*Unverified author*

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

Title produced by software: Central Tendency

Date of computation: Sun, 26 Oct 2008 09:55:24 -0600

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2008/Oct/26/t1225036548pmxvctfyuk2shio.htm/, Retrieved Sun, 26 Oct 2008 15:55:50 +0000

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/2008/Oct/26/t1225036548pmxvctfyuk2shio.htm/}, year = {2008}, } @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 = {2008}, note = {{ISBN} 3-900051-07-0}, url = {http://www.R-project.org}, }

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IsPrivate?

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Dataseries X:

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1,4200 1,4100 1,4200 1,4200 1,4200 1,4200 1,4200 1,4200 1,4300 1,4200 1,4000 1,4100 1,4000 1,4100 1,4000 1,3800 1,3900 1,3900 1,3700 1,3800 1,3700 1,3600 1,3700 1,3700 1,3800 1,3800 1,3800 1,3700 1,3800 1,3600 1,3500 1,3400 1,3300 1,3200 1,3200 1,3200 1,3300 1,3300 1,3200 1,3200 1,3300 1,3300 1,3400 1,3400 1,3300 1,3300 1,3200 1,3000 1,3100 1,3400 1,3500 1,3600 1,3700 1,3600 1,3600 1,3600 1,3500 1,3400 1,3300 1,3200 1,2400 1,2400 1,2400 1,2400 1,2200 1,2700 1,2900 1,2900 1,3000 1,3200 1,3200 1,3200 1,3300 1,3600 1,3600 1,3600 1,3600 1,3600 1,3100 1,3500

