*Unverified author*

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

Title produced by software: Central Tendency

Date of computation: Fri, 12 Mar 2010 04:58:27 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2010/Mar/12/t1268395491qvoomprx79np9lg.htm/, Retrieved Fri, 12 Mar 2010 13:04:53 +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/Mar/12/t1268395491qvoomprx79np9lg.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 «

2 2.4 1.5 1.2 1.5 0.6 2.7 3.7 4.9 6.6 7.4 7.2 5.3 4.7 6.1 6.6 7 7.5 6.6 7.8 4.7 5.4 4.3 4.5 5.8 4.6 5.2 3.6 4.8 6.7 6.3 4.8 8.7 6.8 7.4 9 7.9 9.1 8.7 9.8 6.4 6.1 4.7 4.8 4.2 2.8 6.1 5.8 4.9 4.6 4.1 3.6 5.9 4.5 4.8 5.7 5 7 4.6 2.6 5 4.1 3.2 0 2.3 3.8 4.5 5.9 5 4.2 4.5 6

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 'Gwilym Jenkins' @ 72.249.127.135 Central Tendency - Ungrouped Data Measure Value S.E. Value/S.E. Arithmetic Mean 5.1125 0.239325616644923 21.3621093791443 Geometric Mean 0 Harmonic Mean 0 Quadratic Mean 5.49584438967804 Winsorized Mean ( 1 / 24 ) 5.11111111111111 0.234433652749125 21.8019514313531 Winsorized Mean ( 2 / 24 ) 5.125 0.229501995381727 22.3309605281456 Winsorized Mean ( 3 / 24 ) 5.125 0.223674586875156 22.9127504898915 Winsorized Mean ( 4 / 24 ) 5.125 0.223674586875156 22.9127504898915 Winsorized Mean ( 5 / 24 ) 5.10416666666667 0.204339057238182 24.9789087590687 Winsorized Mean ( 6 / 24 ) 5.12083333333333 0.197548923240681 25.9218488733266 Winsorized Mean ( 7 / 24 ) 5.10138888888889 0.190219511771711 26.8184311975905 Winsorized Mean ( 8 / 24 ) 5.1125 0.183897313278324 27.8008411806559 Winsorized Mean ( 9 / 24 ) 5.125 0.181518438903523 28.2340462542428 Winsorized Mean ( 10 / 24 ) 5.11111111111111 0.174112499782241 29.3552221552357 Winsorized Mean ( 11 / 24 ) 5.14166666666667 0.157974636937367 32.5474187904303 Winsorized Mean ( 12 / 24 ) 5.20833333333333 0.147046430021812 35.4196516879788 Winsorized Mean ( 13 / 24 ) 5.17222222222222 0.141008859728728 36.6801223141049 Winsorized Mean ( 14 / 24 ) 5.17222222222222 0.134853746521152 38.3543086910896 Winsorized Mean ( 15 / 24 ) 5.17222222222222 0.128388687260673 40.2856539199661 Winsorized Mean ( 16 / 24 ) 5.23888888888889 0.118852026520223 44.0790876039246 Winsorized Mean ( 17 / 24 ) 5.23888888888889 0.118852026520223 44.0790876039246 Winsorized Mean ( 18 / 24 ) 5.21388888888889 0.107582365642898 48.4641591373398 Winsorized Mean ( 19 / 24 ) 5.1875 0.103535647395910 50.1035163296322 Winsorized Mean ( 20 / 24 ) 5.15972222222222 0.0916006958987339 56.328417285458 Winsorized Mean ( 21 / 24 ) 5.21805555555556 0.0842282090088352 61.9514010443722 Winsorized Mean ( 22 / 24 ) 5.21805555555556 0.0842282090088352 61.9514010443722 Winsorized Mean ( 23 / 24 ) 5.18611111111111 0.0795700878920594 65.1766417318316 Winsorized Mean ( 24 / 24 ) 5.15277777777778 0.0748230103146346 68.8662185083183 Trimmed Mean ( 1 / 24 ) 5.11857142857143 0.225076870762289 22.7414367866226 Trimmed Mean ( 2 / 24 ) 5.12647058823529 0.213879849910645 23.9689273691610 Trimmed Mean ( 3 / 24 ) 5.12727272727273 0.203690260932656 25.1719090730995 Trimmed Mean ( 4 / 24 ) 5.128125 0.194205094679834 26.4057181839345 Trimmed Mean ( 5 / 24 ) 5.12903225806452 0.182632884428694 28.0838375526346 Trimmed Mean ( 6 / 24 ) 5.135 0.175212945501143 29.3071952264310 Trimmed Mean ( 7 / 24 ) 5.13793103448276 0.168205136228479 30.5456251199352 Trimmed Mean ( 8 / 24 ) 5.14464285714286 0.161625662639779 31.8306064341336 Trimmed Mean ( 9 / 24 ) 5.15 0.155152592772487 33.1931288286743 Trimmed Mean ( 10 / 24 ) 5.15384615384615 0.147668188704322 34.9015329507818 Trimmed Mean ( 11 / 24 ) 5.16 0.140116569545591 36.8264796714213 Trimmed Mean ( 12 / 24 ) 5.1625 0.134600307978108 38.3542955996777 Trimmed Mean ( 13 / 24 ) 5.15652173913043 0.130130078879218 39.6259018940312 Trimmed Mean ( 14 / 24 ) 5.15454545454545 0.125772645708876 40.9830406722667 Trimmed Mean ( 15 / 24 ) 5.15238095238095 0.121509958833342 42.4029520036932 Trimmed Mean ( 16 / 24 ) 5.15 0.117396981571296 43.8682488345951 Trimmed Mean ( 17 / 24 ) 5.13947368421053 0.114057425685361 45.0604040318101 Trimmed Mean ( 18 / 24 ) 5.12777777777778 0.109371299383100 46.8841259699809 Trimmed Mean ( 19 / 24 ) 5.11764705882353 0.105926906847184 48.3130038546913 Trimmed Mean ( 20 / 24 ) 5.109375 0.102130468325979 50.0279209891796 Trimmed Mean ( 21 / 24 ) 5.10333333333333 0.100055540132024 51.0050050861695 Trimmed Mean ( 22 / 24 ) 5.08928571428571 0.0985797673031436 51.6260674326366 Trimmed Mean ( 23 / 24 ) 5.07307692307692 0.095845659956747 52.9296467400432 Trimmed Mean ( 24 / 24 ) 5.05833333333333 0.0930397816322866 54.3674248218355 Median 4.9 Midrange 4.9 Midmean - Weighted Average at Xnp 5.07368421052632 Midmean - Weighted Average at X(n+1)p 5.12777777777778 Midmean - Empirical Distribution Function 5.07368421052632 Midmean - Empirical Distribution Function - Averaging 5.12777777777778 Midmean - Empirical Distribution Function - Interpolation 5.12777777777778 Midmean - Closest Observation 5.07368421052632 Midmean - True Basic - Statistics Graphics Toolkit 5.12777777777778 Midmean - MS Excel (old versions) 5.18536585365854 Number of observations 72

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Mar/12/t1268395491qvoomprx79np9lg/1kkzg1268395105.png (open in new window) http://www.freestatistics.org/blog/date/2010/Mar/12/t1268395491qvoomprx79np9lg/1kkzg1268395105.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Mar/12/t1268395491qvoomprx79np9lg/2el9v1268395105.png (open in new window) http://www.freestatistics.org/blog/date/2010/Mar/12/t1268395491qvoomprx79np9lg/2el9v1268395105.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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