WS3

*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: Mon, 19 Oct 2009 01:43:18 -0600

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2009/Oct/19/t1255938247jw2vsoyjwjgyv0c.htm/, Retrieved Mon, 19 Oct 2009 09:44:09 +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/2009/Oct/19/t1255938247jw2vsoyjwjgyv0c.htm/}, year = {2009}, } @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 = {2009}, 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:

Central Tendeny Task 2.2

Dataseries X:

» Textbox « » Textfile « » CSV «

-1.8 -1.5 -1.5 -1.9 -2.8 -3.1 -2.8 -2.3 -1.7 -1.6 -1.7 -1.8 -1.7 -1.6 -1.4 -1.9 -2.6 -2.8 -2.6 -1.9 -1.5 -1.4 -1.3 -1.2 -1 -0.8 -1.1 -1.7 -2.9 -3.4 -3.1 -2.4 -2 -1.9 -1.9 -2 -2.2 -2.2 -2 -1.9 -1.7 -1.5 -1.3 -1.6 -1.7 -1.5 -1.1 -0.8 -0.7 -0.7 -0.7 -0.8 -1 -1.4 -1.4 -1.8 -1.7 -1.6 -1.2 -0.7 -0.3

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 -1.70655737704918 0.0857263677215293 -19.9070300352944 Geometric Mean NaN Harmonic Mean -1.39145764349674 Quadratic Mean 1.831195972179 Winsorized Mean ( 1 / 20 ) -1.70819672131148 0.0826572051466922 -20.6660353235986 Winsorized Mean ( 2 / 20 ) -1.70819672131148 0.0826572051466922 -20.6660353235986 Winsorized Mean ( 3 / 20 ) -1.69836065573770 0.0800441068056217 -21.2178100739132 Winsorized Mean ( 4 / 20 ) -1.69180327868852 0.0784513730552058 -21.5649925909903 Winsorized Mean ( 5 / 20 ) -1.7 0.0767865539231185 -22.1392927947008 Winsorized Mean ( 6 / 20 ) -1.7 0.0767865539231185 -22.1392927947008 Winsorized Mean ( 7 / 20 ) -1.67704918032787 0.0715707240352033 -23.4320555357660 Winsorized Mean ( 8 / 20 ) -1.70327868852459 0.0665696238968171 -25.5864249911442 Winsorized Mean ( 9 / 20 ) -1.67377049180328 0.0602772120415228 -27.7678816772461 Winsorized Mean ( 10 / 20 ) -1.67377049180328 0.0540644039811547 -30.9588262988473 Winsorized Mean ( 11 / 20 ) -1.65573770491803 0.0507067315437175 -32.6532129859428 Winsorized Mean ( 12 / 20 ) -1.67540983606557 0.0472555971591557 -35.4542093801679 Winsorized Mean ( 13 / 20 ) -1.6327868852459 0.0399946247396116 -40.8251582775511 Winsorized Mean ( 14 / 20 ) -1.65573770491803 0.0360270534478021 -45.9581771603096 Winsorized Mean ( 15 / 20 ) -1.65573770491803 0.0360270534478021 -45.9581771603096 Winsorized Mean ( 16 / 20 ) -1.65573770491803 0.0278093224692074 -59.5389444223746 Winsorized Mean ( 17 / 20 ) -1.65573770491803 0.0278093224692074 -59.5389444223746 Winsorized Mean ( 18 / 20 ) -1.65573770491803 0.0278093224692074 -59.5389444223746 Winsorized Mean ( 19 / 20 ) -1.65573770491803 0.0278093224692074 -59.5389444223746 Winsorized Mean ( 20 / 20 ) -1.68852459016393 0.0230345856209919 -73.3038839051286 Trimmed Mean ( 1 / 20 ) -1.70169491525424 0.0802717304150144 -21.1991806636816 Trimmed Mean ( 2 / 20 ) -1.69473684210526 0.0773309885065869 -21.9153650410263 Trimmed Mean ( 3 / 20 ) -1.68727272727273 0.0736748039499777 -22.9016249356879 Trimmed Mean ( 4 / 20 ) -1.68301886792453 0.0704400355930064 -23.8929304018073 Trimmed Mean ( 5 / 20 ) -1.68039215686275 0.0670393275179862 -25.0657669024485 Trimmed Mean ( 6 / 20 ) -1.67551020408163 0.0633215133244738 -26.4603626179295 Trimmed Mean ( 7 / 20 ) -1.67021276595745 0.0584976017770256 -28.5518160611741 Trimmed Mean ( 8 / 20 ) -1.66888888888889 0.054012926083141 -30.8979536920478 Trimmed Mean ( 9 / 20 ) -1.66279069767442 0.0496971175963554 -33.4584937335755 Trimmed Mean ( 10 / 20 ) -1.66097560975610 0.0460484962785773 -36.070137876116 Trimmed Mean ( 11 / 20 ) -1.65897435897436 0.043110808598958 -38.4816340237807 Trimmed Mean ( 12 / 20 ) -1.65945945945946 0.0401684627200143 -41.3124960998972 Trimmed Mean ( 13 / 20 ) -1.65714285714286 0.0371880784831982 -44.5611315435823 Trimmed Mean ( 14 / 20 ) -1.66060606060606 0.0353391023930018 -46.9906123290474 Trimmed Mean ( 15 / 20 ) -1.66129032258065 0.0339757723150649 -48.8963225670083 Trimmed Mean ( 16 / 20 ) -1.66206896551724 0.0319381302694689 -52.0402713463189 Trimmed Mean ( 17 / 20 ) -1.66296296296296 0.0316444583159909 -52.5514750910626 Trimmed Mean ( 18 / 20 ) -1.664 0.0310268700752536 -53.6309333156738 Trimmed Mean ( 19 / 20 ) -1.66521739130435 0.0298935500414056 -55.7049058742723 Trimmed Mean ( 20 / 20 ) -1.66666666666667 0.0278886675511359 -59.7614304667197 Median -1.7 Midrange -1.85 Midmean - Weighted Average at Xnp -1.69375 Midmean - Weighted Average at X(n+1)p -1.67058823529412 Midmean - Empirical Distribution Function -1.67058823529412 Midmean - Empirical Distribution Function - Averaging -1.67058823529412 Midmean - Empirical Distribution Function - Interpolation -1.67058823529412 Midmean - Closest Observation -1.67058823529412 Midmean - True Basic - Statistics Graphics Toolkit -1.67058823529412 Midmean - MS Excel (old versions) -1.67058823529412 Number of observations 61

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Oct/19/t1255938247jw2vsoyjwjgyv0c/1bl661255938196.png (open in new window) http://www.freestatistics.org/blog/date/2009/Oct/19/t1255938247jw2vsoyjwjgyv0c/1bl661255938196.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Oct/19/t1255938247jw2vsoyjwjgyv0c/2lgor1255938196.png (open in new window) http://www.freestatistics.org/blog/date/2009/Oct/19/t1255938247jw2vsoyjwjgyv0c/2lgor1255938196.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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