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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, 28 Dec 2009 05:36:21 -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/2009/Dec/28/t12620038474qwbrumlmhcy1jj.htm/, Retrieved Sun, 05 May 2024 14:18:39 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=70947, Retrieved Sun, 05 May 2024 14:18:39 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact127
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [paper central ten...] [2009-12-28 12:36:21] [90d336e5f53609c0c5a6217e988a780d] [Current]
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Dataseries X:
4223.4
4627.3
5175.3
4550.7
4639.3
5498.7
5031.0
4033.3
4643.5
4873.2
4608.7
4733.5
3955.6
4590.9
5127.5
5257.3
5416.9
5813.3
5261.9
4669.2
5855.8
5274.6
5516.7
5819.5
5156.0
5377.3
6386.8
5144.0
6138.5
5567.8
5822.6
5145.5
5706.6
6078.5
6074.5
5577.6
5727.5
6067.0
7069.9
5490.0
5948.3
6177.5
6890.1
5756.2
6528.8
6792.0
6657.4
5753.7
5750.9
5968.4
5871.7
7004.9
6363.4
6694.7
7101.6
5364.0
6958.6
6503.3
5316.0
5312.7
4478.0




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=70947&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=70947&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=70947&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 Mean5588.84262295082100.26816969989755.7389512512122
Geometric Mean5534.1805271446
Harmonic Mean5478.8297271264
Quadratic Mean5642.55121513397
Winsorized Mean ( 1 / 20 )5589.5967213114899.800150299590456.0078988311345
Winsorized Mean ( 2 / 20 )5593.6983606557497.741251351730757.2296577268722
Winsorized Mean ( 3 / 20 )5603.9426229508294.485177414990259.3102831181407
Winsorized Mean ( 4 / 20 )5604.2180327868992.501908841866960.5848906574173
Winsorized Mean ( 5 / 20 )5599.4721311475490.062254338065362.1733507816592
Winsorized Mean ( 6 / 20 )5591.652459016487.67515738163163.776930957502
Winsorized Mean ( 7 / 20 )5589.5065573770586.387871032792764.7024459632218
Winsorized Mean ( 8 / 20 )5574.2147540983682.732093594805167.3766915823387
Winsorized Mean ( 9 / 20 )5571.0721311475481.896589236582468.0256917055954
Winsorized Mean ( 10 / 20 )5556.186885245977.579073796497971.6196599590845
Winsorized Mean ( 11 / 20 )5563.5622950819774.645994265681974.5326303147628
Winsorized Mean ( 12 / 20 )5554.473770491863.344579555202387.6866467422252
Winsorized Mean ( 13 / 20 )5579.7918032786956.208494112150399.2695479822956
Winsorized Mean ( 14 / 20 )5588.1688524590250.4580402720201110.748828577826
Winsorized Mean ( 15 / 20 )5591.2426229508249.6855885285293112.532482527410
Winsorized Mean ( 16 / 20 )5589.6688524590249.3083936115528113.361406508067
Winsorized Mean ( 17 / 20 )5565.1163934426244.5690501412538124.865043697475
Winsorized Mean ( 18 / 20 )5564.8803278688542.8114699035055129.985733739387
Winsorized Mean ( 19 / 20 )5566.5622950819735.5180441453666156.724910648216
Winsorized Mean ( 20 / 20 )5562.8573770491834.5576076777593160.973451314147
Trimmed Mean ( 1 / 20 )5590.8847457627196.460445187445357.96038712965
Trimmed Mean ( 2 / 20 )5592.2631578947492.356262996800660.5509900079918
Trimmed Mean ( 3 / 20 )5591.4672727272788.681650479005263.0510059581155
Trimmed Mean ( 4 / 20 )5586.6811320754785.712452165036865.179340818747
Trimmed Mean ( 5 / 20 )5581.4372549019682.779501439160467.4253548024096
Trimmed Mean ( 6 / 20 )5576.9469387755179.92907874121169.7736922107181
Trimmed Mean ( 7 / 20 )5573.7659574468177.060871711295172.3293914754645
Trimmed Mean ( 8 / 20 )5570.7177777777873.746407088573675.5388363678115
Trimmed Mean ( 9 / 20 )5570.097674418670.525700842912378.9796855308867
Trimmed Mean ( 10 / 20 )5569.9365853658566.504017919706283.753384526191
Trimmed Mean ( 11 / 20 )5572.0871794871862.421847513163589.2650153988495
Trimmed Mean ( 12 / 20 )5573.3648648648757.76836424160296.4778029988116
Trimmed Mean ( 13 / 20 )5576.1085714285754.9228288810119101.526244824515
Trimmed Mean ( 14 / 20 )5575.5848484848553.0885022793578105.024338775757
Trimmed Mean ( 15 / 20 )5573.8161290322652.0795318382353107.025081299600
Trimmed Mean ( 16 / 20 )5571.372413793150.6949096502508109.900036359283
Trimmed Mean ( 17 / 20 )5568.7888888888948.6223974199565114.531351483776
Trimmed Mean ( 18 / 20 )5569.31647.0732389226264118.311722912337
Trimmed Mean ( 19 / 20 )5569.9695652173945.1314853046261123.416491339062
Trimmed Mean ( 20 / 20 )5570.4904761904844.7702435748407124.423948395065
Median5567.8
Midrange5528.6
Midmean - Weighted Average at Xnp5557.12666666667
Midmean - Weighted Average at X(n+1)p5573.81612903226
Midmean - Empirical Distribution Function5573.81612903226
Midmean - Empirical Distribution Function - Averaging5573.81612903226
Midmean - Empirical Distribution Function - Interpolation5573.81612903226
Midmean - Closest Observation5559.86875
Midmean - True Basic - Statistics Graphics Toolkit5573.81612903226
Midmean - MS Excel (old versions)5573.81612903226
Number of observations61

