Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationThu, 13 Oct 2016 19:08:57 +0100
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2016/Oct/13/t1476382175bpjh5c0f96yl6k7.htm/, Retrieved Tue, 30 Apr 2024 13:31:32 +0200
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=, Retrieved Tue, 30 Apr 2024 13:31:32 +0200
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact0
Dataseries X:
1.336
1.3649
1.3999
1.4442
1.4349
1.4388
1.4264
1.4343
1.377
1.3706
1.3556
1.3179
1.2905
1.3224
1.3201
1.3162
1.2789
1.2526
1.2288
1.24
1.2856
1.2974
1.2828
1.3119
1.3288
1.3359
1.2964
1.3026
1.2982
1.3189
1.308
1.331
1.3348
1.3635
1.3493
1.3704
1.361
1.3658
1.3823
1.3812
1.3732
1.3592
1.3539
1.3316
1.2901
1.2673
1.2472
1.2331
1.1621
1.135
1.0838
1.0779
1.115
1.1213
1.0996
1.1139
1.1221
1.1235
1.0736
1.0877




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ jenkins.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 & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=0

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

As an alternative you can also use a QR Code:  

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

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean1.288781666666670.013329435480747396.6868903434171
Geometric Mean1.28452257615098
Harmonic Mean1.28006962854624
Quadratic Mean1.29284219512669
Winsorized Mean ( 1 / 20 )1.288763333333330.013292493733012896.9542178630187
Winsorized Mean ( 2 / 20 )1.288830.01321558323014997.5235052101044
Winsorized Mean ( 3 / 20 )1.2889950.013159048019291297.9550342935394
Winsorized Mean ( 4 / 20 )1.289261666666670.0128601076103402100.25278992456
Winsorized Mean ( 5 / 20 )1.2882450.0121950020847664105.637128312527
Winsorized Mean ( 6 / 20 )1.2865950.0119116518052205108.011468185808
Winsorized Mean ( 7 / 20 )1.287201666666670.0117162455401651109.86468850059
Winsorized Mean ( 8 / 20 )1.286748333333330.0116156786921102110.776853203364
Winsorized Mean ( 9 / 20 )1.286388333333330.0114911953746927111.945562788565
Winsorized Mean ( 10 / 20 )1.287871666666670.0109792814877303117.300177439289
Winsorized Mean ( 11 / 20 )1.292803333333330.00982676989612239131.559337096462
Winsorized Mean ( 12 / 20 )1.305223333333330.00689776405541814189.224119996985
Winsorized Mean ( 13 / 20 )1.305960.0066952825959438195.056740516254
Winsorized Mean ( 14 / 20 )1.307243333333330.00635341154260883205.754550065956
Winsorized Mean ( 15 / 20 )1.308418333333330.00594085181534618220.240863431987
Winsorized Mean ( 16 / 20 )1.309378333333330.00561966989986312232.999154161213
Winsorized Mean ( 17 / 20 )1.312523333333330.00477221381231322275.034477698123
Winsorized Mean ( 18 / 20 )1.315493333333330.00415257517724082316.789769524995
Winsorized Mean ( 19 / 20 )1.315271666666670.00374297088238278351.397782135394
Winsorized Mean ( 20 / 20 )1.311771666666670.00295036633909078444.613148301752
Trimmed Mean ( 1 / 20 )1.289812068965520.012996879907951799.2401313315503
Trimmed Mean ( 2 / 20 )1.290935714285710.0126294724439108102.216123438167
Trimmed Mean ( 3 / 20 )1.292105555555560.0122226918387004105.71366541897
Trimmed Mean ( 4 / 20 )1.293301923076920.0117395515273469110.166212062209
Trimmed Mean ( 5 / 20 )1.2945140.0112518820230762115.048664511867
Trimmed Mean ( 6 / 20 )1.296081250.0108653989395554119.285196724957
Trimmed Mean ( 7 / 20 )1.298143478260870.0104469359177375124.260691219212
Trimmed Mean ( 8 / 20 )1.3002750.00995615978178448130.600053484371
Trimmed Mean ( 9 / 20 )1.302690476190480.00932278988610379139.731828358828
Trimmed Mean ( 10 / 20 )1.30540750.00848416729629599153.863950864089
Trimmed Mean ( 11 / 20 )1.308176315789470.00748209853551603174.840829692341
Trimmed Mean ( 12 / 20 )1.310505555555560.00650427325277292201.483779144251
Trimmed Mean ( 13 / 20 )1.311282352941180.00623022571727572210.47108282211
Trimmed Mean ( 14 / 20 )1.312050.00590115488970236222.337834631244
Trimmed Mean ( 15 / 20 )1.312736666666670.00553905565488312236.996475294373
Trimmed Mean ( 16 / 20 )1.313353571428570.00515083720051538254.97866080822
Trimmed Mean ( 17 / 20 )1.313926923076920.0046832091485427280.561230857218
Trimmed Mean ( 18 / 20 )1.314133333333330.00432894566048143303.568914096091
Trimmed Mean ( 19 / 20 )1.313927272727270.00403465604845797325.660293454122
Trimmed Mean ( 20 / 20 )1.3137150.00373447857982314351.780033522703
Median1.31705
Midrange1.2589
Midmean - Weighted Average at Xnp1.31039032258065
Midmean - Weighted Average at X(n+1)p1.31273666666667
Midmean - Empirical Distribution Function1.31039032258065
Midmean - Empirical Distribution Function - Averaging1.31273666666667
Midmean - Empirical Distribution Function - Interpolation1.31273666666667
Midmean - Closest Observation1.31039032258065
Midmean - True Basic - Statistics Graphics Toolkit1.31273666666667
Midmean - MS Excel (old versions)1.31205
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 1.28878166666667 & 0.0133294354807473 & 96.6868903434171 \tabularnewline
