gem. e(t)
| 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 | 1.44615358607018e-08 | 80.3836179040521 | 1.79906506297880e-10 |
| Geometric Mean | NaN | ||
| Harmonic Mean | 1811.72087315632 | ||
| Quadratic Mean | 643.068943232417 | ||
| Winsorized Mean ( 1 / 21 ) | 2.85126664523076 | 78.610501531802 | 0.0362708110197883 |
| Winsorized Mean ( 2 / 21 ) | 3.88071384523077 | 77.4611232837488 | 0.0500988583784834 |
| Winsorized Mean ( 3 / 21 ) | 4.47354619907691 | 77.006764791162 | 0.0580928988668582 |
| Winsorized Mean ( 4 / 21 ) | 4.21999585446154 | 73.9926072772239 | 0.0570326686644615 |
| Winsorized Mean ( 5 / 21 ) | -1.90184645323076 | 71.776139470754 | -0.0264969176003913 |
| Winsorized Mean ( 6 / 21 ) | -1.50396116092309 | 70.5823912900906 | -0.0213078805270549 |
| Winsorized Mean ( 7 / 21 ) | -13.9269473793846 | 68.4309038466263 | -0.203518390033237 |
| Winsorized Mean ( 8 / 21 ) | -14.0894302593846 | 68.3130488687771 | -0.206248008143350 |
| Winsorized Mean ( 9 / 21 ) | -9.29553163169231 | 64.9092749555723 | -0.143208064456963 |
| Winsorized Mean ( 10 / 21 ) | -0.651108923999989 | 63.228648884789 | -0.0102976883973339 |
| Winsorized Mean ( 11 / 21 ) | 0.70330132676922 | 62.6821739090187 | 0.0112201170270521 |
| Winsorized Mean ( 12 / 21 ) | 0.278355111384623 | 62.2889870577388 | 0.00446876927259391 |
| Winsorized Mean ( 13 / 21 ) | -0.289286508615414 | 61.0243721802994 | -0.00474050773944389 |
| Winsorized Mean ( 14 / 21 ) | 59.367230476 | 50.8587567764278 | 1.16729614011162 |
| Winsorized Mean ( 15 / 21 ) | 62.6089957221538 | 48.2065183112084 | 1.29876618174262 |
| Winsorized Mean ( 16 / 21 ) | 64.9055873775385 | 47.7665969524068 | 1.35880702245145 |
| Winsorized Mean ( 17 / 21 ) | 67.6597032913846 | 45.3439140375558 | 1.49214519142185 |
| Winsorized Mean ( 18 / 21 ) | 40.360802436 | 38.5738433397880 | 1.04632566893766 |
| Winsorized Mean ( 19 / 21 ) | 5.34894740215383 | 31.7080261751475 | 0.168693799248416 |
| Winsorized Mean ( 20 / 21 ) | 4.87138995599998 | 29.3606559530492 | 0.16591556959047 |
| Winsorized Mean ( 21 / 21 ) | 20.4946367344615 | 26.8348738985424 | 0.763731434399428 |
| Trimmed Mean ( 1 / 21 ) | 3.77951006253968 | 76.5869558125724 | 0.0493492661046497 |
| Trimmed Mean ( 2 / 21 ) | 4.76862190065574 | 74.1333747558887 | 0.0643248997682646 |
| Trimmed Mean ( 3 / 21 ) | 5.25772379559322 | 71.9016112336194 | 0.0731238661468943 |
| Trimmed Mean ( 4 / 21 ) | 5.55580299894736 | 69.3806621129484 | 0.0800771112547583 |
| Trimmed Mean ( 5 / 21 ) | 5.95047329163636 | 67.451512965541 | 0.0882185295780731 |
| Trimmed Mean ( 6 / 21 ) | 7.87651398377358 | 65.7872024096214 | 0.119727145938366 |
| Trimmed Mean ( 7 / 21 ) | 9.86909857333333 | 64.048284986579 | 0.154088412756116 |
| Trimmed Mean ( 8 / 21 ) | 14.3785533457143 | 62.4260239571558 | 0.230329475341607 |
| Trimmed Mean ( 9 / 21 ) | 19.2998802987234 | 60.3608161214583 | 0.319741871281 |
| Trimmed Mean ( 10 / 21 ) | 23.8892673986667 | 58.5947797794147 | 0.407702998263667 |
| Trimmed Mean ( 11 / 21 ) | 27.5988591683721 | 56.7201343126774 | 0.486579580651725 |
| Trimmed Mean ( 12 / 21 ) | 31.4751590790244 | 54.3679276303349 | 0.578928799586296 |
| Trimmed Mean ( 13 / 21 ) | 35.8080485189744 | 51.3025764739626 | 0.69797758670362 |
| Trimmed Mean ( 14 / 21 ) | 40.6860667659459 | 47.4700155234761 | 0.85708981379677 |
| Trimmed Mean ( 15 / 21 ) | 38.2079532125714 | 45.3325550821689 | 0.842836966575487 |
| Trimmed Mean ( 16 / 21 ) | 35.0037759133333 | 43.0943993701651 | 0.812258122283217 |
| Trimmed Mean ( 17 / 21 ) | 31.0851917496774 | 39.9779507565245 | 0.777558408108356 |
| Trimmed Mean ( 18 / 21 ) | 26.2629944875862 | 36.2135038533927 | 0.725226550678712 |
| Trimmed Mean ( 19 / 21 ) | 24.3774851940741 | 33.3191709579817 | 0.73163540667972 |
| Trimmed Mean ( 20 / 21 ) | 26.9813903656 | 31.5915976988482 | 0.854068560343301 |
| Trimmed Mean ( 21 / 21 ) | 30.1056295539130 | 29.7432697574161 | 1.01218291732726 |
| Median | 40.39809249 | ||
| Midrange | -119.0545665 | ||
| Midmean - Weighted Average at Xnp | 18.006557685625 | ||
| Midmean - Weighted Average at X(n+1)p | 35.0037759133333 | ||
| Midmean - Empirical Distribution Function | 35.0037759133333 | ||
| Midmean - Empirical Distribution Function - Averaging | 35.0037759133333 | ||
| Midmean - Empirical Distribution Function - Interpolation | 35.0037759133333 | ||
| Midmean - Closest Observation | 22.2676124952941 | ||
| Midmean - True Basic - Statistics Graphics Toolkit | 35.0037759133333 | ||
| Midmean - MS Excel (old versions) | 35.0037759133333 | ||
| Number of observations | 65 | ||
 |
| http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Dec/13/t1197535194nvui0j5lmw3uuql/1ckox1197536106.png (open in new window) |
| http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Dec/13/t1197535194nvui0j5lmw3uuql/1ckox1197536106.ps (open in new window) |
 |
| http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Dec/13/t1197535194nvui0j5lmw3uuql/2dwhn1197536106.png (open in new window) |
| http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Dec/13/t1197535194nvui0j5lmw3uuql/2dwhn1197536106.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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