170533227 & 161.129584680015 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 1417.83833333333 & 8.22174569132408 & 172.449791876863 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 1419.505 & 7.5188390230299 & 188.793109634628 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 1426.93275862069 & 16.0343680319712 & 88.9921421147065 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 1426.075 & 15.5204124597924 & 91.8838338668146 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 1425.50555555556 & 15.0033023191513 & 95.0127862008044 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 1424.75192307692 & 14.4218282088909 & 98.7913531100431 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 1424.156 & 13.8629628897156 & 102.730997069647 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 1423.65208333333 & 13.2450328537805 & 107.485734391892 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 1422.57826086957 & 12.7811727150303 & 111.302639639370 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 1421.57954545455 & 12.3867775354164 & 114.765889787715 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 1420.80952380952 & 12.0789802208968 & 117.626612332017 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 1420.4825 & 11.8310596700662 & 120.063843781802 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 1420.41578947368 & 11.6836261435500 & 121.573197569133 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 1420.47222222222 & 11.5254567179491 & 123.246501807608 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 1420.58529411765 & 11.3209349181780 & 125.483036903306 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 1420.553125 & 11.1273529447011 & 127.663167696723 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 1420.62 & 10.8641056145731 & 130.762719951322 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 1420.74285714286 & 10.5635973066681 & 134.494227288089 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 1420.95 & 10.2859115747257 & 138.145266919416 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 1421.30416666667 & 9.94722027875902 & 142.884557377469 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 1421.53181818182 & 9.5770613084487 & 148.430898831959 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 1422.115 & 9.17098478038783 & 155.066771350575 \tabularnewline
Median & 1422.75 &  &  \tabularnewline
Midrange & 1522.1 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 1417.34838709677 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 1420.62 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 1417.34838709677 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 1420.62 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 1420.62 &  &  \tabularnewline
Midmean - Closest Observation & 1417.34838709677 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 1420.62 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 1420.553125 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=16450&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]1430.105[/C][C]17.8197191962062[/C][C]80.2540704628203[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]1423.71668733015[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]1417.47426104538[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]1436.64028628139[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]1427.73333333333[/C][C]16.4501611048843[/C][C]86.7914498970724[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]1427.1[/C][C]16.2709716911441[/C][C]87.7083450877577[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]1427.465[/C][C]16.1372450243962[/C][C]88.457788045107[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]1426.73833333333[/C][C]15.7150385155793[/C][C]90.7880901417405[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]1426.17166666667[/C][C]15.4582210939017[/C][C]92.2597534349729[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]1428.59166666667[/C][C]14.4553808509544[/C][C]98.8276740264747[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]1427.705[/C][C]13.7704513391808[/C][C]103.678882037641[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]1425.89166666667[/C][C]13.0339290596727[/C][C]109.398452311545[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]1422.77166666667[/C][C]12.429737917538[/C][C]114.465138050834[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]1420.905[/C][C]11.6765599920776[/C][C]121.68866523737[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]1420.04333333333[/C][C]11.4243948934608[/C][C]124.299216420307[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]1419.70333333333[/C][C]11.2774613900867[/C][C]125.888556318296[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]1420.80833333333[/C][C]10.8460358275850[/C][C]130.997938409880[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]1420.085[/C][C]10.6935470337883[/C][C]132.798312432065[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]1419.76[/C][C]10.3263707726061[/C][C]137.488768441896[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]1419.30666666667[/C][C]9.70886974828055[/C][C]146.186600857224[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]1418.54166666667[/C][C]9.34190646159015[/C][C]151.847128045982[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]1419.80166666667[/C][C]8.81155170533227[/C][C]161.129584680015[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]1417.83833333333[/C][C]8.22174569132408[/C][C]172.449791876863[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]1419.505[/C][C]7.5188390230299[/C][C]188.793109634628[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]1426.93275862069[/C][C]16.0343680319712[/C][C]88.9921421147065[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]1426.075[/C][C]15.5204124597924[/C][C]91.8838338668146[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]1425.50555555556[/C][C]15.0033023191513[/C][C]95.0127862008044[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]1424.75192307692[/C][C]14.4218282088909[/C][C]98.7913531100431[