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 5588.84262295082 & 100.268169699897 & 55.7389512512122 \tabularnewline
Geometric Mean & 5534.1805271446 &  &  \tabularnewline
Harmonic Mean & 5478.8297271264 &  &  \tabularnewline
Quadratic Mean & 5642.55121513397 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 5589.59672131148 & 99.8001502995904 & 56.0078988311345 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 5593.69836065574 & 97.7412513517307 & 57.2296577268722 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 5603.94262295082 & 94.4851774149902 & 59.3102831181407 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 5604.21803278689 & 92.5019088418669 & 60.5848906574173 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 5599.47213114754 & 90.0622543380653 & 62.1733507816592 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 5591.6524590164 & 87.675157381631 & 63.776930957502 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 5589.50655737705 & 86.3878710327927 & 64.7024459632218 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 5574.21475409836 & 82.7320935948051 & 67.3766915823387 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 5571.07213114754 & 81.8965892365824 & 68.0256917055954 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 5556.1868852459 & 77.5790737964979 & 71.6196599590845 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 5563.56229508197 & 74.6459942656819 & 74.5326303147628 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 5554.4737704918 & 63.3445795552023 & 87.6866467422252 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 5579.79180327869 & 56.2084941121503 & 99.2695479822956 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 5588.16885245902 & 50.4580402720201 & 110.748828577826 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 5591.24262295082 & 49.6855885285293 & 112.532482527410 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 5589.66885245902 & 49.3083936115528 & 113.361406508067 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 5565.11639344262 & 44.5690501412538 & 124.865043697475 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 5564.88032786885 & 42.8114699035055 & 129.985733739387 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 5566.56229508197 & 35.5180441453666 & 156.724910648216 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 5562.85737704918 & 34.5576076777593 & 160.973451314147 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 5590.88474576271 & 96.4604451874453 & 57.96038712965 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 5592.26315789474 & 92.3562629968006 & 60.5509900079918 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 5591.46727272727 & 88.6816504790052 & 63.0510059581155 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 5586.68113207547 & 85.7124521650368 & 65.179340818747 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 5581.43725490196 & 82.7795014391604 & 67.4253548024096 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 5576.94693877551 & 79.929078741211 & 69.7736922107181 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 5573.76595744681 & 77.0608717112951 & 72.3293914754645 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 5570.71777777778 & 73.7464070885736 & 75.5388363678115 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 5570.0976744186 & 70.5257008429123 & 78.9796855308867 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 5569.93658536585 & 66.5040179197062 & 83.753384526191 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 5572.08717948718 & 62.4218475131635 & 89.2650153988495 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 5573.36486486487 & 57.768364241602 & 96.4778029988116 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 5576.10857142857 & 54.9228288810119 & 101.526244824515 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 5575.58484848485 & 53.0885022793578 & 105.024338775757 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 5573.81612903226 & 52.0795318382353 & 107.025081299600 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 5571.3724137931 & 50.6949096502508 & 109.900036359283 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 5568.78888888889 & 48.6223974199565 & 114.531351483776 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 5569.316 & 47.0732389226264 & 118.311722912337 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 5569.96956521739 & 45.1314853046261 & 123.416491339062 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 5570.49047619048 & 44.7702435748407 & 124.423948395065 \tabularnewline
Median & 5567.8 &  &  \tabularnewline
Midrange & 5528.6 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 5557.12666666667 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 5573.81612903226 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 5573.81612903226 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 5573.81612903226 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 5573.81612903226 &  &  \tabularnewline
