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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, 12 Dec 2008 05:50:01 -0700
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/Dec/12/t1229086483b57qhzh3n2yen4a.htm/, Retrieved Fri, 17 May 2024 14:29:12 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=32649, Retrieved Fri, 17 May 2024 14:29:12 +0000
QR Codes:

Original text written by user:in samenwerking met stéphanie claes, kevin engels en katrien bourdiaudhy
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact169
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
F     [Univariate Data Series] [blog 1e tijdreeks...] [2008-10-13 19:23:31] [7173087adebe3e3a714c80ea2417b3eb]
-   PD  [Univariate Data Series] [tijdreeksen opnie...] [2008-10-19 17:21:24] [7173087adebe3e3a714c80ea2417b3eb]
-   PD    [Univariate Data Series] [tijdreeksen opnie...] [2008-10-19 19:01:42] [7173087adebe3e3a714c80ea2417b3eb]
- RMPD        [Central Tendency] [back to back reek...] [2008-12-12 12:50:01] [95d95b0e883740fcbc85e18ec42dcafb] [Current]
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Dataseries X:
4892
6792
6290
5557
6105
4134
5590
7895
5947
5270
4864
5184
6093
7245
7041
6468
7210
4975
6699
6598
6426
6071
4913
5525
6403
6785
7481
7616
7825
5549
7257
8149
7837
7328
5973
6623
7007
8296
7358
8028
7609
5133
7308
7495
7597
7154
5543
6089
6572
6935
7269
7686
6994
5112
6576
6987
7035
6271
5082
4803




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 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 & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=32649&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=32649&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=32649&T=0

As an alternative you can also use a QR Code:  

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

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean6509.15131.02080273219049.680278736384
Geometric Mean6427.02149567108
Harmonic Mean6340.72705815675
Quadratic Mean6586.49028820864
Winsorized Mean ( 1 / 20 )6517.85127.48166994637551.1277425432358
Winsorized Mean ( 2 / 20 )6515.85126.17712826713151.6405000611934
Winsorized Mean ( 3 / 20 )6510.6124.56559817456752.2664370854305
Winsorized Mean ( 4 / 20 )6508.13333333333123.54153780445152.6797176803386
Winsorized Mean ( 5 / 20 )6512.3122.24332338820953.2732571358423
Winsorized Mean ( 6 / 20 )6509.1117.55545800265855.3704618279215
Winsorized Mean ( 7 / 20 )6504.43333333333115.4783966556656.3259754352896
Winsorized Mean ( 8 / 20 )6506.3114.75616325779556.6967369358965
Winsorized Mean ( 9 / 20 )6512.15112.92460067608457.668125111902
Winsorized Mean ( 10 / 20 )6509.48333333333107.38549148093860.6179032526831
Winsorized Mean ( 11 / 20 )6553.6666666666798.240566219989366.7103918353961
Winsorized Mean ( 12 / 20 )6532.6666666666793.793834698743969.6492118874222
Winsorized Mean ( 13 / 20 )6527.4666666666792.600199102501870.4908491550998
Winsorized Mean ( 14 / 20 )6524.6666666666791.58573417476971.241080561913
Winsorized Mean ( 15 / 20 )6523.1666666666788.709925834821873.533672870078
Winsorized Mean ( 16 / 20 )6615.1666666666772.182694166259991.6447736271774
Winsorized Mean ( 17 / 20 )6619.1333333333370.52081660324193.8607017353956
Winsorized Mean ( 18 / 20 )6638.0333333333364.4630493145517102.974237240045
Winsorized Mean ( 19 / 20 )662660.9771467795807108.663660894984
Winsorized Mean ( 20 / 20 )6589.6666666666755.4042293081982118.937971865112
Trimmed Mean ( 1 / 20 )6519.29310344828125.32968986114252.0171486155536
Trimmed Mean ( 2 / 20 )6520.83928571429122.64318103773953.1691956335324
Trimmed Mean ( 3 / 20 )6523.61111111111120.14185191629754.2992388335758
Trimmed Mean ( 4 / 20 )6528.61538461538117.74356724396955.4477457871467
Trimmed Mean ( 5 / 20 )6534.76115.07257181306756.7881633045934
Trimmed Mean ( 6 / 20 )6540.375112.08665841122458.3510570544861
Trimmed Mean ( 7 / 20 )6547.17391304348109.68032734770359.6932382622085
Trimmed Mean ( 8 / 20 )6555.5107.08631252316961.2169739114109
Trimmed Mean ( 9 / 20 )6564.28571428571103.81754569480763.2290589259624
Trimmed Mean ( 10 / 20 )6572.97599.952395640278565.7610551292404
Trimmed Mean ( 11 / 20 )658396.280240857178868.3733229309756
Trimmed Mean ( 12 / 20 )6587.4444444444493.888564853390370.1623723265014
Trimmed Mean ( 13 / 20 )6595.591.628913794376471.9805542473296
Trimmed Mean ( 14 / 20 )6605.312588.589717116777474.5607133082161
Trimmed Mean ( 15 / 20 )6616.8333333333384.34086672999278.4534661532041
Trimmed Mean ( 16 / 20 )6630.2142857142978.880399003420284.0540155663615
Trimmed Mean ( 17 / 20 )6632.3846153846276.903097405322786.2434003201225
Trimmed Mean ( 18 / 20 )6634.3333333333374.137300813967389.4871172877046
Trimmed Mean ( 19 / 20 )6633.7727272727371.852962288893192.3242760764807
Trimmed Mean ( 20 / 20 )663569.164030810058695.9313666697844
Median6610.5
Midrange6215
Midmean - Weighted Average at Xnp6582.64516129032
