*Unverified author*

R Software Module: /rwasp_centraltendency.wasp (opens new window with default values)

Title produced by software: Central Tendency

Date of computation: Thu, 03 Jun 2010 15:36:30 +0000

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2010/Jun/03/t1275579564ld8rekv5y2gpimi.htm/, Retrieved Thu, 03 Jun 2010 17:39:25 +0200

BibTeX entries for LaTeX users:

@Manual{KEY, author = {{YOUR NAME}}, publisher = {Office for Research Development and Education}, title = {Statistical Computations at FreeStatistics.org, URL http://www.freestatistics.org/blog/date/2010/Jun/03/t1275579564ld8rekv5y2gpimi.htm/}, year = {2010}, } @Manual{R, title = {R: A Language and Environment for Statistical Computing}, author = {{R Development Core Team}}, organization = {R Foundation for Statistical Computing}, address = {Vienna, Austria}, year = {2010}, note = {{ISBN} 3-900051-07-0}, url = {http://www.R-project.org}, }

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

KDGP1W52

Dataseries X:

» Textbox « » Textfile « » CSV «

25000 25284 12434,5 33955 14980,5 50831 4198,5 34566 35000 11055,5 20807 21887,29 16977,5 19613,5 14570 24416,5 16825,5 13980 21450,5 27239,5 19078,5 20459,1 20373,5 19306,5 16723,16 11638 20917 17903,5 28218,5 15268 21555 23143 16691 17932,5 30512 41931,5 10853,5 25939,5 14900 25127,76 22063,5 25306,5 31217,5 23201,5 38148 26264 16359 27945,5 16218,5 36003,5 20323,5 20100,5 18741 24426,75 19174,5 13766 18999 21745 34469 13248 16218,5 36003,5 20323,5 20100,5 18741 24426,75 19174,5 13766 18999 21745 34469 13248

Output produced by software:

Summary of computational transaction Raw Input view raw input (R code) Raw Output view raw output of R engine Computing time 2 seconds R Server 'RServer@AstonUniversity' @ vre.aston.ac.uk Central Tendency - Ungrouped Data Measure Value S.E. Value/S.E. Arithmetic Mean 22062.2195833333 955.41750874442 23.0917053344844 Geometric Mean 20636.0632936084 Harmonic Mean 19028.1610088962 Quadratic Mean 23485.1429350624 Winsorized Mean ( 1 / 24 ) 22031.0459722222 888.980942633441 24.7823602460581 Winsorized Mean ( 2 / 24 ) 21931.5598611111 857.369501234996 25.5800560079637 Winsorized Mean ( 3 / 24 ) 21866.4765277778 830.462467843903 26.330481357633 Winsorized Mean ( 4 / 24 ) 21910.7265277778 823.035334883188 26.6218540068969 Winsorized Mean ( 5 / 24 ) 21897.5320833333 797.666850068865 27.4519770772007 Winsorized Mean ( 6 / 24 ) 21861.3654166667 789.383640720732 27.6942215279589 Winsorized Mean ( 7 / 24 ) 21902.2959722222 779.672461636612 28.0916629096365 Winsorized Mean ( 8 / 24 ) 21902.2959722222 779.672461636612 28.0916629096365 Winsorized Mean ( 9 / 24 ) 21864.7959722222 761.275420868975 28.7212687719041 Winsorized Mean ( 10 / 24 ) 21566.5320833333 667.787412469549 32.2955055465601 Winsorized Mean ( 11 / 24 ) 21509.1640277778 638.717829760083 33.6755340552449 Winsorized Mean ( 12 / 24 ) 21140.3306944444 564.774808376 37.4314335216776 Winsorized Mean ( 13 / 24 ) 21142.94875 548.210733201653 38.5671922665965 Winsorized Mean ( 14 / 24 ) 21190.4904166667 497.44454832788 42.5986986647996 Winsorized Mean ( 15 / 24 ) 20987.26125 463.71591882331 45.258875958487 Winsorized Mean ( 16 / 24 ) 20946.3723611111 447.758319970011 46.7805318782552 Winsorized Mean ( 17 / 24 ) 20875.3029166667 413.4783351065 50.4870537202144 Winsorized Mean ( 18 / 24 ) 20877.7179166667 411.484985510843 50.7374962679326 Winsorized Mean ( 19 / 24 ) 20863.4943055556 401.458160663176 51.9692868394823 Winsorized Mean ( 20 / 24 ) 20870.2276388889 390.200863766516 53.4858570978894 Winsorized Mean ( 21 / 24 ) 20973.1130555556 328.502455246173 63.8446158335065 Winsorized Mean ( 22 / 24 ) 20981.9741666667 327.338012159493 64.0988012001592 Winsorized Mean ( 23 / 24 ) 21236.9706944444 294.401893171738 72.1359854912887 Winsorized Mean ( 24 / 24 ) 20831.9706944444 234.562132266153 88.8121645773871 Trimmed Mean ( 1 / 24 ) 21906.433 853.429950561338 25.6686948771732 Trimmed Mean ( 2 / 24 ) 21774.4898529412 810.589037148658 26.8625516199127 Trimmed Mean ( 3 / 24 ) 21688.8153030303 780.004732600376 27.8060047542586 Trimmed Mean ( 4 / 24 ) 21622.19234375 755.905079207019 28.6043749916759 Trimmed Mean ( 5 / 24 ) 21538.4243548387 729.412257240058 29.5284650635507 Trimmed Mean ( 6 / 24 ) 21452.2385 705.465531392478 30.4086274174964 Trimmed Mean ( 7 / 24 ) 21367.5915517241 678.531088982901 31.4909543551697 Trimmed Mean ( 8 / 24 ) 21269.3805357143 647.704697209087 32.8380828908027 Trimmed Mean ( 9 / 24 ) 21163.8946296296 608.865979141973 34.7595289515999 Trimmed Mean ( 10 / 24 ) 21056.0636538462 564.527371529259 37.2985699467627 Trimmed Mean ( 11 / 24 ) 20982.5562 534.360178414575 39.2666913583538 Trimmed Mean ( 12 / 24 ) 20910.7460416667 503.322141596202 41.5454523326785 Trimmed Mean ( 13 / 24 ) 20880.8002173913 482.99954162584 43.2315114567268 Trimmed Mean ( 14 / 24 ) 20847.8025 460.630769134657 45.2592486150345 Trimmed Mean ( 15 / 24 ) 20805.8407142857 443.751104068037 46.8862849546752 Trimmed Mean ( 16 / 24 ) 20784.07025 429.843104355663 48.3526897125764 Trimmed Mean ( 17 / 24 ) 20764.8502631579 414.924119509128 50.0449342104372 Trimmed Mean ( 18 / 24 ) 20751.8558333333 403.192507876816 51.4688527884886 Trimmed Mean ( 19 / 24 ) 20737.0485294118 387.013698551961 53.5822080897934 Trimmed Mean ( 20 / 24 ) 20722.0746875 366.801481739987 56.4939775848266 Trimmed Mean ( 21 / 24 ) 20704.2963333333 340.950351535667 60.7252529292888 Trimmed Mean ( 22 / 24 ) 20671.38 324.085107754104 63.7838009381294 Trimmed Mean ( 23 / 24 ) 20632.2842307692 298.09535591984 69.2137056852284 Trimmed Mean ( 24 / 24 ) 20553.4120833333 268.223497375897 76.6279326174364 Median 20348.5 Midrange 27514.75 Midmean - Weighted Average at Xnp 20642.102972973 Midmean - Weighted Average at X(n+1)p 20751.8558333333 Midmean - Empirical Distribution Function 20642.102972973 Midmean - Empirical Distribution Function - Averaging 20751.8558333333 Midmean - Empirical Distribution Function - Interpolation 20751.8558333333 Midmean - Closest Observation 20642.102972973 Midmean - True Basic - Statistics Graphics Toolkit 20751.8558333333 Midmean - MS Excel (old versions) 20764.8502631579 Number of observations 72

