Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationTue, 06 Mar 2012 12:15:48 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2012/Mar/06/t1331054192ae4ksv0vzfx4cgv.htm/, Retrieved Wed, 01 May 2024 14:04:19 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=163548, Retrieved Wed, 01 May 2024 14:04:19 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact139
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [Kleding en kledin...] [2012-03-06 17:15:48] [675223405f94cd8491f4a89fc80aa26c] [Current]
Feedback Forum

Post a new message
Dataseries X:
219,20
232,50
235,60
171,00
165,90
187,60
218,20
249,80
256,50
224,90
200,00
182,50
230,30
252,80
270,60
196,90
184,70
202,50
258,20
283,10
268,50
283,80
231,10
212,10
238,50
262,80
245,50
198,20
167,20
184,20
254,90
246,40
264,50
242,40
186,70
254,70
230,10
253,60
228,00
183,80
150,00
178,50
228,40
228,70
236,70
218,20
173,50
189,10
194,60
213,70
216,30
173,90
156,90
182,90
216,40
234,00
257,30
225,70
201,70
189,20




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gertrude Mary Cox' @ cox.wessa.net

\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 & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=163548&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]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=163548&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=163548&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'Gertrude Mary Cox' @ cox.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean218.7583333333334.336374394672650.447289238237
Geometric Mean216.158103613943
Harmonic Mean213.505137255795
Quadratic Mean221.279580696759
Winsorized Mean ( 1 / 20 )218.8616666666674.3039267917362750.8516239372126
Winsorized Mean ( 2 / 20 )218.7454.1376508967653252.866954090063
Winsorized Mean ( 3 / 20 )218.7054.1017423781514153.3200235014679
Winsorized Mean ( 4 / 20 )218.6916666666673.9957797593363954.7306608067373
Winsorized Mean ( 5 / 20 )218.7583333333333.9271237671943255.7044662459473
Winsorized Mean ( 6 / 20 )218.3383333333333.8350134551923856.9328728267475
Winsorized Mean ( 7 / 20 )218.773.714472611241258.8966517986782
Winsorized Mean ( 8 / 20 )219.1966666666673.6006198200465860.8774815508934
Winsorized Mean ( 9 / 20 )219.0166666666673.5486204581934261.7188198193973
Winsorized Mean ( 10 / 20 )219.1333333333333.517198797665262.303368657694
Winsorized Mean ( 11 / 20 )219.0053.4704022341317563.1065176958636
Winsorized Mean ( 12 / 20 )218.9453.4265187362274163.8972137187429
Winsorized Mean ( 13 / 20 )218.7283333333333.2463800715163167.3760707356642
Winsorized Mean ( 14 / 20 )218.1453.0852129787575170.7066259289018
Winsorized Mean ( 15 / 20 )218.2952.9878647450082673.0605360783814
Winsorized Mean ( 16 / 20 )217.4952.8585350688968376.0861751764116
Winsorized Mean ( 17 / 20 )217.922.4455780456573389.1077675427147
Winsorized Mean ( 18 / 20 )218.072.2586885600497196.54717514273
Winsorized Mean ( 19 / 20 )218.1333333333332.14517283181164101.685668445239
Winsorized Mean ( 20 / 20 )218.21.97819469145181110.302591015377
Trimmed Mean ( 1 / 20 )218.8224137931034.1743716127319652.4204441036559
Trimmed Mean ( 2 / 20 )218.7803571428574.0146731034482854.4951859106393
Trimmed Mean ( 3 / 20 )218.83.9281003102669455.7012252024519
Trimmed Mean ( 4 / 20 )218.8365384615383.8361944488670757.0452153503759
Trimmed Mean ( 5 / 20 )218.883.7609312785043958.1983513634001
Trimmed Mean ( 6 / 20 )218.9104166666673.6868756107788359.3755905479065
Trimmed Mean ( 7 / 20 )219.0347826086963.6179640595434260.5408951011906
Trimmed Mean ( 8 / 20 )219.0863636363643.5607230049918161.5286174547204
Trimmed Mean ( 9 / 20 )219.0666666666673.5128628193776962.3612927491073
Trimmed Mean ( 10 / 20 )219.0753.4583395118882163.3468747781758
Trimmed Mean ( 11 / 20 )219.0657894736843.3885743850409764.6483637605128
Trimmed Mean ( 12 / 20 )219.0753.301763297545166.3509101827151
Trimmed Mean ( 13 / 20 )219.0941176470593.1899238117413268.6831819746376
Trimmed Mean ( 14 / 20 )219.1468753.0823246894886771.0979202636677
Trimmed Mean ( 15 / 20 )219.292.9723180705711373.7774339062789
Trimmed Mean ( 16 / 20 )219.4321428571432.8375787687895877.3307670858932
Trimmed Mean ( 17 / 20 )219.7115384615382.6728453690522282.2013652587194
Trimmed Mean ( 18 / 20 )219.9752.5744019285758585.447030457163
Trimmed Mean ( 19 / 20 )220.2636363636362.4812678774000988.7705992447828
Trimmed Mean ( 20 / 20 )220.62.3620463919861493.3935932623691
Median222.05
Midrange216.9
Midmean - Weighted Average at Xnp218.267741935484
Midmean - Weighted Average at X(n+1)p219.29
Midmean - Empirical Distribution Function218.267741935484
Midmean - Empirical Distribution Function - Averaging219.29
Midmean - Empirical Distribution Function - Interpolation219.29
Midmean - Closest Observation218.267741935484
