BDM 6

*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: Wed, 21 Oct 2009 02:35:49 -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/21/t1256114185xl11hvfxczoukyt.htm/, Retrieved Wed, 21 Oct 2009 10:36:25 +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/2009/Oct/21/t1256114185xl11hvfxczoukyt.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:

Dataseries X:

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-17.676666666667 -12.676666666667 -24.976666666667 -16.176666666667 -16.976666666667 -13.876666666667 -26.576666666667 -37.576666666667 -13.176666666667 1.323333333333 -18.276666666667 -30.176666666667 -24.676666666667 -19.076666666667 -15.576666666667 -15.676666666667 -20.176666666667 -14.776666666667 -27.776666666667 -44.276666666667 -10.476666666667 -4.476666666667 -22.076666666667 -29.376666666667 -21.876666666667 -18.676666666667 3.623333333333 -3.576666666667 -9.976666666667 10.123333333333 -16.176666666667 -22.776666666667 8.723333333333 9.923333333333 7.523333333333 0.823333333333 -5.776666666667 -4.876666666667 15.123333333333 11.023333333333 2.823333333333 13.123333333333 -13.676666666667 -15.976666666667 -1.876666666667 7.323333333333 19.123333333333 0.523333333333 19.023333333333 16.523333333333 59.623333333333 43.223333333333 57.923333333333 85.923333333333 13.223333333333 23.523333333333 45.323333333333 55.923333333333 56.423333333333 24 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 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 Central Tendency - Ungrouped Data Measure Value S.E. Value/S.E. Arithmetic Mean -3.33361694730231e-13 3.43066461471851 -9.71711700700838e-14 Geometric Mean NaN Harmonic Mean 21.7639958847098 Quadratic Mean 26.3514349177084 Winsorized Mean ( 1 / 20 ) -0.326666666667 3.24521333728921 -0.100661076088104 Winsorized Mean ( 2 / 20 ) -0.136666666667000 3.18382493911613 -0.0429253081687778 Winsorized Mean ( 3 / 20 ) -0.171666666667 3.1544931858996 -0.0544197297475042 Winsorized Mean ( 4 / 20 ) -0.098333333333667 3.12799649932855 -0.0314365228205258 Winsorized Mean ( 5 / 20 ) -0.881666666667 2.85716408032876 -0.308581041157969 Winsorized Mean ( 6 / 20 ) -0.931666666667 2.77612645737629 -0.335599505631856 Winsorized Mean ( 7 / 20 ) -3.136666666667 2.22986179298611 -1.40666416032294 Winsorized Mean ( 8 / 20 ) -2.95000000000033 2.17578983212924 -1.35582948152370 Winsorized Mean ( 9 / 20 ) -3.50500000000033 2.02890425976484 -1.72753346203068 Winsorized Mean ( 10 / 20 ) -3.48833333333367 2.02059885354078 -1.72638588170082 Winsorized Mean ( 11 / 20 ) -3.63500000000033 1.88860438064496 -1.92470166714268 Winsorized Mean ( 12 / 20 ) -3.69500000000033 1.80632675258377 -2.04558781777163 Winsorized Mean ( 13 / 20 ) -4.02000000000033 1.72252010667242 -2.33378988403578 Winsorized Mean ( 14 / 20 ) -3.95000000000033 1.70518462752160 -2.31646470197275 Winsorized Mean ( 15 / 20 ) -4.32500000000033 1.59649243296429 -2.70906388949798 Winsorized Mean ( 16 / 20 ) -4.37833333333367 1.53142504380183 -2.85899290406292 Winsorized Mean ( 17 / 20 ) -4.20833333333367 1.49110070379275 -2.82229987728488 Winsorized Mean ( 18 / 20 ) -4.56833333333367 1.43389417158028 -3.185962690886 Winsorized Mean ( 19 / 20 ) -4.88500000000033 1.36607460994071 -3.57593938460824 Winsorized Mean ( 20 / 20 ) -4.851666666667 1.3421010280495 -3.61497872758358 Trimmed Mean ( 1 / 20 ) -0.718045977011828 3.12527025762554 -0.229754842884331 Trimmed Mean ( 2 / 20 ) -1.13738095238129 2.97616361459740 -0.382163449214517 Trimmed Mean ( 3 / 20 ) -1.69333333333367 2.83071867271425 -0.598199089742114 Trimmed Mean ( 4 / 20 ) -2.27858974359008 2.66048891840426 -0.85645526573242 Trimmed Mean ( 5 / 20 ) -2.932666666667 2.45052124401053 -1.19675219051249 Trimmed Mean ( 6 / 20 ) -3.445416666667 2.28819851608745 -1.50573328425990 Trimmed Mean ( 7 / 20 ) -3.99188405797135 2.10322725884091 -1.89798037334838 Trimmed Mean ( 8 / 20 ) -4.15848484848518 2.04893174024583 -2.02958681678007 Trimmed Mean ( 9 / 20 ) -4.37428571428605 1.99126573680049 -2.19673629362725 Trimmed Mean ( 10 / 20 ) -4.519166666667 1.95487847186049 -2.31173790684085 Trimmed Mean ( 11 / 20 ) -4.68192982456174 1.90549832331289 -2.45706320875778 Trimmed Mean ( 12 / 20 ) -4.84055555555589 1.87176664185256 -2.58608923106194 Trimmed Mean ( 13 / 20 ) -5.00901960784347 1.84328874012441 -2.71743623167003 Trimmed Mean ( 14 / 20 ) -5.151666666667 1.82178793780247 -2.82780808883892 Trimmed Mean ( 15 / 20 ) -5.32333333333367 1.78925100449549 -2.97517414826584 Trimmed Mean ( 16 / 20 ) -5.46595238095271 1.76864473931533 -3.09047501708493 Trimmed Mean ( 17 / 20 ) -5.62282051282085 1.74914687573669 -3.21460741280099 Trimmed Mean ( 18 / 20 ) -5.83083333333367 1.72081227835665 -3.38841918242357 Trimmed Mean ( 19 / 20 ) -6.02212121212155 1.68704931160051 -3.56961777626307 Trimmed Mean ( 20 / 20 ) -6.201666666667 1.64772370895506 -3.7637782553969 Median -5.326666666667 Midrange 20.823333333333 Midmean - Weighted Average at Xnp -5.74118279569926 Midmean - Weighted Average at X(n+1)p -5.32333333333367 Midmean - Empirical Distribution Function -5.74118279569926 Midmean - Empirical Distribution Function - Averaging -5.32333333333367 Midmean - Empirical Distribution Function - Interpolation -5.32333333333367 Midmean - Closest Observation -5.74118279569926 Midmean - True Basic - Statistics Graphics Toolkit -5.32333333333367 Midmean - MS Excel (old versions) -5.151666666667 Number of observations 60

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Oct/21/t1256114185xl11hvfxczoukyt/1pp2f1256114145.png (open in new window) http://www.freestatistics.org/blog/date/2009/Oct/21/t1256114185xl11hvfxczoukyt/1pp2f1256114145.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Oct/21/t1256114185xl11hvfxczoukyt/236pz1256114145.png (open in new window) http://www.freestatistics.org/blog/date/2009/Oct/21/t1256114185xl11hvfxczoukyt/236pz1256114145.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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