*The author of this computation has been verified*

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

Title produced by software: Central Tendency

Date of computation: Thu, 16 Dec 2010 13:13:31 +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/Dec/16/t1292505735ihb5cisiq9sig1e.htm/, Retrieved Thu, 16 Dec 2010 14:22:16 +0100

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/Dec/16/t1292505735ihb5cisiq9sig1e.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:

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Dataseries X:

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-49.5493497703707 -34.5244589213124 -3.91006280789517 14.6313371136598 -16.7358782201586 -48.8615512151807 -77.8868483141492 -52.8243216396381 -45.4459004030628 -11.8820480510030 -25.5304783937354 20.2338922716193 -21.9420653281128 23.1907193380687 14.2843898128731 -36.3573860047354 33.4686325324833 -34.0974551131747 -5.09014031706005 -4.25345940866923 14.8564460348288 18.8607130375245 -2.46525460356892 -1.06098760087327 -17.290892109167 -15.5131820397076 -17.2049426803877 -36.6798487063743 -13.1060400146913 0.0857206259887766 53.7756017864013 56.6662296033538 3.76485816524712 54.9836940524584 -38.9231939514776 -19.5189269487819 31.9337349072222 11.4479582495412 -25.8786696625430 56.3992435318715 -2.89893769557475 14.1096472059418 -28.3133945167058 -20.4064607522117 66.8966785623235 -39.3512642805164 48.3239868281212 29.2125572581408 14.2248044635090 26.8845625839714 24.3119726420195 -17.2382153060072 -15.8952814463814 -2.91808969021696 -1.74390510248044 etc...

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 -3.51480867628065e-15 3.98518676077935 -8.81968371187023e-16 Geometric Mean NaN Harmonic Mean 7.73734700872154 Quadratic Mean 32.3758102942182 Winsorized Mean ( 1 / 22 ) 0.302648911196904 3.87163266056254 0.078170874597625 Winsorized Mean ( 2 / 22 ) 0.172409501374161 3.79513244013528 0.0454291132374856 Winsorized Mean ( 3 / 22 ) 0.0871262936674265 3.76212140263328 0.0231588203417473 Winsorized Mean ( 4 / 22 ) 0.275106278182984 3.71938690762529 0.073965490822957 Winsorized Mean ( 5 / 22 ) 0.570499454624245 3.6238309163194 0.157429931969255 Winsorized Mean ( 6 / 22 ) 0.52686296024484 3.58844228572656 0.146822191439583 Winsorized Mean ( 7 / 22 ) 0.00201501390619742 3.45643976273712 0.000582973824083586 Winsorized Mean ( 8 / 22 ) -0.410746030404096 3.27103763795865 -0.125570560741218 Winsorized Mean ( 9 / 22 ) -1.59722443973504 3.03278867366454 -0.526652072267567 Winsorized Mean ( 10 / 22 ) -1.55274243105416 2.94603272089308 -0.527062180960246 Winsorized Mean ( 11 / 22 ) -1.92939783777626 2.8587481853712 -0.674910034975932 Winsorized Mean ( 12 / 22 ) -1.40947088991352 2.63639265945841 -0.534621003763172 Winsorized Mean ( 13 / 22 ) -1.80130437082672 2.53994506130542 -0.709190288509993 Winsorized Mean ( 14 / 22 ) -1.52684762899138 2.42462429411769 -0.62972545177231 Winsorized Mean ( 15 / 22 ) -1.98009745110241 2.33233654544929 -0.848975871413519 Winsorized Mean ( 16 / 22 ) -1.42242253534694 2.20754499633925 -0.644345885454534 Winsorized Mean ( 17 / 22 ) -1.50361490825158 2.14591629505292 -0.700686653863403 Winsorized Mean ( 18 / 22 ) -1.19427060447367 2.07202903135648 -0.576377351089445 Winsorized Mean ( 19 / 22 ) -1.01795035305944 2.02587953566451 -0.502473288830343 Winsorized Mean ( 20 / 22 ) -1.37598033417078 1.78798506172254 -0.769570374847073 Winsorized Mean ( 21 / 22 ) -1.4569657391412 1.77212437547988 -0.82215772171559 Winsorized Mean ( 22 / 22 ) -1.51995676156044 1.76035716369528 -0.863436575774087 Trimmed Mean ( 1 / 22 ) 0.0954633865770333 3.76674828905103 0.0253437127334791 Trimmed Mean ( 2 / 22 ) -0.124876774526639 3.64016919501896 -0.0343052116087115 Trimmed Mean ( 3 / 22 ) -0.28814054899675 3.5369608459648 -0.0814655749795704 Trimmed Mean ( 4 / 22 ) -0.430190709779235 3.42672182996723 -0.125540014954569 Trimmed Mean ( 5 / 22 ) -0.637449035189185 3.30773958486088 -0.192714395687832 Trimmed Mean ( 6 / 22 ) -0.931749212707366 3.19250790824238 -0.291854942724429 Trimmed Mean ( 7 / 22 ) -1.23906687178849 3.0594376872216 -0.40499823773621 Trimmed Mean ( 8 / 22 ) -1.47198700159674 2.93172247652019 -0.502089475857863 Trimmed Mean ( 9 / 22 ) -1.65337257575466 2.82207649854644 -0.585870927526685 Trimmed Mean ( 10 / 22 ) -1.66226601573886 2.74524841941136 -0.605506592403498 Trimmed Mean ( 11 / 22 ) -1.67857286056969 2.66714444594335 -0.629352063448515 Trimmed Mean ( 12 / 22 ) -1.6430437411768 2.58624713409469 -0.635300362257122 Trimmed Mean ( 13 / 22 ) -1.67485142620655 2.53328589714856 -0.661137942658486 Trimmed Mean ( 14 / 22 ) -1.6581406820457 2.48338928407394 -0.667692613751463 Trimmed Mean ( 15 / 22 ) -1.67512260203535 2.44084871821553 -0.686286941724113 Trimmed Mean ( 16 / 22 ) -1.63620200224966 2.40109233407971 -0.681440683903052 Trimmed Mean ( 17 / 22 ) -1.66332932096648 2.37218122161167 -0.701181387750975 Trimmed Mean ( 18 / 22 ) -1.68363456888279 2.34038336857143 -0.719384093859153 Trimmed Mean ( 19 / 22 ) -1.74644565243722 2.30688834083128 -0.757056863795969 Trimmed Mean ( 20 / 22 ) -1.84159026268734 2.26183823818777 -0.814200693752026 Trimmed Mean ( 21 / 22 ) -1.90398199310856 2.25952901188784 -0.842645517314148 Trimmed Mean ( 22 / 22 ) -1.96599045897981 2.24363117870165 -0.876253850295258 Median -2.89893769557475 Midrange -3.1025600637537 Midmean - Weighted Average at Xnp -2.27944006912815 Midmean - Weighted Average at X(n+1)p -1.63620200224966 Midmean - Empirical Distribution Function -1.63620200224966 Midmean - Empirical Distribution Function - Averaging -1.63620200224966 Midmean - Empirical Distribution Function - Interpolation -1.66332932096648 Midmean - Closest Observation -2.27944006912815 Midmean - True Basic - Statistics Graphics Toolkit -1.63620200224966 Midmean - MS Excel (old versions) -1.63620200224966 Number of observations 67

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/16/t1292505735ihb5cisiq9sig1e/167zn1292505208.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/16/t1292505735ihb5cisiq9sig1e/167zn1292505208.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/16/t1292505735ihb5cisiq9sig1e/2hygq1292505208.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/16/t1292505735ihb5cisiq9sig1e/2hygq1292505208.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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