Midmean - Closest Observation & 5559.86875 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 5573.81612903226 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 5573.81612903226 &  &  \tabularnewline
Number of observations & 61 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=70947&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]5588.84262295082[/C][C]100.268169699897[/C][C]55.7389512512122[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]5534.1805271446[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]5478.8297271264[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]5642.55121513397[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]5589.59672131148[/C][C]99.8001502995904[/C][C]56.0078988311345[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]5593.69836065574[/C][C]97.7412513517307[/C][C]57.2296577268722[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]5603.94262295082[/C][C]94.4851774149902[/C][C]59.3102831181407[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]5604.21803278689[/C][C]92.5019088418669[/C][C]60.5848906574173[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]5599.47213114754[/C][C]90.0622543380653[/C][C]62.1733507816592[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]5591.6524590164[/C][C]87.675157381631[/C][C]63.776930957502[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]5589.50655737705[/C][C]86.3878710327927[/C][C]64.7024459632218[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]5574.21475409836[/C][C]82.7320935948051[/C][C]67.3766915823387[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]5571.07213114754[/C][C]81.8965892365824[/C][C]68.0256917055954[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]5556.1868852459[/C][C]77.5790737964979[/C][C]71.6196599590845[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]5563.56229508197[/C][C]74.6459942656819[/C][C]74.5326303147628[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]5554.4737704918[/C][C]63.3445795552023[/C][C]87.6866467422252[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]5579.79180327869[/C][C]56.2084941121503[/C][C]99.2695479822956[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]5588.16885245902[/C][C]50.4580402720201[/C][C]110.748828577826[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]5591.24262295082[/C][C]49.6855885285293[/C][C]112.532482527410[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]5589.66885245902[/C][C]49.3083936115528[/C][C]113.361406508067[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]5565.11639344262[/C][C]44.5690501412538[/C][C]124.865043697475[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]5564.88032786885[/C][C]42.8114699035055[/C][C]129.985733739387[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]5566.56229508197[/C][C]35.5180441453666[/C][C]156.724910648216[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]5562.85737704918[/C][C]34.5576076777593[/C][C]160.973451314147[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]5590.88474576271[/C][C]96.4604451874453[/C][C]57.96038712965[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]5592.26315789474[/C][C]92.3562629968006[/C][C]60.5509900079918[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]5591.46727272727[/C][C]88.6816504790052[/C][C]63.0510059581155[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]5586.68113207547[/C][C]85.7124521650368[/C][C]65.179340818747[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]5581.43725490196[/C][C]82.7795014391604[/C][C]67.4253548024096[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]5576.94693877551[/C][C]79.929078741211[/C][C]69.7736922107181[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]5573.76595744681[/C][C]77.0608717112951[/C][C]72.3293914754645[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]5570.71777777778[/C][C]73.7464070885736[/C][C]75.5388363678115[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]5570.0976744186[/C][C]70.5257008429123[/C][C]78.9796855308867[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]5569.93658536585[/C][C]66.5040179197062[/C][C]83.753384526191[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]5572.08717948718[/C][C]62.4218475131635[/C][C]89.2650153988495[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]5573.36486486487[/C][C]57.768364241602[/C][C]96.4778029988116[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]5576.10857142857[/C][C]54.9228288810119[/C][C]101.526244824515[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]5575.58484848485[/C][C]53.0885022793578[/C][C]105.024338775757[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]5573.81612903226[/C][C]52.0795318382353[/C][C]107.025081299600[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]5571.3724137931[/C][C]50.6949096502508[/C][C]109.900036359283[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]5568.78888888889[/C][C]48.6223974199565[/C][C]114.531351483776[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]5569.316[/C][C]47.0732389226264[/C][C]118.311722912337[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]5569.96956521739[/C][C]45.1314853046261[/C][C]123.416491339062[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]5570.49047619048[/C][C]44.7702435748407[/C][C]124.423948395065[/C][/ROW]