Geometric Mean & 1.28452257615098 &  &  \tabularnewline
Harmonic Mean & 1.28006962854624 &  &  \tabularnewline
Quadratic Mean & 1.29284219512669 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 1.28876333333333 & 0.0132924937330128 & 96.9542178630187 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 1.28883 & 0.013215583230149 & 97.5235052101044 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 1.288995 & 0.0131590480192912 & 97.9550342935394 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 1.28926166666667 & 0.0128601076103402 & 100.25278992456 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 1.288245 & 0.0121950020847664 & 105.637128312527 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 1.286595 & 0.0119116518052205 & 108.011468185808 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 1.28720166666667 & 0.0117162455401651 & 109.86468850059 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 1.28674833333333 & 0.0116156786921102 & 110.776853203364 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 1.28638833333333 & 0.0114911953746927 & 111.945562788565 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 1.28787166666667 & 0.0109792814877303 & 117.300177439289 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 1.29280333333333 & 0.00982676989612239 & 131.559337096462 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 1.30522333333333 & 0.00689776405541814 & 189.224119996985 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 1.30596 & 0.0066952825959438 & 195.056740516254 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 1.30724333333333 & 0.00635341154260883 & 205.754550065956 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 1.30841833333333 & 0.00594085181534618 & 220.240863431987 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 1.30937833333333 & 0.00561966989986312 & 232.999154161213 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 1.31252333333333 & 0.00477221381231322 & 275.034477698123 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 1.31549333333333 & 0.00415257517724082 & 316.789769524995 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 1.31527166666667 & 0.00374297088238278 & 351.397782135394 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 1.31177166666667 & 0.00295036633909078 & 444.613148301752 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 1.28981206896552 & 0.0129968799079517 & 99.2401313315503 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 1.29093571428571 & 0.0126294724439108 & 102.216123438167 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 1.29210555555556 & 0.0122226918387004 & 105.71366541897 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 1.29330192307692 & 0.0117395515273469 & 110.166212062209 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 1.294514 & 0.0112518820230762 & 115.048664511867 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 1.29608125 & 0.0108653989395554 & 119.285196724957 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 1.29814347826087 & 0.0104469359177375 & 124.260691219212 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 1.300275 & 0.00995615978178448 & 130.600053484371 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 1.30269047619048 & 0.00932278988610379 & 139.731828358828 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 1.3054075 & 0.00848416729629599 & 153.863950864089 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 1.30817631578947 & 0.00748209853551603 & 174.840829692341 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 1.31050555555556 & 0.00650427325277292 & 201.483779144251 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 1.31128235294118 & 0.00623022571727572 & 210.47108282211 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 1.31205 & 0.00590115488970236 & 222.337834631244 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 1.31273666666667 & 0.00553905565488312 & 236.996475294373 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 1.31335357142857 & 0.00515083720051538 & 254.97866080822 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 1.31392692307692 & 0.0046832091485427 & 280.561230857218 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 1.31413333333333 & 0.00432894566048143 & 303.568914096091 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 1.31392727272727 & 0.00403465604845797 & 325.660293454122 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 1.313715 & 0.00373447857982314 & 351.780033522703 \tabularnewline
Median & 1.31705 &  &  \tabularnewline
Midrange & 1.2589 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 1.31039032258065 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 1.31273666666667 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 1.31039032258065 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 1.31273666666667 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 1.31273666666667 &  &  \tabularnewline