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Jun/03/t1275579564ld8rekv5y2gpimi/1fkru1275579387.png (open in new window) http://www.freestatistics.org/blog/date/2010/Jun/03/t1275579564ld8rekv5y2gpimi/1fkru1275579387.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Jun/03/t1275579564ld8rekv5y2gpimi/2fkru1275579387.png (open in new window) http://www.freestatistics.org/blog/date/2010/Jun/03/t1275579564ld8rekv5y2gpimi/2fkru1275579387.ps (open in new window)

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('http://www.xycoon.com/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('http://www.xycoon.com/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('http://www.xycoon.com/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('http://www.xycoon.com/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('http://www.xycoon.com/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('http://www.xycoon.com/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('http://www.xycoon.com/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('http://www.xycoon.com/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('http://www.xycoon.com/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('http://www.xycoon.com/midmean.htm', 'Midmean', 'click to view the definition of the Midmean') mylabel <- paste(mymid,hyperlink('http://www.xycoon.com/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('http://www.xycoon.com/midmean.htm', 'Midmean', 'click to view the definition of the Midmean') mylabel <- paste(mymid,hyperlink('http://www.xycoon.com/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('http://www.xycoon.com/midmean.htm', 'Midmean', 'click to view the definition of the Midmean') mylabel <- paste(mymid,hyperlink('http://www.xycoon.com/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('http://www.xycoon.com/midmean.htm', 'Midmean', 'click to view the definition of the Midmean') mylabel <- paste(mymid,hyperlink('http://www.xycoon.com/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('http://www.xycoon.com/midmean.htm', 'Midmean', 'click to view the definition of the Midmean') mylabel <- paste(mymid,hyperlink('http://www.xycoon.com/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('http://www.xycoon.com/midmean.htm', 'Midmean', 'click to view the definition of the Midmean') mylabel <- paste(mymid,hyperlink('http://www.xycoon.com/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('http://www.xycoon.com/midmean.htm', 'Midmean', 'click to view the definition of the Midmean') mylabel <- paste(mymid,hyperlink('http://www.xycoon.com/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('http://www.xycoon.com/midmean.htm', 'Midmean', 'click to view the definition of the Midmean') mylabel <- paste(mymid,hyperlink('http://www.xycoon.com/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')

Copyright

This work is licensed under a Creative Commons Attribution-Noncommercial-Share Alike 3.0 License.

Software written by Ed van Stee & Patrick Wessa

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