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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 computationMon, 20 Oct 2008 14:47:40 -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/20/t1224535692n19xqscgifsi75m.htm/, Retrieved Sun, 19 May 2024 13:21:29 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=18119, Retrieved Sun, 19 May 2024 13:21:29 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact101
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [Central Tendency ...] [2008-10-20 20:47:40] [d592f629d96b926609f311957d74fcca] [Current]
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Dataseries X:
10413.00
10709.00
10662.00
10570.00
10297.00
10635.00
10872.00
10296.00
10383.00
10431.00
10574.00
10653.00
10805.00
10872.00
10625.00
10407.00
10463.00
10556.00
10646.00
10702.00
11353.00
11346.00
11451.00
11964.00
12574.00
13031.00
13812.00
14544.00
14931.00
14886.00
16005.00
17064.00
15168.00
16050.00
15839.00
15137.00
14954.00
15648.00
15305.00
15579.00
16348.00
15928.00
16171.00
15937.00
15713.00
15594.00
15683.00
16438.00
17032.00
17696.00
17745.00
19394.00
20148.00
20108.00
18584.00
18441.00
18391.00
19178.00
18079.00
18483.00




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=18119&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=18119&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=18119&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 Mean14155.05408.58108298115934.6444086366396
Geometric Mean13806.2145028864
Harmonic Mean13464.9649175676
Quadratic Mean14498.7865727906
Winsorized Mean ( 1 / 20 )14154.4408.41318822533734.6570590962173
Winsorized Mean ( 2 / 20 )14133.4666666667402.37795318929435.1248535230203
Winsorized Mean ( 3 / 20 )14123.8666666667399.8350044357435.3242375229221
Winsorized Mean ( 4 / 20 )14084.6666666667391.67050148381135.9604989737754
Winsorized Mean ( 5 / 20 )14077.75389.80691846918436.114674555508
Winsorized Mean ( 6 / 20 )14076.75388.4988730542336.2336958388938
Winsorized Mean ( 7 / 20 )14081.7666666667385.69532219497936.5100789569545
Winsorized Mean ( 8 / 20 )14042.0333333333377.69657654785537.1780794564712
Winsorized Mean ( 9 / 20 )13992.5333333333368.7413907578137.9467390535598
Winsorized Mean ( 10 / 20 )13992.8666666667366.00617717817338.2312308894582
Winsorized Mean ( 11 / 20 )13878.8333333333346.73843441717240.0268097093478
Winsorized Mean ( 12 / 20 )13874.6333333333345.3957036090140.1702545467662
Winsorized Mean ( 13 / 20 )13747.45326.15833857504542.1496199056609
Winsorized Mean ( 14 / 20 )13728.55322.90861244557342.5152797753698
Winsorized Mean ( 15 / 20 )13694.3315.31085576413643.4311085383112
Winsorized Mean ( 16 / 20 )13663.9310.76252373507343.9689439890395
Winsorized Mean ( 17 / 20 )13678.35304.7424992704244.8849439534924
Winsorized Mean ( 18 / 20 )13678.05298.91071397555945.7596511616456
Winsorized Mean ( 19 / 20 )13675.2298.54593359025545.8060166338383
Winsorized Mean ( 20 / 20 )13803.5333333333269.97289094569251.1293311153603
Trimmed Mean ( 1 / 20 )14118.2586206897404.18113804766534.9305232027544
Trimmed Mean ( 2 / 20 )14079.5357142857398.66379087976835.3168159145207
Trimmed Mean ( 3 / 20 )14049.5740740741395.447847031435.5282603750236
Trimmed Mean ( 4 / 20 )14021392.20590042194935.7490797178617
Trimmed Mean ( 5 / 20 )14001.9390.75451268497635.832983485691
Trimmed Mean ( 6 / 20 )13982.9375388.91979930215535.9532672933849
Trimmed Mean ( 7 / 20 )13962.5434782609386.3341970286136.1411016307906
Trimmed Mean ( 8 / 20 )13939.3181818182383.12481719743236.3832295798133
Trimmed Mean ( 9 / 20 )13920.9761904762380.42484272426736.5932363690722
Trimmed Mean ( 10 / 20 )13909.05378.40930043254236.756628296665
Trimmed Mean ( 11 / 20 )13895.8157894737375.50287165612537.0058842111841
Trimmed Mean ( 12 / 20 )13898.3888888889375.41388224278537.0215102485225
Trimmed Mean ( 13 / 20 )13901.8823529412374.28585300386937.1424200016383
Trimmed Mean ( 14 / 20 )13924.15625375.91000099697637.0411965977783
Trimmed Mean ( 15 / 20 )13952.1376.97793267529337.0103891784497
Trimmed Mean ( 16 / 20 )13988.9285714286378.16234486037236.9918601403682
Trimmed Mean ( 17 / 20 )14035.8076923077378.35681986201237.096748242642
Trimmed Mean ( 18 / 20 )14088.375377.51059977680237.3191507955792
Trimmed Mean ( 19 / 20 )14150.5454545455374.57147652638337.7779578567263
Trimmed Mean ( 20 / 20 )14225.6365.62665312266938.9074480170002
Median14942.5
Midrange15222
Midmean - Weighted Average at Xnp13845.9677419355
Midmean - Weighted Average at X(n+1)p13952.1
Midmean - Empirical Distribution Function13845.9677419355
Midmean - Empirical Distribution Function - Averaging13952.1
Midmean - Empirical Distribution Function - Interpolation13952.1
Midmean - Closest Observation13845.9677419355
Midmean - True Basic - Statistics Graphics Toolkit13952.1
