central tendency US Dollar

*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, 17 Dec 2009 09:57:05 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2009/Dec/17/t126106906388g1qc1lqk1d5nh.htm/, Retrieved Thu, 17 Dec 2009 17:57:45 +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/2009/Dec/17/t126106906388g1qc1lqk1d5nh.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?

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Dataseries X:

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-0.0289 0.0025 0.004 -0.0006 0.0155 -0.0031 0.0061 -0.0193 -0.0113 -0.0155 -0.0279 -0.0135 -0.0263 -0.0361 -0.0413 -0.024 -0.0368 -0.0591 -0.0208 -0.0114 -0.0317 -0.0092 -0.0123 -0.027 -0.0058 0.01 0.0163 -0.003 0.013 0.032 0.0518 0.0494 0.0737 0.0822 0.0464 0.1077 0.1466 0.1115 0.1066 0.1134 0.1716 0.143 0.1587 0.1809 0.1876 0.1684 0.0889 0.0246 -0.107 -0.1178 -0.0822 -0.1312 -0.1296 -0.0877 -0.0485 0.0162 0.0364 0.0531 0.0643

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 0.0188728813559322 0.0100966081042325 1.86922986027562 Geometric Mean NaN Harmonic Mean -0.0294663097756343 Quadratic Mean 0.0791757056986634 Winsorized Mean ( 1 / 19 ) 0.0187864406779661 0.0100575438036300 1.86789548668789 Winsorized Mean ( 2 / 19 ) 0.0188711864406780 0.00987304273402398 1.91138506629218 Winsorized Mean ( 3 / 19 ) 0.0192576271186441 0.00970261107234618 1.98478811271030 Winsorized Mean ( 4 / 19 ) 0.0199084745762712 0.0092520243691711 2.15179659952137 Winsorized Mean ( 5 / 19 ) 0.0193491525423729 0.00890031237274541 2.17398578072652 Winsorized Mean ( 6 / 19 ) 0.0213322033898305 0.00838293730601342 2.54471703784878 Winsorized Mean ( 7 / 19 ) 0.0190779661016949 0.00734753347760586 2.59651298763613 Winsorized Mean ( 8 / 19 ) 0.0197966101694915 0.00714101306527935 2.77224113560939 Winsorized Mean ( 9 / 19 ) 0.0199033898305085 0.00691418339395695 2.87863203742964 Winsorized Mean ( 10 / 19 ) 0.019835593220339 0.00685670428877835 2.89287570018177 Winsorized Mean ( 11 / 19 ) 0.0173559322033898 0.00604336088772834 2.87190067345355 Winsorized Mean ( 12 / 19 ) 0.0165627118644068 0.00568955788753496 2.91107186038012 Winsorized Mean ( 13 / 19 ) 0.0149101694915254 0.00529318822482006 2.81685986937150 Winsorized Mean ( 14 / 19 ) 0.0128932203389831 0.00484515089818915 2.66105650988121 Winsorized Mean ( 15 / 19 ) 0.0102237288135593 0.0043141939758103 2.36978885763686 Winsorized Mean ( 16 / 19 ) 0.0104949152542373 0.00416375529017672 2.52054083941899 Winsorized Mean ( 17 / 19 ) 0.0107254237288136 0.0039158317284061 2.73898994459071 Winsorized Mean ( 18 / 19 ) 0.0102677966101695 0.00369746342409479 2.77698395696321 Winsorized Mean ( 19 / 19 ) 0.00827118644067797 0.00299631085350707 2.76045672330587 Trimmed Mean ( 1 / 19 ) 0.0185456140350877 0.0096597338386303 1.91988872001026 Trimmed Mean ( 2 / 19 ) 0.0182872727272727 0.00916620276311746 1.99507617274802 Trimmed Mean ( 3 / 19 ) 0.0179622641509434 0.00867714547546783 2.07006603746896 Trimmed Mean ( 4 / 19 ) 0.0174627450980392 0.0081468699442488 2.14349133072474 Trimmed Mean ( 5 / 19 ) 0.0167265306122449 0.0076657860198389 2.18197202073694 Trimmed Mean ( 6 / 19 ) 0.0160680851063830 0.00718268365966956 2.23705871895828 Trimmed Mean ( 7 / 19 ) 0.0149177777777778 0.00673143259167403 2.21613714088577 Trimmed Mean ( 8 / 19 ) 0.0141023255813953 0.00648573568017467 2.17436020781771 Trimmed Mean ( 9 / 19 ) 0.0130780487804878 0.00621613901831856 2.10388614893387 Trimmed Mean ( 10 / 19 ) 0.0119307692307692 0.00591652247891765 2.01651718104379 Trimmed Mean ( 11 / 19 ) 0.0106702702702703 0.00551749587527772 1.93389728084449 Trimmed Mean ( 12 / 19 ) 0.00964571428571429 0.00523384965707778 1.84294829192702 Trimmed Mean ( 13 / 19 ) 0.00861515151515151 0.00494409488838767 1.74251338407484 Trimmed Mean ( 14 / 19 ) 0.00769354838709677 0.0046625041393135 1.65008934195382 Trimmed Mean ( 15 / 19 ) 0.00693793103448276 0.00441012162570657 1.57318360428919 Trimmed Mean ( 16 / 19 ) 0.00645925925925926 0.00422832080677343 1.52761806741628 Trimmed Mean ( 17 / 19 ) 0.005864 0.00399133177439978 1.46918380416567 Trimmed Mean ( 18 / 19 ) 0.0051304347826087 0.00370335514357869 1.38534776809198 Trimmed Mean ( 19 / 19 ) 0.00432857142857143 0.00331884333592825 1.30424096302237 Median 0.0025 Midrange 0.0282 Midmean - Weighted Average at Xnp 0.00580666666666667 Midmean - Weighted Average at X(n+1)p 0.00769354838709677 Midmean - Empirical Distribution Function 0.00769354838709677 Midmean - Empirical Distribution Function - Averaging 0.00769354838709677 Midmean - Empirical Distribution Function - Interpolation 0.00693793103448276 Midmean - Closest Observation 0.00580666666666667 Midmean - True Basic - Statistics Graphics Toolkit 0.00769354838709677 Midmean - MS Excel (old versions) 0.00769354838709677 Number of observations 59

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/17/t126106906388g1qc1lqk1d5nh/1tpzp1261069024.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/17/t126106906388g1qc1lqk1d5nh/1tpzp1261069024.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/17/t126106906388g1qc1lqk1d5nh/27dp11261069024.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/17/t126106906388g1qc1lqk1d5nh/27dp11261069024.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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