Midmean - Weighted Average at X(n+1)p6616.83333333333
Midmean - Empirical Distribution Function6582.64516129032
Midmean - Empirical Distribution Function - Averaging6616.83333333333
Midmean - Empirical Distribution Function - Interpolation6616.83333333333
Midmean - Closest Observation6582.64516129032
Midmean - True Basic - Statistics Graphics Toolkit6616.83333333333
Midmean - MS Excel (old versions)6605.3125
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 6509.15 & 131.020802732190 & 49.680278736384 \tabularnewline
Geometric Mean & 6427.02149567108 &  &  \tabularnewline
Harmonic Mean & 6340.72705815675 &  &  \tabularnewline
Quadratic Mean & 6586.49028820864 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 6517.85 & 127.481669946375 & 51.1277425432358 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 6515.85 & 126.177128267131 & 51.6405000611934 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 6510.6 & 124.565598174567 & 52.2664370854305 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 6508.13333333333 & 123.541537804451 & 52.6797176803386 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 6512.3 & 122.243323388209 & 53.2732571358423 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 6509.1 & 117.555458002658 & 55.3704618279215 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 6504.43333333333 & 115.47839665566 & 56.3259754352896 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 6506.3 & 114.756163257795 & 56.6967369358965 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 6512.15 & 112.924600676084 & 57.668125111902 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 6509.48333333333 & 107.385491480938 & 60.6179032526831 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 6553.66666666667 & 98.2405662199893 & 66.7103918353961 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 6532.66666666667 & 93.7938346987439 & 69.6492118874222 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 6527.46666666667 & 92.6001991025018 & 70.4908491550998 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 6524.66666666667 & 91.585734174769 & 71.241080561913 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 6523.16666666667 & 88.7099258348218 & 73.533672870078 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 6615.16666666667 & 72.1826941662599 & 91.6447736271774 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 6619.13333333333 & 70.520816603241 & 93.8607017353956 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 6638.03333333333 & 64.4630493145517 & 102.974237240045 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 6626 & 60.9771467795807 & 108.663660894984 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 6589.66666666667 & 55.4042293081982 & 118.937971865112 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 6519.29310344828 & 125.329689861142 & 52.0171486155536 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 6520.83928571429 & 122.643181037739 & 53.1691956335324 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 6523.61111111111 & 120.141851916297 & 54.2992388335758 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 6528.61538461538 & 117.743567243969 & 55.4477457871467 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 6534.76 & 115.072571813067 & 56.7881633045934 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 6540.375 & 112.086658411224 & 58.3510570544861 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 6547.17391304348 & 109.680327347703 & 59.6932382622085 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 6555.5 & 107.086312523169 & 61.2169739114109 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 6564.28571428571 & 103.817545694807 & 63.2290589259624 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 6572.975 & 99.9523956402785 & 65.7610551292404 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 6583 & 96.2802408571788 & 68.3733229309756 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 6587.44444444444 & 93.8885648533903 & 70.1623723265014 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 6595.5 & 91.6289137943764 & 71.9805542473296 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 6605.3125 & 88.5897171167774 & 74.5607133082161 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 6616.83333333333 & 84.340866729992 & 78.4534661532041 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 6630.21428571429 & 78.8803990034202 & 84.0540155663615 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 6632.38461538462 & 76.9030974053227 & 86.2434003201225 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 6634.33333333333 & 74.1373008139673 & 89.4871172877046 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 6633.77272727273 & 71.8529622888931 & 92.3242760764807 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 6635 & 69.1640308100586 & 95.9313666697844 \tabularnewline
