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paper E

R Software Module: rwasp_centraltendency.wasp (opens new window with default values)
Title produced by software: Central Tendency
Date of computation: Sun, 09 Dec 2007 08:05:25 -0700
 
Cite this page as follows:
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2007/Dec/09/t1197211893d8m56bv2xy2dqly.htm/, Retrieved Sun, 09 Dec 2007 15:51:35 +0100
 
User-defined keywords:
 
Dataseries X:
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4.38286530113361e-07 4.89061633371374e-05 1.67265345533732e-05 1.37894550531681e-06 -6.8042996595898e-05 -5.3158085315235e-06 7.19293424095167e-06 -8.1802518523442e-06 2.81246745274391e-05 -1.07378248659871e-05 -1.17646115611273e-05 1.36283414744172e-05 1.02445938004814e-05 1.65372868358445e-05 7.00932212243953e-06 3.61909923845820e-05 -1.35766053162004e-05 3.94152454119291e-06 5.17586566693997e-06 -2.61867212484896e-05 9.51352823646371e-05 -2.02658689338797e-05 3.47655961053665e-06 -1.28573477729784e-05 -3.32273426796430e-05 2.19773141374728e-05 1.31467562598063e-05 -4.32453068957603e-05 -6.51854100768632e-05 3.39930010620256e-05 -1.62269121388263e-05 -4.13219376247184e-05 -7.63874811343553e-05 3.57981866302331e-05 4.83981922932459e-05 4.38263660561688e-05 -3.39356794455244e-05 -2.35115967581124e-06 2.11767077215946e-06 1.62485862455450e-05 -4.74682615718288e-06 3.27817122244229e-05 -5.25736345316916e-05 3.79327739482647e-05 -2.17703633091116e-05 -3.06719024846608e-06 4.60255502102123e-05 -2.71568681913542e-05 -4.60517410067598e-05 -2.35958911375903e-05 6.09369573479348e-06 -1.64074082797469e-05 3.76048600688543e-05 -4.50367079885662e-05 -8.2453741012431e-06 4.31298882102447e-06 -3.06644842030854e-05 -5.15916808903879e-06 -4.23357597323296e-06 -7.67043750451449e-06 -5.69013786316641e-06 -4.02284504670001e-05 2.12175156220227e-05 2.09435852341699e-05 2.27083108709056e-05 -1.94803103309229e-05 -5.6960976312441e-06 -6.3915013606134e-05 -4.51663042721391e-05
 
Text written by user:
 
Output produced by software:


Summary of compuational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135


Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean-3.27725909500567e-063.85774636487154e-06-0.849526844182458
Geometric MeanNaN
Harmonic Mean2.78794761737426e-05
Quadratic Mean3.19801579771272e-05
Winsorized Mean ( 1 / 23 )-3.82631176875991e-063.62612513347925e-06-1.05520676422123
Winsorized Mean ( 2 / 23 )-3.75820697237894e-063.60180920137902e-06-1.04342200329214
Winsorized Mean ( 3 / 23 )-3.80613069465304e-063.56645334767151e-06-1.06720327552806
Winsorized Mean ( 4 / 23 )-3.27614838042702e-063.38822030532274e-06-0.966923070285702
Winsorized Mean ( 5 / 23 )-3.23061929223661e-063.20709524153673e-06-1.00733500221484
Winsorized Mean ( 6 / 23 )-3.18213904395745e-063.18670255963763e-06-0.998567950539855
Winsorized Mean ( 7 / 23 )-3.31242744692696e-063.15745593017413e-06-1.04908113372917
Winsorized Mean ( 8 / 23 )-3.15027146565658e-063.10919231736551e-06-1.01321216061857
Winsorized Mean ( 9 / 23 )-3.13485620006948e-063.01908002929295e-06-1.03834816223923
Winsorized Mean ( 10 / 23 )-3.15192890729911e-062.95817914375177e-06-1.06549629151317
Winsorized Mean ( 11 / 23 )-2.89115982658301e-062.6485630299806e-06-1.09159562897175
Winsorized Mean ( 12 / 23 )-3.70994711191381e-062.47175259734989e-06-1.50093788346433
Winsorized Mean ( 13 / 23 )-3.36481374002073e-062.36670207496263e-06-1.42173101364009
Winsorized Mean ( 14 / 23 )-2.80728555236949e-062.22458912089136e-06-1.26193440667581
Winsorized Mean ( 15 / 23 )-2.65593412736693e-062.18141921190645e-06-1.21752577994661
Winsorized Mean ( 16 / 23 )-3.03302875227067e-061.93533116797883e-06-1.56718850109681
Winsorized Mean ( 17 / 23 )-2.6298872756598e-061.85908804980988e-06-1.41461146820278
Winsorized Mean ( 18 / 23 )-2.31272367959048e-061.78894617072904e-06-1.29278550547331
Winsorized Mean ( 19 / 23 )-2.81792711720278e-061.64886762642875e-06-1.70900748612918
Winsorized Mean ( 20 / 23 )-2.06682078776363e-061.49922704440768e-06-1.37859091821559
Winsorized Mean ( 21 / 23 )-2.89515401510406e-061.36273224880129e-06-2.12452153946658
Winsorized Mean ( 22 / 23 )-3.02312155440674e-061.10726211095558e-06-2.73026731836580
Winsorized Mean ( 23 / 23 )-2.84457307950345e-061.06557650614203e-06-2.66951557500303
Trimmed Mean ( 1 / 23 )-3.65490565351751e-063.51991257127095e-06-1.03835126001377
Trimmed Mean ( 2 / 23 )-3.47295146964481e-063.39247551489650e-06-1.02372189700262
Trimmed Mean ( 3 / 23 )-3.31674012290945e-063.25469460720956e-06-1.01906339094379
Trimmed Mean ( 4 / 23 )-3.13221580897333e-063.10417985002044e-06-1.00903167996297
Trimmed Mean ( 5 / 23 )-3.09013382833645e-062.99121284314867e-06-1.03307052703199
Trimmed Mean ( 6 / 23 )-3.05612155812904e-062.91317559037063e-06-1.04906877849413
Trimmed Mean ( 7 / 23 )-3.02977244745583e-062.82262269261565e-06-1.07338910559393
Trimmed Mean ( 8 / 23 )-2.97720318879408e-062.7179710971009e-06-1.09537705973757
Trimmed Mean ( 9 / 23 )-2.94793428903057e-062.59973516089326e-06-1.13393638451144
Trimmed Mean ( 10 / 23 )-2.91868800362993e-062.47412198950431e-06-1.17968637602008
Trimmed Mean ( 11 / 23 )-2.91868800362993e-062.32934241363512e-06-1.25300942727226
Trimmed Mean ( 12 / 23 )-2.88351042260453e-062.22530362371796e-06-1.29578291783252
Trimmed Mean ( 13 / 23 )-2.77299853973178e-062.13455178956648e-06-1.29910108215035
Trimmed Mean ( 14 / 23 )-2.69638456445985e-062.04193008235196e-06-1.32050778220284
Trimmed Mean ( 15 / 23 )-2.68236960444929e-061.95560496499663e-06-1.37163161909538
Trimmed Mean ( 16 / 23 )-2.68565617727575e-061.84966242491752e-06-1.45197098729813
Trimmed Mean ( 17 / 23 )-2.64285491357102e-061.77351458819647e-06-1.49017940487233
Trimmed Mean ( 18 / 23 )-2.64444986368844e-061.68809101732612e-06-1.56653275003925
Trimmed Mean ( 19 / 23 )-2.68546976817367e-061.58681339212627e-06-1.692366463189
Trimmed Mean ( 20 / 23 )-2.66888255023718e-061.48618568370861e-06-1.79579347284337
Trimmed Mean ( 21 / 23 )-2.74581266433102e-061.38904031878899e-06-1.97676959206260
Trimmed Mean ( 22 / 23 )-2.74581266433102e-061.2935491465486e-06-2.12269682343133
Trimmed Mean ( 23 / 23 )-2.68569358797147e-061.24776747622851e-06-2.1523990960954
Median-4.23357597323296e-06
Midrange9.3739006151409e-06
Midmean - Weighted Average at Xnp-3.2069767297303e-06
Midmean - Weighted Average at X(n+1)p-2.64285491357102e-06
Midmean - Empirical Distribution Function-2.64285491357102e-06
Midmean - Empirical Distribution Function - Averaging-2.64285491357102e-06
Midmean - Empirical Distribution Function - Interpolation-2.64285491357102e-06
Midmean - Closest Observation-3.22488369757155e-06
Midmean - True Basic - Statistics Graphics Toolkit-2.64285491357102e-06
Midmean - MS Excel (old versions)-2.64285491357102e-06
Number of observations69
 
Charts produced by software:
http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Dec/09/t1197211893d8m56bv2xy2dqly/19sq01197212721.png (open in new window)
http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Dec/09/t1197211893d8m56bv2xy2dqly/19sq01197212721.ps (open in new window)


http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Dec/09/t1197211893d8m56bv2xy2dqly/2idrv1197212721.png (open in new window)
http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Dec/09/t1197211893d8m56bv2xy2dqly/2idrv1197212721.ps (open in new window)


 
Parameters:
 
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')
 





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