Midmean - True Basic - Statistics Graphics Toolkit219.29
Midmean - MS Excel (old versions)219.146875
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 218.758333333333 & 4.3363743946726 & 50.447289238237 \tabularnewline
Geometric Mean & 216.158103613943 &  &  \tabularnewline
Harmonic Mean & 213.505137255795 &  &  \tabularnewline
Quadratic Mean & 221.279580696759 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 218.861666666667 & 4.30392679173627 & 50.8516239372126 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 218.745 & 4.13765089676532 & 52.866954090063 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 218.705 & 4.10174237815141 & 53.3200235014679 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 218.691666666667 & 3.99577975933639 & 54.7306608067373 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 218.758333333333 & 3.92712376719432 & 55.7044662459473 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 218.338333333333 & 3.83501345519238 & 56.9328728267475 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 218.77 & 3.7144726112412 & 58.8966517986782 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 219.196666666667 & 3.60061982004658 & 60.8774815508934 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 219.016666666667 & 3.54862045819342 & 61.7188198193973 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 219.133333333333 & 3.5171987976652 & 62.303368657694 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 219.005 & 3.47040223413175 & 63.1065176958636 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 218.945 & 3.42651873622741 & 63.8972137187429 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 218.728333333333 & 3.24638007151631 & 67.3760707356642 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 218.145 & 3.08521297875751 & 70.7066259289018 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 218.295 & 2.98786474500826 & 73.0605360783814 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 217.495 & 2.85853506889683 & 76.0861751764116 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 217.92 & 2.44557804565733 & 89.1077675427147 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 218.07 & 2.25868856004971 & 96.54717514273 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 218.133333333333 & 2.14517283181164 & 101.685668445239 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 218.2 & 1.97819469145181 & 110.302591015377 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 218.822413793103 & 4.17437161273196 & 52.4204441036559 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 218.780357142857 & 4.01467310344828 & 54.4951859106393 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 218.8 & 3.92810031026694 & 55.7012252024519 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 218.836538461538 & 3.83619444886707 & 57.0452153503759 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 218.88 & 3.76093127850439 & 58.1983513634001 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 218.910416666667 & 3.68687561077883 & 59.3755905479065 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 219.034782608696 & 3.61796405954342 & 60.5408951011906 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 219.086363636364 & 3.56072300499181 & 61.5286174547204 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 219.066666666667 & 3.51286281937769 & 62.3612927491073 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 219.075 & 3.45833951188821 & 63.3468747781758 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 219.065789473684 & 3.38857438504097 & 64.6483637605128 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 219.075 & 3.3017632975451 & 66.3509101827151 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 219.094117647059 & 3.18992381174132 & 68.6831819746376 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 219.146875 & 3.08232468948867 & 71.0979202636677 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 219.29 & 2.97231807057113 & 73.7774339062789 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 219.432142857143 & 2.83757876878958 & 77.3307670858932 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 219.711538461538 & 2.67284536905222 & 82.2013652587194 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 219.975 & 2.57440192857585 & 85.447030457163 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 220.263636363636 & 2.48126787740009 & 88.7705992447828 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 220.6 & 2.36204639198614 & 93.3935932623691 \tabularnewline
Median & 222.05 &  &  \tabularnewline