Median & 6610.5 &  &  \tabularnewline
Midrange & 6215 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 6582.64516129032 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 6616.83333333333 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 6582.64516129032 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 6616.83333333333 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 6616.83333333333 &  &  \tabularnewline
Midmean - Closest Observation & 6582.64516129032 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 6616.83333333333 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 6605.3125 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=32649&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]6509.15[/C][C]131.020802732190[/C][C]49.680278736384[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]6427.02149567108[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]6340.72705815675[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]6586.49028820864[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]6517.85[/C][C]127.481669946375[/C][C]51.1277425432358[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]6515.85[/C][C]126.177128267131[/C][C]51.6405000611934[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]6510.6[/C][C]124.565598174567[/C][C]52.2664370854305[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]6508.13333333333[/C][C]123.541537804451[/C][C]52.6797176803386[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]6512.3[/C][C]122.243323388209[/C][C]53.2732571358423[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]6509.1[/C][C]117.555458002658[/C][C]55.3704618279215[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]6504.43333333333[/C][C]115.47839665566[/C][C]56.3259754352896[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]6506.3[/C][C]114.756163257795[/C][C]56.6967369358965[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]6512.15[/C][C]112.924600676084[/C][C]57.668125111902[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]6509.48333333333[/C][C]107.385491480938[/C][C]60.6179032526831[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]6553.66666666667[/C][C]98.2405662199893[/C][C]66.7103918353961[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]6532.66666666667[/C][C]93.7938346987439[/C][C]69.6492118874222[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]6527.46666666667[/C][C]92.6001991025018[/C][C]70.4908491550998[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]6524.66666666667[/C][C]91.585734174769[/C][C]71.241080561913[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]6523.16666666667[/C][C]88.7099258348218[/C][C]73.533672870078[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]6615.16666666667[/C][C]72.1826941662599[/C][C]91.6447736271774[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]6619.13333333333[/C][C]70.520816603241[/C][C]93.8607017353956[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]6638.03333333333[/C][C]64.4630493145517[/C][C]102.974237240045[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]6626[/C][C]60.9771467795807[/C][C]108.663660894984[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]6589.66666666667[/C][C]55.4042293081982[/C][C]118.937971865112[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]6519.29310344828[/C][C]125.329689861142[/C][C]52.0171486155536[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]6520.83928571429[/C][C]122.643181037739[/C][C]53.1691956335324[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]6523.61111111111[/C][C]120.141851916297[/C][C]54.2992388335758[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]6528.61538461538[/C][C]117.743567243969[/C][C]55.4477457871467[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]6534.76[/C][C]115.072571813067[/C][C]56.7881633045934[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]6540.375[/C][C]112.086658411224[/C][C]58.3510570544861[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]6547.17391304348[/C][C]109.680327347703[/C][C]59.6932382622085[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]6555.5[/C][C]107.086312523169[/C][C]61.2169739114109[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]6564.28571428571[/C][C]103.817545694807[/C][C]63.2290589259624[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]6572.975[/C][C]99.9523956402785[/C][C]65.7610551292404[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]6583[/C][C]96.2802408571788[/C][C]68.3733229309756[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]6587.44444444444[/C][C]93.8885648533903[/C][C]70.1623723265014[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]6595.5[/C][C]91.6289137943764[/C][C]71.9805542473296[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]6605.3125[/C][C]88.5897171167774[/C][C]74.5607133082161[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]6616.83333333333[/C][C]84.340866729992[/C][C]78.4534661532041[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]6630.21428571429[/C][C]78.8803990034202[/C][C]84.0540155663615[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]6632.38461538462[/C][C]76.9030974053227[/C][C]86.2434003201225[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]6634.33333333333[/C][C]74.1373008139673[/C][C]89.4871172877046[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]6633.77272727273[/C][C]71.8529622888931[/C][C]92.3242760764807[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]6635[/C][C]69.1640308100586[/C][C]95.9313666697844[/C][/ROW]