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 1 seconds R Server 'George Udny Yule' @ 72.249.76.132 Central Tendency - Ungrouped Data Measure Value S.E. Value/S.E. Arithmetic Mean 1.34975 0.00528005262248422 255.631921972201 Geometric Mean 1.34892257790503 Harmonic Mean 1.34808314817409 Quadratic Mean 1.35056562224869 Winsorized Mean ( 1 / 26 ) 1.349875 0.0051848542513358 260.349651998844 Winsorized Mean ( 2 / 26 ) 1.349875 0.0051848542513358 260.349651998844 Winsorized Mean ( 3 / 26 ) 1.349875 0.0051848542513358 260.349651998844 Winsorized Mean ( 4 / 26 ) 1.349875 0.0051848542513358 260.349651998844 Winsorized Mean ( 5 / 26 ) 1.35175 0.00472595513084224 286.026837448856 Winsorized Mean ( 6 / 26 ) 1.35325 0.00442509743867546 305.812475036722 Winsorized Mean ( 7 / 26 ) 1.35325 0.00442509743867546 305.812475036722 Winsorized Mean ( 8 / 26 ) 1.35425 0.00425372137893635 318.368289635987 Winsorized Mean ( 9 / 26 ) 1.353125 0.00404325407079652 334.662372511613 Winsorized Mean ( 10 / 26 ) 1.354375 0.00384775024683584 351.991400978730 Winsorized Mean ( 11 / 26 ) 1.354375 0.00384775024683584 351.99140097873 Winsorized Mean ( 12 / 26 ) 1.354375 0.00337453114417958 401.352052220955 Winsorized Mean ( 13 / 26 ) 1.354375 0.00337453114417958 401.352052220955 Winsorized Mean ( 14 / 26 ) 1.354375 0.00337453114417958 401.352052220955 Winsorized Mean ( 15 / 26 ) 1.3525 0.00306831500371544 440.795680483344 Winsorized Mean ( 16 / 26 ) 1.3525 0.00306831500371544 440.795680483344 Winsorized Mean ( 17 / 26 ) 1.350375 0.00275843786052536 489.543382261587 Winsorized Mean ( 18 / 26 ) 1.350375 0.00275843786052536 489.543382261587 Winsorized Mean ( 19 / 26 ) 1.350375 0.00275843786052536 489.543382261587 Winsorized Mean ( 20 / 26 ) 1.350375 0.00275843786052536 489.543382261587 Winsorized Mean ( 21 / 26 ) 1.350375 0.00275843786052536 489.543382261587 Winsorized Mean ( 22 / 26 ) 1.353125 0.00239721456240943 564.457191783443 Winsorized Mean ( 23 / 26 ) 1.35025 0.00201242186734092 670.957726067712 Winsorized Mean ( 24 / 26 ) 1.35025 0.00201242186734092 670.957726067712 Winsorized Mean ( 25 / 26 ) 1.35025 0.00201242186734092 670.957726067712 Winsorized Mean ( 26 / 26 ) 1.35025 0.00201242186734092 670.957726067712 Trimmed Mean ( 1 / 26 ) 1.35038461538462 0.00504538941035359 267.647252878739 Trimmed Mean ( 2 / 26 ) 1.35092105263158 0.0048816794334009 276.732848000721 Trimmed Mean ( 3 / 26 ) 1.35148648648649 0.0046882936620268 288.268309093553 Trimmed Mean ( 4 / 26 ) 1.35208333333333 0.0044578424327167 303.304424447624 Trimmed Mean ( 5 / 26 ) 1.35271428571429 0.00417981657582154 323.630059160768 Trimmed Mean ( 6 / 26 ) 1.35294117647059 0.00400317490071957 337.967041167099 Trimmed Mean ( 7 / 26 ) 1.35287878787879 0.00387908834791923 348.762045753478 Trimmed Mean ( 8 / 26 ) 1.3528125 0.00372989817246853 362.694217763237 Trimmed Mean ( 9 / 26 ) 1.35258064516129 0.00359163111410510 376.592306445229 Trimmed Mean ( 10 / 26 ) 1.3525 0.00347407671756799 389.312070502234 Trimmed Mean ( 11 / 26 ) 1.35224137931034 0.00337281311773709 400.923897087307 Trimmed Mean ( 12 / 26 ) 1.35196428571429 0.00324757294847377 416.299897543381 Trimmed Mean ( 13 / 26 ) 1.35166666666667 0.00319142369252112 423.530936940214 Trimmed Mean ( 14 / 26 ) 1.35134615384615 0.00311940414401755 433.206500811314 Trimmed Mean ( 15 / 26 ) 1.351 0.00302708858577387 446.303423807672 Trimmed Mean ( 16 / 26 ) 1.35083333333333 0.00297497442228311 454.065528501805 Trimmed Mean ( 17 / 26 ) 1.35065217391304 0.00290596876864704 464.785509220004 Trimmed Mean ( 18 / 26 ) 1.35068181818182 0.00287876469706181 469.187988709317 Trimmed Mean ( 19 / 26 ) 1.35071428571429 0.00283893735216726 475.781645791918 Trimmed Mean ( 20 / 26 ) 1.35075 0.00278244266418684 485.454747149211 Trimmed Mean ( 21 / 26 ) 1.35078947368421 0.00270349804872935 499.645070696124 Trimmed Mean ( 22 / 26 ) 1.35083333333333 0.00259349001852532 520.855420180652 Trimmed Mean ( 23 / 26 ) 1.35058823529412 0.00253113152993908 533.590696223765 Trimmed Mean ( 24 / 26 ) 1.350625 0.00253752085642152 532.261635045116 Trimmed Mean ( 25 / 26 ) 1.35066666666667 0.00253405918216156 533.005178479905 Trimmed Mean ( 26 / 26 ) 1.35071428571429 0.00251601071176942 536.847589478017 Median 1.355 Midrange 1.325 Midmean - Weighted Average at Xnp 1.34764705882353 Midmean - Weighted Average at X(n+1)p 1.34764705882353 Midmean - Empirical Distribution Function 1.34764705882353 Midmean - Empirical Distribution Function - Averaging 1.34764705882353 Midmean - Empirical Distribution Function - Interpolation 1.34764705882353 Midmean - Closest Observation 1.34764705882353 Midmean - True Basic - Statistics Graphics Toolkit 1.34764705882353 Midmean - MS Excel (old versions) 1.34764705882353 Number of observations 80

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Oct/26/t1225036548pmxvctfyuk2shio/1qyxk1225036522.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Oct/26/t1225036548pmxvctfyuk2shio/1qyxk1225036522.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Oct/26/t1225036548pmxvctfyuk2shio/27zqd1225036522.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Oct/26/t1225036548pmxvctfyuk2shio/27zqd1225036522.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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