[ROW][C]Median[/C][C]5567.8[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]5528.6[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]5557.12666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]5573.81612903226[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]5573.81612903226[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]5573.81612903226[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]5573.81612903226[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]5559.86875[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]5573.81612903226[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]5573.81612903226[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]61[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=70947&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=70947&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 Mean5588.84262295082100.26816969989755.7389512512122
Geometric Mean5534.1805271446
Harmonic Mean5478.8297271264
Quadratic Mean5642.55121513397
Winsorized Mean ( 1 / 20 )5589.5967213114899.800150299590456.0078988311345
Winsorized Mean ( 2 / 20 )5593.6983606557497.741251351730757.2296577268722
Winsorized Mean ( 3 / 20 )5603.9426229508294.485177414990259.3102831181407
Winsorized Mean ( 4 / 20 )5604.2180327868992.501908841866960.5848906574173
Winsorized Mean ( 5 / 20 )5599.4721311475490.062254338065362.1733507816592
Winsorized Mean ( 6 / 20 )5591.652459016487.67515738163163.776930957502
Winsorized Mean ( 7 / 20 )5589.5065573770586.387871032792764.7024459632218
Winsorized Mean ( 8 / 20 )5574.2147540983682.732093594805167.3766915823387
Winsorized Mean ( 9 / 20 )5571.0721311475481.896589236582468.0256917055954
Winsorized Mean ( 10 / 20 )5556.186885245977.579073796497971.6196599590845
Winsorized Mean ( 11 / 20 )5563.5622950819774.645994265681974.5326303147628
Winsorized Mean ( 12 / 20 )5554.473770491863.344579555202387.6866467422252
Winsorized Mean ( 13 / 20 )5579.7918032786956.208494112150399.2695479822956
Winsorized Mean ( 14 / 20 )5588.1688524590250.4580402720201110.748828577826
Winsorized Mean ( 15 / 20 )5591.2426229508249.6855885285293112.532482527410
Winsorized Mean ( 16 / 20 )5589.6688524590249.3083936115528113.361406508067
Winsorized Mean ( 17 / 20 )5565.1163934426244.5690501412538124.865043697475
Winsorized Mean ( 18 / 20 )5564.8803278688542.8114699035055129.985733739387
Winsorized Mean ( 19 / 20 )5566.5622950819735.5180441453666156.724910648216
Winsorized Mean ( 20 / 20 )5562.8573770491834.5576076777593160.973451314147
Trimmed Mean ( 1 / 20 )5590.8847457627196.460445187445357.96038712965
Trimmed Mean ( 2 / 20 )5592.2631578947492.356262996800660.5509900079918
Trimmed Mean ( 3 / 20 )5591.4672727272788.681650479005263.0510059581155
Trimmed Mean ( 4 / 20 )5586.6811320754785.712452165036865.179340818747
Trimmed Mean ( 5 / 20 )5581.4372549019682.779501439160467.4253548024096
Trimmed Mean ( 6 / 20 )5576.9469387755179.92907874121169.7736922107181
Trimmed Mean ( 7 / 20 )5573.7659574468177.060871711295172.3293914754645
Trimmed Mean ( 8 / 20 )5570.7177777777873.746407088573675.5388363678115
Trimmed Mean ( 9 / 20 )5570.097674418670.525700842912378.9796855308867
Trimmed Mean ( 10 / 20 )5569.9365853658566.504017919706283.753384526191
Trimmed Mean ( 11 / 20 )5572.0871794871862.421847513163589.2650153988495
Trimmed Mean ( 12 / 20 )5573.3648648648757.76836424160296.4778029988116
Trimmed Mean ( 13 / 20 )5576.1085714285754.9228288810119101.526244824515
Trimmed Mean ( 14 / 20 )5575.5848484848553.0885022793578105.024338775757
Trimmed Mean ( 15 / 20 )5573.8161290322652.0795318382353107.025081299600
Trimmed Mean ( 16 / 20 )5571.372413793150.6949096502508109.900036359283
Trimmed Mean ( 17 / 20 )5568.7888888888948.6223974199565114.531351483776
Trimmed Mean ( 18 / 20 )5569.31647.0732389226264118.311722912337
Trimmed Mean ( 19 / 20 )5569.9695652173945.1314853046261123.416491339062
Trimmed Mean ( 20 / 20 )5570.4904761904844.7702435748407124.423948395065
Median5567.8
Midrange5528.6
Midmean - Weighted Average at Xnp5557.12666666667
Midmean - Weighted Average at X(n+1)p5573.81612903226
Midmean - Empirical Distribution Function5573.81612903226
Midmean - Empirical Distribution Function - Averaging5573.81612903226
Midmean - Empirical Distribution Function - Interpolation5573.81612903226
Midmean - Closest Observation5559.86875
Midmean - True Basic - Statistics Graphics Toolkit5573.81612903226
Midmean - MS Excel (old versions)5573.81612903226
Number of observations61



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')