Midmean - MS Excel (old versions)13924.15625
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 14155.05 & 408.581082981159 & 34.6444086366396 \tabularnewline
Geometric Mean & 13806.2145028864 &  &  \tabularnewline
Harmonic Mean & 13464.9649175676 &  &  \tabularnewline
Quadratic Mean & 14498.7865727906 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 14154.4 & 408.413188225337 & 34.6570590962173 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 14133.4666666667 & 402.377953189294 & 35.1248535230203 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 14123.8666666667 & 399.83500443574 & 35.3242375229221 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 14084.6666666667 & 391.670501483811 & 35.9604989737754 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 14077.75 & 389.806918469184 & 36.114674555508 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 14076.75 & 388.49887305423 & 36.2336958388938 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 14081.7666666667 & 385.695322194979 & 36.5100789569545 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 14042.0333333333 & 377.696576547855 & 37.1780794564712 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 13992.5333333333 & 368.74139075781 & 37.9467390535598 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 13992.8666666667 & 366.006177178173 & 38.2312308894582 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 13878.8333333333 & 346.738434417172 & 40.0268097093478 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 13874.6333333333 & 345.39570360901 & 40.1702545467662 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 13747.45 & 326.158338575045 & 42.1496199056609 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 13728.55 & 322.908612445573 & 42.5152797753698 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 13694.3 & 315.310855764136 & 43.4311085383112 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 13663.9 & 310.762523735073 & 43.9689439890395 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 13678.35 & 304.74249927042 & 44.8849439534924 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 13678.05 & 298.910713975559 & 45.7596511616456 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 13675.2 & 298.545933590255 & 45.8060166338383 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 13803.5333333333 & 269.972890945692 & 51.1293311153603 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 14118.2586206897 & 404.181138047665 & 34.9305232027544 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 14079.5357142857 & 398.663790879768 & 35.3168159145207 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 14049.5740740741 & 395.4478470314 & 35.5282603750236 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 14021 & 392.205900421949 & 35.7490797178617 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 14001.9 & 390.754512684976 & 35.832983485691 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 13982.9375 & 388.919799302155 & 35.9532672933849 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 13962.5434782609 & 386.33419702861 & 36.1411016307906 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 13939.3181818182 & 383.124817197432 & 36.3832295798133 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 13920.9761904762 & 380.424842724267 & 36.5932363690722 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 13909.05 & 378.409300432542 & 36.756628296665 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 13895.8157894737 & 375.502871656125 & 37.0058842111841 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 13898.3888888889 & 375.413882242785 & 37.0215102485225 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 13901.8823529412 & 374.285853003869 & 37.1424200016383 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 13924.15625 & 375.910000996976 & 37.0411965977783 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 13952.1 & 376.977932675293 & 37.0103891784497 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 13988.9285714286 & 378.162344860372 & 36.9918601403682 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 14035.8076923077 & 378.356819862012 & 37.096748242642 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 14088.375 & 377.510599776802 & 37.3191507955792 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 14150.5454545455 & 374.571476526383 & 37.7779578567263 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 14225.6 & 365.626653122669 & 38.9074480170002 \tabularnewline
Median & 14942.5 &  &  \tabularnewline