Midrange & 216.9 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 218.267741935484 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 219.29 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 218.267741935484 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 219.29 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 219.29 &  &  \tabularnewline
Midmean - Closest Observation & 218.267741935484 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 219.29 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 219.146875 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=163548&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]218.758333333333[/C][C]4.3363743946726[/C][C]50.447289238237[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]216.158103613943[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]213.505137255795[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]221.279580696759[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]218.861666666667[/C][C]4.30392679173627[/C][C]50.8516239372126[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]218.745[/C][C]4.13765089676532[/C][C]52.866954090063[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]218.705[/C][C]4.10174237815141[/C][C]53.3200235014679[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]218.691666666667[/C][C]3.99577975933639[/C][C]54.7306608067373[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]218.758333333333[/C][C]3.92712376719432[/C][C]55.7044662459473[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]218.338333333333[/C][C]3.83501345519238[/C][C]56.9328728267475[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]218.77[/C][C]3.7144726112412[/C][C]58.8966517986782[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]219.196666666667[/C][C]3.60061982004658[/C][C]60.8774815508934[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]219.016666666667[/C][C]3.54862045819342[/C][C]61.7188198193973[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]219.133333333333[/C][C]3.5171987976652[/C][C]62.303368657694[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]219.005[/C][C]3.47040223413175[/C][C]63.1065176958636[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]218.945[/C][C]3.42651873622741[/C][C]63.8972137187429[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]218.728333333333[/C][C]3.24638007151631[/C][C]67.3760707356642[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]218.145[/C][C]3.08521297875751[/C][C]70.7066259289018[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]218.295[/C][C]2.98786474500826[/C][C]73.0605360783814[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]217.495[/C][C]2.85853506889683[/C][C]76.0861751764116[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]217.92[/C][C]2.44557804565733[/C][C]89.1077675427147[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]218.07[/C][C]2.25868856004971[/C][C]96.54717514273[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]218.133333333333[/C][C]2.14517283181164[/C][C]101.685668445239[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]218.2[/C][C]1.97819469145181[/C][C]110.302591015377[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]218.822413793103[/C][C]4.17437161273196[/C][C]52.4204441036559[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]218.780357142857[/C][C]4.01467310344828[/C][C]54.4951859106393[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]218.8[/C][C]3.92810031026694[/C][C]55.7012252024519[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]218.836538461538[/C][C]3.83619444886707[/C][C]57.0452153503759[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]218.88[/C][C]3.76093127850439[/C][C]58.1983513634001[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]218.910416666667[/C][C]3.68687561077883[/C][C]59.3755905479065[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]219.034782608696[/C][C]3.61796405954342[/C][C]60.5408951011906[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]219.086363636364[/C][C]3.56072300499181[/C][C]61.5286174547204[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]219.066666666667[/C][C]3.51286281937769[/C][C]62.3612927491073[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]219.075[/C][C]3.45833951188821[/C][C]63.3468747781758[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]219.065789473684[/C][C]3.38857438504097[/C][C]64.6483637605128[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]219.075[/C][C]3.3017632975451[/C][C]66.3509101827151[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]219.094117647059[/C][C]3.18992381174132[/C][C]68.6831819746376[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]219.146875[/C][C]3.08232468948867[/C][C]71.0979202636677[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]219.29[/C][C]2.97231807057113[/C][C]73.7774339062789[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]219.432142857143[/C][C]2.83757876878958[/C][C]77.3307670858932[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]219.711538461538[/C][C]2.67284536905222[/C][C]82.2013652587194[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]219.975[/C][C]2.57440192857585[/C][C]85.447030457163[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]220.263636363636[/C][C]2.48126787740009[/C][C]88.7705992447828[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]220.6[/C][C]2.36204639198614[/C][C]93.3935932623691[/C][/ROW]