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]1424.156[/C][C]13.8629628897156[/C][C]102.730997069647[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]1423.65208333333[/C][C]13.2450328537805[/C][C]107.485734391892[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]1422.57826086957[/C][C]12.7811727150303[/C][C]111.302639639370[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]1421.57954545455[/C][C]12.3867775354164[/C][C]114.765889787715[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]1420.80952380952[/C][C]12.0789802208968[/C][C]117.626612332017[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]1420.4825[/C][C]11.8310596700662[/C][C]120.063843781802[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]1420.41578947368[/C][C]11.6836261435500[/C][C]121.573197569133[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]1420.47222222222[/C][C]11.5254567179491[/C][C]123.246501807608[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]1420.58529411765[/C][C]11.3209349181780[/C][C]125.483036903306[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]1420.553125[/C][C]11.1273529447011[/C][C]127.663167696723[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]1420.62[/C][C]10.8641056145731[/C][C]130.762719951322[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]1420.74285714286[/C][C]10.5635973066681[/C][C]134.494227288089[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]1420.95[/C][C]10.2859115747257[/C][C]138.145266919416[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]1421.30416666667[/C][C]9.94722027875902[/C][C]142.884557377469[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]1421.53181818182[/C][C]9.5770613084487[/C][C]148.430898831959[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]1422.115[/C][C]9.17098478038783[/C][C]155.066771350575[/C][/ROW]
[ROW][C]Median[/C][C]1422.75[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]1522.1[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]1417.34838709677[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]1420.62[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]1417.34838709677[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]1420.62[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]1420.62[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]1417.34838709677[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]1420.62[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]1420.553125[/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=16450&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=16450&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 Mean1430.10517.819719196206280.2540704628203
Geometric Mean1423.71668733015
Harmonic Mean1417.47426104538
Quadratic Mean1436.64028628139
Winsorized Mean ( 1 / 20 )1427.7333333333316.450161104884386.7914498970724
Winsorized Mean ( 2 / 20 )1427.116.270971691144187.7083450877577
Winsorized Mean ( 3 / 20 )1427.46516.137245024396288.457788045107
Winsorized Mean ( 4 / 20 )1426.7383333333315.715038515579390.7880901417405
Winsorized Mean ( 5 / 20 )1426.1716666666715.458221093901792.2597534349729
Winsorized Mean ( 6 / 20 )1428.5916666666714.455380850954498.8276740264747
Winsorized Mean ( 7 / 20 )1427.70513.7704513391808103.678882037641
Winsorized Mean ( 8 / 20 )1425.8916666666713.0339290596727109.398452311545
Winsorized Mean ( 9 / 20 )1422.7716666666712.429737917538114.465138050834
Winsorized Mean ( 10 / 20 )1420.90511.6765599920776121.68866523737
Winsorized Mean ( 11 / 20 )1420.0433333333311.4243948934608124.299216420307
Winsorized Mean ( 12 / 20 )1419.7033333333311.2774613900867125.888556318296
Winsorized Mean ( 13 / 20 )1420.8083333333310.8460358275850130.997938409880
Winsorized Mean ( 14 / 20 )1420.08510.6935470337883132.798312432065
Winsorized Mean ( 15 / 20 )1419.7610.3263707726061137.488768441896
Winsorized Mean ( 16 / 20 )1419.306666666679.70886974828055146.186600857224
Winsorized Mean ( 17 / 20 )1418.541666666679.34190646159015151.847128045982
Winsorized Mean ( 18 / 20 )1419.801666666678.81155170533227161.129584680015
Winsorized Mean ( 19 / 20 )1417.838333333338.22174569132408172.449791876863
Winsorized Mean ( 20 / 20 )1419.5057.5188390230299188.793109634628
Trimmed Mean ( 1 / 20 )1426.9327586206916.034368031971288.9921421147065
Trimmed Mean ( 2 / 20 )1426.07515.520412459792491.8838338668146
Trimmed Mean ( 3 / 20 )1425.5055555555615.003302319151395.0127862008044
Trimmed Mean ( 4 / 20 )1424.7519230769214.421828208890998.7913531100431
Trimmed Mean ( 5 / 20 )1424.15613.8629628897156102.730997069647
Trimmed Mean ( 6 / 20 )1423.6520833333313.2450328537805107.485734391892
Trimmed Mean ( 7 / 20 )1422.5782608695712.7811727150303111.302639639370
Trimmed Mean ( 8 / 20 )1421.5795454545512.3867775354164114.765889787715
Trimmed Mean ( 9 / 20 )1420.8095238095212.0789802208968117.626612332017
Trimmed Mean ( 10 / 20 )1420.482511.8310596700662120.063843781802
Trimmed Mean ( 11 / 20 )1420.4157894736811.6836261435500121.573197569133
Trimmed Mean ( 12 / 20 )1420.4722222222211.5254567179491123.246501807608
Trimmed Mean ( 13 / 20 )1420.5852941176511.3209349181780125.483036903306
Trimmed Mean ( 14 / 20 )1420.55312511.1273529447011127.663167696723
Trimmed Mean ( 15 / 20 )1420.6210.8641056145731130.762719951322
Trimmed Mean ( 16 / 20 )1420.7428571428610.5635973066681134.494227288089
Trimmed Mean ( 17 / 20 )1420.9510.2859115747257138.145266919416
Trimmed Mean ( 18 / 20 )1421.304166666679.94722027875902142.884557377469
Trimmed Mean ( 19 / 20 )1421.531818181829.5770613084487148.430898831959
Trimmed Mean ( 20 / 20 )1422.1159.17098478038783155.066771350575
Median1422.75
Midrange1522.1
Midmean - Weighted Average at Xnp1417.34838709677
Midmean - Weighted Average at X(n+1)p1420.62
Midmean - Empirical Distribution Function1417.34838709677
Midmean - Empirical Distribution Function - Averaging1420.62
Midmean - Empirical Distribution Function - Interpolation1420.62
Midmean - Closest Observation1417.34838709677
Midmean - True Basic - Statistics Graphics Toolkit1420.62
Midmean - MS Excel (old versions)1420.553125
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')