Midrange & 15222 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 13845.9677419355 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 13952.1 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 13845.9677419355 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 13952.1 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 13952.1 &  &  \tabularnewline
Midmean - Closest Observation & 13845.9677419355 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 13952.1 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 13924.15625 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=18119&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]14155.05[/C][C]408.581082981159[/C][C]34.6444086366396[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]13806.2145028864[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]13464.9649175676[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]14498.7865727906[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]14154.4[/C][C]408.413188225337[/C][C]34.6570590962173[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]14133.4666666667[/C][C]402.377953189294[/C][C]35.1248535230203[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]14123.8666666667[/C][C]399.83500443574[/C][C]35.3242375229221[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]14084.6666666667[/C][C]391.670501483811[/C][C]35.9604989737754[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]14077.75[/C][C]389.806918469184[/C][C]36.114674555508[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]14076.75[/C][C]388.49887305423[/C][C]36.2336958388938[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]14081.7666666667[/C][C]385.695322194979[/C][C]36.5100789569545[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]14042.0333333333[/C][C]377.696576547855[/C][C]37.1780794564712[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]13992.5333333333[/C][C]368.74139075781[/C][C]37.9467390535598[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]13992.8666666667[/C][C]366.006177178173[/C][C]38.2312308894582[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]13878.8333333333[/C][C]346.738434417172[/C][C]40.0268097093478[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]13874.6333333333[/C][C]345.39570360901[/C][C]40.1702545467662[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]13747.45[/C][C]326.158338575045[/C][C]42.1496199056609[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]13728.55[/C][C]322.908612445573[/C][C]42.5152797753698[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]13694.3[/C][C]315.310855764136[/C][C]43.4311085383112[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]13663.9[/C][C]310.762523735073[/C][C]43.9689439890395[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]13678.35[/C][C]304.74249927042[/C][C]44.8849439534924[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]13678.05[/C][C]298.910713975559[/C][C]45.7596511616456[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]13675.2[/C][C]298.545933590255[/C][C]45.8060166338383[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]13803.5333333333[/C][C]269.972890945692[/C][C]51.1293311153603[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]14118.2586206897[/C][C]404.181138047665[/C][C]34.9305232027544[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]14079.5357142857[/C][C]398.663790879768[/C][C]35.3168159145207[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]14049.5740740741[/C][C]395.4478470314[/C][C]35.5282603750236[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]14021[/C][C]392.205900421949[/C][C]35.7490797178617[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]14001.9[/C][C]390.754512684976[/C][C]35.832983485691[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]13982.9375[/C][C]388.919799302155[/C][C]35.9532672933849[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]13962.5434782609[/C][C]386.33419702861[/C][C]36.1411016307906[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]13939.3181818182[/C][C]383.124817197432[/C][C]36.3832295798133[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]13920.9761904762[/C][C]380.424842724267[/C][C]36.5932363690722[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]13909.05[/C][C]378.409300432542[/C][C]36.756628296665[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]13895.8157894737[/C][C]375.502871656125[/C][C]37.0058842111841[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]13898.3888888889[/C][C]375.413882242785[/C][C]37.0215102485225[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]13901.8823529412[/C][C]374.285853003869[/C][C]37.1424200016383[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]13924.15625[/C][C]375.910000996976[/C][C]37.0411965977783[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]13952.1[/C][C]376.977932675293[/C][C]37.0103891784497[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]13988.9285714286[/C][C]378.162344860372[/C][C]36.9918601403682[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]14035.8076923077[/C][C]378.356819862012[/C][C]37.096748242642[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]14088.375[/C][C]377.510599776802[/C][C]37.3191507955792[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]14150.5454545455[/C][C]374.571476526383[/C][C]37.7779578567263[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]14225.6[/C][C]365.626653122669[/C][C]38.9074480170002[/C][/ROW]
