*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: Tue, 20 Oct 2009 12:23:37 -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/20/t12560630528pmbawo19mvae1s.htm/, Retrieved Tue, 20 Oct 2009 20:24:12 +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/20/t12560630528pmbawo19mvae1s.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:

HSWWS3Q2

Dataseries X:

» Textbox « » Textfile « » CSV «

-17110,4747 -17110,4992 -17110,4322 -17110,5400 -17110,4909 -17110,5147 -17110,5239 -17110,4885 -17110,4630 -17110,5156 -17110,4756 -17110,5162 -17110,4278 -17110,4677 -17110,4732 -17110,5306 -17110,5103 -17110,5030 -17110,5634 -17110,5305 -17110,4301 -17110,4769 -17110,4805 -17110,5734 -17110,4335 -17110,4937 -17110,4796 -17110,4819 -17110,4676 -17110,5224 -17110,4869 -17110,4944 -17110,4252 -17110,4235 -17110,4572 -17110,5289 -17110,4232 -17110,4420 -17110,4497 -17110,4805 -17110,4755 -17110,4633 -17110,4581 -17110,4057 -17110,3983 -17110,3913 -17110,3862 -17110,4585 -17110,3921 -17110,4224 -17110,4269 -17110,5119 -17110,5719 -17110,4999 -17110,5732 -17110,4686 -17110,4433 -17110,4527 -17110,4128 -17110,4529 -17110,4183 -17110,4881 -17110,4955 -17110,5312 -17110,5572 -17110,5468 -17110,5117 -17110,5208 -17110,4610 -17110,4572 -17110,4307 -17110,4575