[ROW][C]Median[/C][C]222.05[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]216.9[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]218.267741935484[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]219.29[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]218.267741935484[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]219.29[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]219.29[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]218.267741935484[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]219.29[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]219.146875[/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=163548&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=163548&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 Mean218.7583333333334.336374394672650.447289238237
Geometric Mean216.158103613943
Harmonic Mean213.505137255795
Quadratic Mean221.279580696759
Winsorized Mean ( 1 / 20 )218.8616666666674.3039267917362750.8516239372126
Winsorized Mean ( 2 / 20 )218.7454.1376508967653252.866954090063
Winsorized Mean ( 3 / 20 )218.7054.1017423781514153.3200235014679
Winsorized Mean ( 4 / 20 )218.6916666666673.9957797593363954.7306608067373
Winsorized Mean ( 5 / 20 )218.7583333333333.9271237671943255.7044662459473
Winsorized Mean ( 6 / 20 )218.3383333333333.8350134551923856.9328728267475
Winsorized Mean ( 7 / 20 )218.773.714472611241258.8966517986782
Winsorized Mean ( 8 / 20 )219.1966666666673.6006198200465860.8774815508934
Winsorized Mean ( 9 / 20 )219.0166666666673.5486204581934261.7188198193973
Winsorized Mean ( 10 / 20 )219.1333333333333.517198797665262.303368657694
Winsorized Mean ( 11 / 20 )219.0053.4704022341317563.1065176958636
Winsorized Mean ( 12 / 20 )218.9453.4265187362274163.8972137187429
Winsorized Mean ( 13 / 20 )218.7283333333333.2463800715163167.3760707356642
Winsorized Mean ( 14 / 20 )218.1453.0852129787575170.7066259289018
Winsorized Mean ( 15 / 20 )218.2952.9878647450082673.0605360783814
Winsorized Mean ( 16 / 20 )217.4952.8585350688968376.0861751764116
Winsorized Mean ( 17 / 20 )217.922.4455780456573389.1077675427147
Winsorized Mean ( 18 / 20 )218.072.2586885600497196.54717514273
Winsorized Mean ( 19 / 20 )218.1333333333332.14517283181164101.685668445239
Winsorized Mean ( 20 / 20 )218.21.97819469145181110.302591015377
Trimmed Mean ( 1 / 20 )218.8224137931034.1743716127319652.4204441036559
Trimmed Mean ( 2 / 20 )218.7803571428574.0146731034482854.4951859106393
Trimmed Mean ( 3 / 20 )218.83.9281003102669455.7012252024519
Trimmed Mean ( 4 / 20 )218.8365384615383.8361944488670757.0452153503759
Trimmed Mean ( 5 / 20 )218.883.7609312785043958.1983513634001
Trimmed Mean ( 6 / 20 )218.9104166666673.6868756107788359.3755905479065
Trimmed Mean ( 7 / 20 )219.0347826086963.6179640595434260.5408951011906
Trimmed Mean ( 8 / 20 )219.0863636363643.5607230049918161.5286174547204
Trimmed Mean ( 9 / 20 )219.0666666666673.5128628193776962.3612927491073
Trimmed Mean ( 10 / 20 )219.0753.4583395118882163.3468747781758
Trimmed Mean ( 11 / 20 )219.0657894736843.3885743850409764.6483637605128
Trimmed Mean ( 12 / 20 )219.0753.301763297545166.3509101827151
Trimmed Mean ( 13 / 20 )219.0941176470593.1899238117413268.6831819746376
Trimmed Mean ( 14 / 20 )219.1468753.0823246894886771.0979202636677
Trimmed Mean ( 15 / 20 )219.292.9723180705711373.7774339062789
Trimmed Mean ( 16 / 20 )219.4321428571432.8375787687895877.3307670858932
Trimmed Mean ( 17 / 20 )219.7115384615382.6728453690522282.2013652587194
Trimmed Mean ( 18 / 20 )219.9752.5744019285758585.447030457163
Trimmed Mean ( 19 / 20 )220.2636363636362.4812678774000988.7705992447828
Trimmed Mean ( 20 / 20 )220.62.3620463919861493.3935932623691
Median222.05
Midrange216.9
Midmean - Weighted Average at Xnp218.267741935484
Midmean - Weighted Average at X(n+1)p219.29
Midmean - Empirical Distribution Function218.267741935484
Midmean - Empirical Distribution Function - Averaging219.29
Midmean - Empirical Distribution Function - Interpolation219.29
Midmean - Closest Observation218.267741935484
Midmean - True Basic - Statistics Graphics Toolkit219.29
Midmean - MS Excel (old versions)219.146875
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')