[ROW][C]Median[/C][C]14942.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]15222[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]13845.9677419355[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]13952.1[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]13845.9677419355[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]13952.1[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]13952.1[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]13845.9677419355[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]13952.1[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]13924.15625[/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=18119&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=18119&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 Mean14155.05408.58108298115934.6444086366396
Geometric Mean13806.2145028864
Harmonic Mean13464.9649175676
Quadratic Mean14498.7865727906
Winsorized Mean ( 1 / 20 )14154.4408.41318822533734.6570590962173
Winsorized Mean ( 2 / 20 )14133.4666666667402.37795318929435.1248535230203
Winsorized Mean ( 3 / 20 )14123.8666666667399.8350044357435.3242375229221
Winsorized Mean ( 4 / 20 )14084.6666666667391.67050148381135.9604989737754
Winsorized Mean ( 5 / 20 )14077.75389.80691846918436.114674555508
Winsorized Mean ( 6 / 20 )14076.75388.4988730542336.2336958388938
Winsorized Mean ( 7 / 20 )14081.7666666667385.69532219497936.5100789569545
Winsorized Mean ( 8 / 20 )14042.0333333333377.69657654785537.1780794564712
Winsorized Mean ( 9 / 20 )13992.5333333333368.7413907578137.9467390535598
Winsorized Mean ( 10 / 20 )13992.8666666667366.00617717817338.2312308894582
Winsorized Mean ( 11 / 20 )13878.8333333333346.73843441717240.0268097093478
Winsorized Mean ( 12 / 20 )13874.6333333333345.3957036090140.1702545467662
Winsorized Mean ( 13 / 20 )13747.45326.15833857504542.1496199056609
Winsorized Mean ( 14 / 20 )13728.55322.90861244557342.5152797753698
Winsorized Mean ( 15 / 20 )13694.3315.31085576413643.4311085383112
Winsorized Mean ( 16 / 20 )13663.9310.76252373507343.9689439890395
Winsorized Mean ( 17 / 20 )13678.35304.7424992704244.8849439534924
Winsorized Mean ( 18 / 20 )13678.05298.91071397555945.7596511616456
Winsorized Mean ( 19 / 20 )13675.2298.54593359025545.8060166338383
Winsorized Mean ( 20 / 20 )13803.5333333333269.97289094569251.1293311153603
Trimmed Mean ( 1 / 20 )14118.2586206897404.18113804766534.9305232027544
Trimmed Mean ( 2 / 20 )14079.5357142857398.66379087976835.3168159145207
Trimmed Mean ( 3 / 20 )14049.5740740741395.447847031435.5282603750236
Trimmed Mean ( 4 / 20 )14021392.20590042194935.7490797178617
Trimmed Mean ( 5 / 20 )14001.9390.75451268497635.832983485691
Trimmed Mean ( 6 / 20 )13982.9375388.91979930215535.9532672933849
Trimmed Mean ( 7 / 20 )13962.5434782609386.3341970286136.1411016307906
Trimmed Mean ( 8 / 20 )13939.3181818182383.12481719743236.3832295798133
Trimmed Mean ( 9 / 20 )13920.9761904762380.42484272426736.5932363690722
Trimmed Mean ( 10 / 20 )13909.05378.40930043254236.756628296665
Trimmed Mean ( 11 / 20 )13895.8157894737375.50287165612537.0058842111841
Trimmed Mean ( 12 / 20 )13898.3888888889375.41388224278537.0215102485225
Trimmed Mean ( 13 / 20 )13901.8823529412374.28585300386937.1424200016383
Trimmed Mean ( 14 / 20 )13924.15625375.91000099697637.0411965977783
Trimmed Mean ( 15 / 20 )13952.1376.97793267529337.0103891784497
Trimmed Mean ( 16 / 20 )13988.9285714286378.16234486037236.9918601403682
Trimmed Mean ( 17 / 20 )14035.8076923077378.35681986201237.096748242642
Trimmed Mean ( 18 / 20 )14088.375377.51059977680237.3191507955792
Trimmed Mean ( 19 / 20 )14150.5454545455374.57147652638337.7779578567263
Trimmed Mean ( 20 / 20 )14225.6365.62665312266938.9074480170002
Median14942.5
Midrange15222
Midmean - Weighted Average at Xnp13845.9677419355
Midmean - Weighted Average at X(n+1)p13952.1
Midmean - Empirical Distribution Function13845.9677419355
Midmean - Empirical Distribution Function - Averaging13952.1
Midmean - Empirical Distribution Function - Interpolation13952.1
Midmean - Closest Observation13845.9677419355
Midmean - True Basic - Statistics Graphics Toolkit13952.1
Midmean - MS Excel (old versions)13924.15625
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')