Case III Question III++
| Summary of compuational 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 | 1.00000059173715e-10 | 0.870089857556193 | 1.14930726183366e-10 |
| Geometric Mean | NaN | ||
| Harmonic Mean | -231.072384278325 | ||
| Quadratic Mean | 6.68328700963135 | ||
| Winsorized Mean ( 1 / 20 ) | -0.0785959594 | 0.83100745129267 | -0.094579127151917 |
| Winsorized Mean ( 2 / 20 ) | -0.161666666733333 | 0.796430646025235 | -0.202989007944592 |
| Winsorized Mean ( 3 / 20 ) | -0.132545454283333 | 0.761535560680234 | -0.174050249426223 |
| Winsorized Mean ( 4 / 20 ) | -0.11808080815 | 0.725325206324983 | -0.162797055886534 |
| Winsorized Mean ( 5 / 20 ) | -0.140252525233333 | 0.715540639319978 | -0.196009167790419 |
| Winsorized Mean ( 6 / 20 ) | -0.189040404133333 | 0.698168797722045 | -0.270766045045448 |
| Winsorized Mean ( 7 / 20 ) | -0.110343434383333 | 0.667681369066071 | -0.165263611500314 |
| Winsorized Mean ( 8 / 20 ) | -0.0143434343833333 | 0.646736813087469 | -0.0221781628833821 |
| Winsorized Mean ( 9 / 20 ) | -0.121161616333333 | 0.608475729480848 | -0.199123170346841 |
| Winsorized Mean ( 10 / 20 ) | -0.204797979833333 | 0.587798437332705 | -0.348415318629732 |
| Winsorized Mean ( 11 / 20 ) | -0.164020202133333 | 0.580924157958633 | -0.282343572540864 |
| Winsorized Mean ( 12 / 20 ) | -0.184262626333333 | 0.576097616064799 | -0.319846187859607 |
| Winsorized Mean ( 13 / 20 ) | -0.182686868816667 | 0.566973758944116 | -0.322213975399650 |
| Winsorized Mean ( 14 / 20 ) | -0.0674343435499999 | 0.546699129252014 | -0.123348181736200 |
| Winsorized Mean ( 15 / 20 ) | -0.0731919192999996 | 0.541530546190386 | -0.135157508315824 |
| Winsorized Mean ( 16 / 20 ) | -0.102767676900000 | 0.536447965814158 | -0.191570633964528 |
| Winsorized Mean ( 17 / 20 ) | -0.5566161618 | 0.427573598731097 | -1.30180199023481 |
| Winsorized Mean ( 18 / 20 ) | -0.5006161617 | 0.401263331968156 | -1.24760007161514 |
| Winsorized Mean ( 19 / 20 ) | -0.540151515283333 | 0.382630772822812 | -1.41167818599229 |
| Winsorized Mean ( 20 / 20 ) | -0.66095959595 | 0.340003907840687 | -1.9439764682343 |
| Trimmed Mean ( 1 / 20 ) | -0.118787878689655 | 0.793403155014135 | -0.149719443310682 |
| Trimmed Mean ( 2 / 20 ) | -0.161850649357143 | 0.746713111705044 | -0.216750779944888 |
| Trimmed Mean ( 3 / 20 ) | -0.161952861925926 | 0.712596956139462 | -0.227271335543328 |
| Trimmed Mean ( 4 / 20 ) | -0.173263403326923 | 0.687475380545851 | -0.252028520918601 |
| Trimmed Mean ( 5 / 20 ) | -0.18981818188 | 0.670390788494155 | -0.283145569924034 |
| Trimmed Mean ( 6 / 20 ) | -0.202209596041667 | 0.651911495226863 | -0.310179522101076 |
| Trimmed Mean ( 7 / 20 ) | -0.205072463847826 | 0.633592041839142 | -0.323666413568828 |
| Trimmed Mean ( 8 / 20 ) | -0.223526170886364 | 0.618662865209746 | -0.361305298016524 |
| Trimmed Mean ( 9 / 20 ) | -0.260880230976190 | 0.604473957729359 | -0.431582250385374 |
| Trimmed Mean ( 10 / 20 ) | -0.28416666675 | 0.595565811526144 | -0.477137305819855 |
| Trimmed Mean ( 11 / 20 ) | -0.296698564684211 | 0.588117047361043 | -0.504488972077132 |
| Trimmed Mean ( 12 / 20 ) | -0.316801346888889 | 0.578588941375444 | -0.547541309959669 |
| Trimmed Mean ( 13 / 20 ) | -0.336292335205882 | 0.565611843431852 | -0.594563814586037 |
| Trimmed Mean ( 14 / 20 ) | -0.35844696978125 | 0.548915214449443 | -0.65300971870632 |
| Trimmed Mean ( 15 / 20 ) | -0.4000202021 | 0.529865022855633 | -0.754947363659045 |
| Trimmed Mean ( 16 / 20 ) | -0.446709956785714 | 0.502435706348664 | -0.889088795125801 |
| Trimmed Mean ( 17 / 20 ) | -0.496317016384615 | 0.461761876934027 | -1.07483324452860 |
| Trimmed Mean ( 18 / 20 ) | -0.487449495 | 0.443683889528035 | -1.09864141228684 |
| Trimmed Mean ( 19 / 20 ) | -0.4854545455 | 0.423944234703858 | -1.14509057031784 |
| Trimmed Mean ( 20 / 20 ) | -0.47681818185 | 0.397744182519105 | -1.19880617443625 |
| Median | -0.452727273 | ||
| Midrange | 3.444848485 | ||
| Midmean - Weighted Average at Xnp | -0.545884653064516 | ||
| Midmean - Weighted Average at X(n+1)p | -0.4000202021 | ||
| Midmean - Empirical Distribution Function | -0.545884653064516 | ||
| Midmean - Empirical Distribution Function - Averaging | -0.4000202021 | ||
| Midmean - Empirical Distribution Function - Interpolation | -0.4000202021 | ||
| Midmean - Closest Observation | -0.545884653064516 | ||
| Midmean - True Basic - Statistics Graphics Toolkit | -0.4000202021 | ||
| Midmean - MS Excel (old versions) | -0.358446969781250 | ||
| Number of observations | 60 | ||
 |
| http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/22/t1195756692g4b2len1ygfbqp3/1b7sp1195757118.png (open in new window) |
| http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/22/t1195756692g4b2len1ygfbqp3/1b7sp1195757118.ps (open in new window) |
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| http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/22/t1195756692g4b2len1ygfbqp3/2rrdo1195757118.png (open in new window) |
| http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/22/t1195756692g4b2len1ygfbqp3/2rrdo1195757118.ps (open in new window) |
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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