Midmean - Closest Observation & 1.31039032258065 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 1.31273666666667 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 1.31205 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]1.28878166666667[/C][C]0.0133294354807473[/C][C]96.6868903434171[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]1.28452257615098[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]1.28006962854624[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]1.29284219512669[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]1.28876333333333[/C][C]0.0132924937330128[/C][C]96.9542178630187[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]1.28883[/C][C]0.013215583230149[/C][C]97.5235052101044[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]1.288995[/C][C]0.0131590480192912[/C][C]97.9550342935394[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]1.28926166666667[/C][C]0.0128601076103402[/C][C]100.25278992456[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]1.288245[/C][C]0.0121950020847664[/C][C]105.637128312527[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]1.286595[/C][C]0.0119116518052205[/C][C]108.011468185808[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]1.28720166666667[/C][C]0.0117162455401651[/C][C]109.86468850059[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]1.28674833333333[/C][C]0.0116156786921102[/C][C]110.776853203364[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]1.28638833333333[/C][C]0.0114911953746927[/C][C]111.945562788565[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]1.28787166666667[/C][C]0.0109792814877303[/C][C]117.300177439289[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]1.29280333333333[/C][C]0.00982676989612239[/C][C]131.559337096462[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]1.30522333333333[/C][C]0.00689776405541814[/C][C]189.224119996985[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]1.30596[/C][C]0.0066952825959438[/C][C]195.056740516254[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]1.30724333333333[/C][C]0.00635341154260883[/C][C]205.754550065956[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]1.30841833333333[/C][C]0.00594085181534618[/C][C]220.240863431987[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]1.30937833333333[/C][C]0.00561966989986312[/C][C]232.999154161213[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]1.31252333333333[/C][C]0.00477221381231322[/C][C]275.034477698123[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]1.31549333333333[/C][C]0.00415257517724082[/C][C]316.789769524995[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]1.31527166666667[/C][C]0.00374297088238278[/C][C]351.397782135394[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]1.31177166666667[/C][C]0.00295036633909078[/C][C]444.613148301752[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]1.28981206896552[/C][C]0.0129968799079517[/C][C]99.2401313315503[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]1.29093571428571[/C][C]0.0126294724439108[/C][C]102.216123438167[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]1.29210555555556[/C][C]0.0122226918387004[/C][C]105.71366541897[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]1.29330192307692[/C][C]0.0117395515273469[/C][C]110.166212062209[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]1.294514[/C][C]0.0112518820230762[/C][C]115.048664511867[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]1.29608125[/C][C]0.0108653989395554[/C][C]119.285196724957[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]1.29814347826087[/C][C]0.0104469359177375[/C][C]124.260691219212[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]1.300275[/C][C]0.00995615978178448[/C][C]130.600053484371[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]1.30269047619048[/C][C]0.00932278988610379[/C][C]139.731828358828[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]1.3054075[/C][C]0.00848416729629599[/C][C]153.863950864089[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]1.30817631578947[/C][C]0.00748209853551603[/C][C]174.840829692341[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]1.31050555555556[/C][C]0.00650427325277292[/C][C]201.483779144251[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]1.31128235294118[/C][C]0.00623022571727572[/C][C]210.47108282211[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]1.31205[/C][C]0.00590115488970236[/C][C]222.337834631244[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]1.31273666666667[/C][C]0.00553905565488312[/C][C]236.996475294373[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]1.31335357142857[/C][C]0.00515083720051538[/C][C]254.97866080822[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]1.31392692307692[/C][C]0.0046832091485427[/C][C]280.561230857218[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]1.31413333333333[/C][C]0.00432894566048143[/C][C]303.568914096091[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]1.31392727272727[/C][C]0.00403465604845797[/C][C]325.660293454122[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]1.313715[/C][C]0.00373447857982314[/C][C]351.780033522703[/C][/ROW]