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 3 seconds R Server 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 Central Tendency - Ungrouped Data Measure Value S.E. Value/S.E. Arithmetic Mean -17110.4768555556 0.00545862044144768 -3134578.97267129 Geometric Mean NaN Harmonic Mean -17110.4768554319 Quadratic Mean 17110.4768556174 Winsorized Mean ( 1 / 24 ) -17110.4769236111 0.00544179454838965 -3144271.02520335 Winsorized Mean ( 2 / 24 ) -17110.4769097222 0.00542793741092648 -3152298.12253891 Winsorized Mean ( 3 / 24 ) -17110.4768138889 0.00528795813099618 -3235743.6254257 Winsorized Mean ( 4 / 24 ) -17110.4768805556 0.00512698857899632 -3337334.69792616 Winsorized Mean ( 5 / 24 ) -17110.4766513889 0.00488033885383453 -3506001.76828808 Winsorized Mean ( 6 / 24 ) -17110.4765430556 0.00468649160310662 -3651020.4204171 Winsorized Mean ( 7 / 24 ) -17110.4760861111 0.00446161612087085 -3835039.95470847 Winsorized Mean ( 8 / 24 ) -17110.4761083333 0.00443504800661505 -3858013.73126342 Winsorized Mean ( 9 / 24 ) -17110.4761333333 0.00442659482943299 -3865381.13214329 Winsorized Mean ( 10 / 24 ) -17110.4761472222 0.00434913918244513 -3934221.33195621 Winsorized Mean ( 11 / 24 ) -17110.4756430556 0.00417894427108997 -4094449.34727323 Winsorized Mean ( 12 / 24 ) -17110.4755430556 0.00411397900631587 -4159106.18814223 Winsorized Mean ( 13 / 24 ) -17110.4756694444 0.00400059445831493 -4276983.29529043 Winsorized Mean ( 14 / 24 ) -17110.4748916667 0.00384295727500379 -4452423.91919379 Winsorized Mean ( 15 / 24 ) -17110.4750791667 0.00377372771700982 -4534104.30276736 Winsorized Mean ( 16 / 24 ) -17110.4751680556 0.00369750043854721 -4627578.94216192 Winsorized Mean ( 17 / 24 ) -17110.4765138889 0.00328945195339577 -5201619.22299104 Winsorized Mean ( 18 / 24 ) -17110.4767888889 0.00323414729817285 -5290568.18115722 Winsorized Mean ( 19 / 24 ) -17110.4781083333 0.00293907871374620 -5821714.82114681 Winsorized Mean ( 20 / 24 ) -17110.4769138889 0.00252113546708661 -6786813.77389909 Winsorized Mean ( 21 / 24 ) -17110.4760680556 0.00238359007966567 -7178447.4243388 Winsorized Mean ( 22 / 24 ) -17110.4771680556 0.00217832079362194 -7854893.19027507 Winsorized Mean ( 23 / 24 ) -17110.4759861111 0.00201332154331549 -8498630.5555217 Winsorized Mean ( 24 / 24 ) -17110.4757194444 0.00195040888820041 -8772763.4051298 Trimmed Mean ( 1 / 24 ) -17110.4767714286 0.00528249860213868 -3239087.79919056 Trimmed Mean ( 2 / 24 ) -17110.4766102941 0.00509295815197309 -3359634.24393449 Trimmed Mean ( 3 / 24 ) -17110.4764469697 0.00487490755141214 -3509907.88369170 Trimmed Mean ( 4 / 24 ) -17110.476309375 0.00467923674773382 -3656681.04262126 Trimmed Mean ( 5 / 24 ) -17110.4761435484 0.00450485936638571 -3798226.48210132 Trimmed Mean ( 6 / 24 ) -17110.4760216667 0.00437459802294778 -3911325.32221484 Trimmed Mean ( 7 / 24 ) -17110.4759137931 0.00427147678250953 -4005751.82425328 Trimmed Mean ( 8 / 24 ) -17110.4758821429 0.00420263222024341 -4071371.22295033 Trimmed Mean ( 9 / 24 ) -17110.4758444444 0.00412207982031634 -4150932.68211661 Trimmed Mean ( 10 / 24 ) -17110.4758 0.00402211645956934 -4254097.5558505 Trimmed Mean ( 11 / 24 ) -17110.47575 0.00391347358622274 -4372196.55965914 Trimmed Mean ( 12 / 24 ) -17110.4757645833 0.00381403191471173 -4486191.03017562 Trimmed Mean ( 13 / 24 ) -17110.4757934783 0.00370025250757059 -4624137.34156542 Trimmed Mean ( 14 / 24 ) -17110.4758090909 0.00357852683581975 -4781430.06720567 Trimmed Mean ( 15 / 24 ) -17110.4759214286 0.00345553224353187 -4951618.07662373 Trimmed Mean ( 16 / 24 ) -17110.4760225 0.00330845166261189 -5171747.32091807 Trimmed Mean ( 17 / 24 ) -17110.4761236842 0.00312961223609724 -5467283.11141246 Trimmed Mean ( 18 / 24 ) -17110.4760777778 0.0029982246363217 -5706869.28207266 Trimmed Mean ( 19 / 24 ) -17110.4759941176 0.00282953275926449 -6047102.98479293 Trimmed Mean ( 20 / 24 ) -17110.47574375 0.00267770415581869 -6389979.90370546 Trimmed Mean ( 21 / 24 ) -17110.4756033333 0.00259048428136279 -6605126.20224507 Trimmed Mean ( 22 / 24 ) -17110.4755464286 0.00250194888129412 -6838858.96884444 Trimmed Mean ( 23 / 24 ) -17110.4753423077 0.00242905599310656 -7044084.3648173 Trimmed Mean ( 24 / 24 ) -17110.4752583333 0.00236962906550213 -7220739.94931673 Median -17110.47555 Midrange -17110.4798 Midmean - Weighted Average at Xnp -17110.4770459459 Midmean - Weighted Average at X(n+1)p -17110.4760777778 Midmean - Empirical Distribution Function -17110.4770459459 Midmean - Empirical Distribution Function - Averaging -17110.4760777778 Midmean - Empirical Distribution Function - Interpolation -17110.4760777778 Midmean - Closest Observation -17110.4770459459 Midmean - True Basic - Statistics Graphics Toolkit -17110.4760777778 Midmean - MS Excel (old versions) -17110.4761236842 Number of observations 72

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Oct/20/t12560630528pmbawo19mvae1s/1ovv01256063012.png (open in new window) http://www.freestatistics.org/blog/date/2009/Oct/20/t12560630528pmbawo19mvae1s/1ovv01256063012.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Oct/20/t12560630528pmbawo19mvae1s/2fz8d1256063012.png (open in new window) http://www.freestatistics.org/blog/date/2009/Oct/20/t12560630528pmbawo19mvae1s/2fz8d1256063012.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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