[ROW][C]Median[/C][C]6610.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]6215[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]6582.64516129032[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]6616.83333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]6582.64516129032[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]6616.83333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]6616.83333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]6582.64516129032[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]6616.83333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]6605.3125[/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=32649&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=32649&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 Mean6509.15131.02080273219049.680278736384
Geometric Mean6427.02149567108
Harmonic Mean6340.72705815675
Quadratic Mean6586.49028820864
Winsorized Mean ( 1 / 20 )6517.85127.48166994637551.1277425432358
Winsorized Mean ( 2 / 20 )6515.85126.17712826713151.6405000611934
Winsorized Mean ( 3 / 20 )6510.6124.56559817456752.2664370854305
Winsorized Mean ( 4 / 20 )6508.13333333333123.54153780445152.6797176803386
Winsorized Mean ( 5 / 20 )6512.3122.24332338820953.2732571358423
Winsorized Mean ( 6 / 20 )6509.1117.55545800265855.3704618279215
Winsorized Mean ( 7 / 20 )6504.43333333333115.4783966556656.3259754352896
Winsorized Mean ( 8 / 20 )6506.3114.75616325779556.6967369358965
Winsorized Mean ( 9 / 20 )6512.15112.92460067608457.668125111902
Winsorized Mean ( 10 / 20 )6509.48333333333107.38549148093860.6179032526831
Winsorized Mean ( 11 / 20 )6553.6666666666798.240566219989366.7103918353961
Winsorized Mean ( 12 / 20 )6532.6666666666793.793834698743969.6492118874222
Winsorized Mean ( 13 / 20 )6527.4666666666792.600199102501870.4908491550998
Winsorized Mean ( 14 / 20 )6524.6666666666791.58573417476971.241080561913
Winsorized Mean ( 15 / 20 )6523.1666666666788.709925834821873.533672870078
Winsorized Mean ( 16 / 20 )6615.1666666666772.182694166259991.6447736271774
Winsorized Mean ( 17 / 20 )6619.1333333333370.52081660324193.8607017353956
Winsorized Mean ( 18 / 20 )6638.0333333333364.4630493145517102.974237240045
Winsorized Mean ( 19 / 20 )662660.9771467795807108.663660894984
Winsorized Mean ( 20 / 20 )6589.6666666666755.4042293081982118.937971865112
Trimmed Mean ( 1 / 20 )6519.29310344828125.32968986114252.0171486155536
Trimmed Mean ( 2 / 20 )6520.83928571429122.64318103773953.1691956335324
Trimmed Mean ( 3 / 20 )6523.61111111111120.14185191629754.2992388335758
Trimmed Mean ( 4 / 20 )6528.61538461538117.74356724396955.4477457871467
Trimmed Mean ( 5 / 20 )6534.76115.07257181306756.7881633045934
Trimmed Mean ( 6 / 20 )6540.375112.08665841122458.3510570544861
Trimmed Mean ( 7 / 20 )6547.17391304348109.68032734770359.6932382622085
Trimmed Mean ( 8 / 20 )6555.5107.08631252316961.2169739114109
Trimmed Mean ( 9 / 20 )6564.28571428571103.81754569480763.2290589259624
Trimmed Mean ( 10 / 20 )6572.97599.952395640278565.7610551292404
Trimmed Mean ( 11 / 20 )658396.280240857178868.3733229309756
Trimmed Mean ( 12 / 20 )6587.4444444444493.888564853390370.1623723265014
Trimmed Mean ( 13 / 20 )6595.591.628913794376471.9805542473296
Trimmed Mean ( 14 / 20 )6605.312588.589717116777474.5607133082161
Trimmed Mean ( 15 / 20 )6616.8333333333384.34086672999278.4534661532041
Trimmed Mean ( 16 / 20 )6630.2142857142978.880399003420284.0540155663615
Trimmed Mean ( 17 / 20 )6632.3846153846276.903097405322786.2434003201225
Trimmed Mean ( 18 / 20 )6634.3333333333374.137300813967389.4871172877046
Trimmed Mean ( 19 / 20 )6633.7727272727371.852962288893192.3242760764807
Trimmed Mean ( 20 / 20 )663569.164030810058695.9313666697844
Median6610.5
Midrange6215
Midmean - Weighted Average at Xnp6582.64516129032
Midmean - Weighted Average at X(n+1)p6616.83333333333
Midmean - Empirical Distribution Function6582.64516129032
Midmean - Empirical Distribution Function - Averaging6616.83333333333
Midmean - Empirical Distribution Function - Interpolation6616.83333333333
Midmean - Closest Observation6582.64516129032
Midmean - True Basic - Statistics Graphics Toolkit6616.83333333333
Midmean - MS Excel (old versions)6605.3125
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')