[ROW][C]Median[/C][C]1.31705[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]1.2589[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]1.31039032258065[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]1.31273666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]1.31039032258065[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]1.31273666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]1.31273666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]1.31039032258065[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]1.31273666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]1.31205[/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=&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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 Mean1.288781666666670.013329435480747396.6868903434171
Geometric Mean1.28452257615098
Harmonic Mean1.28006962854624
Quadratic Mean1.29284219512669
Winsorized Mean ( 1 / 20 )1.288763333333330.013292493733012896.9542178630187
Winsorized Mean ( 2 / 20 )1.288830.01321558323014997.5235052101044
Winsorized Mean ( 3 / 20 )1.2889950.013159048019291297.9550342935394
Winsorized Mean ( 4 / 20 )1.289261666666670.0128601076103402100.25278992456
Winsorized Mean ( 5 / 20 )1.2882450.0121950020847664105.637128312527
Winsorized Mean ( 6 / 20 )1.2865950.0119116518052205108.011468185808
Winsorized Mean ( 7 / 20 )1.287201666666670.0117162455401651109.86468850059
Winsorized Mean ( 8 / 20 )1.286748333333330.0116156786921102110.776853203364
Winsorized Mean ( 9 / 20 )1.286388333333330.0114911953746927111.945562788565
Winsorized Mean ( 10 / 20 )1.287871666666670.0109792814877303117.300177439289
Winsorized Mean ( 11 / 20 )1.292803333333330.00982676989612239131.559337096462
Winsorized Mean ( 12 / 20 )1.305223333333330.00689776405541814189.224119996985
Winsorized Mean ( 13 / 20 )1.305960.0066952825959438195.056740516254
Winsorized Mean ( 14 / 20 )1.307243333333330.00635341154260883205.754550065956
Winsorized Mean ( 15 / 20 )1.308418333333330.00594085181534618220.240863431987
Winsorized Mean ( 16 / 20 )1.309378333333330.00561966989986312232.999154161213
Winsorized Mean ( 17 / 20 )1.312523333333330.00477221381231322275.034477698123
Winsorized Mean ( 18 / 20 )1.315493333333330.00415257517724082316.789769524995
Winsorized Mean ( 19 / 20 )1.315271666666670.00374297088238278351.397782135394
Winsorized Mean ( 20 / 20 )1.311771666666670.00295036633909078444.613148301752
Trimmed Mean ( 1 / 20 )1.289812068965520.012996879907951799.2401313315503
Trimmed Mean ( 2 / 20 )1.290935714285710.0126294724439108102.216123438167
Trimmed Mean ( 3 / 20 )1.292105555555560.0122226918387004105.71366541897
Trimmed Mean ( 4 / 20 )1.293301923076920.0117395515273469110.166212062209
Trimmed Mean ( 5 / 20 )1.2945140.0112518820230762115.048664511867
Trimmed Mean ( 6 / 20 )1.296081250.0108653989395554119.285196724957
Trimmed Mean ( 7 / 20 )1.298143478260870.0104469359177375124.260691219212
Trimmed Mean ( 8 / 20 )1.3002750.00995615978178448130.600053484371
Trimmed Mean ( 9 / 20 )1.302690476190480.00932278988610379139.731828358828
Trimmed Mean ( 10 / 20 )1.30540750.00848416729629599153.863950864089
Trimmed Mean ( 11 / 20 )1.308176315789470.00748209853551603174.840829692341
Trimmed Mean ( 12 / 20 )1.310505555555560.00650427325277292201.483779144251
Trimmed Mean ( 13 / 20 )1.311282352941180.00623022571727572210.47108282211
Trimmed Mean ( 14 / 20 )1.312050.00590115488970236222.337834631244
Trimmed Mean ( 15 / 20 )1.312736666666670.00553905565488312236.996475294373
Trimmed Mean ( 16 / 20 )1.313353571428570.00515083720051538254.97866080822
Trimmed Mean ( 17 / 20 )1.313926923076920.0046832091485427280.561230857218
Trimmed Mean ( 18 / 20 )1.314133333333330.00432894566048143303.568914096091
Trimmed Mean ( 19 / 20 )1.313927272727270.00403465604845797325.660293454122
Trimmed Mean ( 20 / 20 )1.3137150.00373447857982314351.780033522703
Median1.31705
Midrange1.2589
Midmean - Weighted Average at Xnp1.31039032258065
Midmean - Weighted Average at X(n+1)p1.31273666666667
Midmean - Empirical Distribution Function1.31039032258065
Midmean - Empirical Distribution Function - Averaging1.31273666666667
Midmean - Empirical Distribution Function - Interpolation1.31273666666667
Midmean - Closest Observation1.31039032258065
Midmean - True Basic - Statistics Graphics Toolkit1.31273666666667
Midmean - MS Excel (old versions)1.31205
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')