| 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 | 25253.6527777778 | 858.007319726421 | 29.4329106490956 |
| Geometric Mean | 24195.2258777478 | ||
| Harmonic Mean | 23101.5796548688 | ||
| Quadratic Mean | 26268.1463836061 | ||
| Winsorized Mean ( 1 / 24 ) | 25236.6111111111 | 847.457751093655 | 29.7791967546971 |
| Winsorized Mean ( 2 / 24 ) | 25246.1388888889 | 827.129696091915 | 30.5225879425848 |
| Winsorized Mean ( 3 / 24 ) | 25193.0972222222 | 804.656211681937 | 31.3091440250765 |
| Winsorized Mean ( 4 / 24 ) | 25193.2638888889 | 800.873543516477 | 31.4572307861117 |
| Winsorized Mean ( 5 / 24 ) | 25243.2638888889 | 767.413994302574 | 32.8939321882317 |
| Winsorized Mean ( 6 / 24 ) | 25359.5972222222 | 735.272116932812 | 34.4900841990443 |
| Winsorized Mean ( 7 / 24 ) | 25318.0833333333 | 724.527818486872 | 34.9442529152413 |
| Winsorized Mean ( 8 / 24 ) | 25263.9722222222 | 708.432996847264 | 35.6617666521101 |
| Winsorized Mean ( 9 / 24 ) | 25245.3472222222 | 697.384056012529 | 36.200063658709 |
| Winsorized Mean ( 10 / 24 ) | 25248.2638888889 | 685.113738370736 | 36.8526603318912 |
| Winsorized Mean ( 11 / 24 ) | 24922.2361111111 | 622.920655456338 | 40.0086847222198 |
| Winsorized Mean ( 12 / 24 ) | 24840.5694444444 | 604.33254929345 | 41.1041395560881 |
| Winsorized Mean ( 13 / 24 ) | 24817.0972222222 | 577.812622318052 | 42.950078042016 |
| Winsorized Mean ( 14 / 24 ) | 24642.2916666667 | 535.102475610366 | 46.0515373967544 |
| Winsorized Mean ( 15 / 24 ) | 24702.0833333333 | 516.31573715535 | 47.8429797035238 |
| Winsorized Mean ( 16 / 24 ) | 24761.6388888889 | 491.11743306631 | 50.4189776654611 |
| Winsorized Mean ( 17 / 24 ) | 24733.0694444444 | 479.884194480341 | 51.5396625455179 |
| Winsorized Mean ( 18 / 24 ) | 24808.0694444444 | 448.906397773312 | 55.2633456941106 |
| Winsorized Mean ( 19 / 24 ) | 24824.1666666667 | 440.742030180296 | 56.323574714469 |
| Winsorized Mean ( 20 / 24 ) | 24826.3888888889 | 420.859931086942 | 58.9896710403638 |
| Winsorized Mean ( 21 / 24 ) | 24995.8472222222 | 395.420514983338 | 63.213329291414 |
| Winsorized Mean ( 22 / 24 ) | 25005.9305555556 | 369.980521378738 | 67.5871542165803 |
| Winsorized Mean ( 23 / 24 ) | 24867.2916666667 | 348.461739500530 | 71.3630474964349 |
| Winsorized Mean ( 24 / 24 ) | 24781.2916666667 | 330.672922308915 | 74.9420046057353 |
| Trimmed Mean ( 1 / 24 ) | 25206.2285714286 | 817.989009926686 | 30.8148743632726 |
| Trimmed Mean ( 2 / 24 ) | 25174.0588235294 | 782.836550295555 | 32.1574903650387 |
| Trimmed Mean ( 3 / 24 ) | 25134.7424242424 | 754.032087484341 | 33.3337835901637 |
| Trimmed Mean ( 4 / 24 ) | 25112.859375 | 730.022336670115 | 34.400124644882 |
| Trimmed Mean ( 5 / 24 ) | 25089.5161290323 | 702.440223397564 | 35.7176529665104 |
| Trimmed Mean ( 6 / 24 ) | 25052.6166666667 | 679.982010019452 | 36.8430580478886 |
| Trimmed Mean ( 7 / 24 ) | 24989.1034482759 | 661.725541665296 | 37.7635467801173 |
| Trimmed Mean ( 8 / 24 ) | 24928.6785714286 | 642.075598427122 | 38.8251455630704 |
| Trimmed Mean ( 9 / 24 ) | 24872.7962962963 | 621.815321832094 | 40.0002949798857 |
| Trimmed Mean ( 10 / 24 ) | 24815.4807692308 | 599.155952001893 | 41.4173984023985 |
| Trimmed Mean ( 11 / 24 ) | 24753.16 | 573.478154564989 | 43.1632134597637 |
| Trimmed Mean ( 12 / 24 ) | 24730.1041666667 | 556.417359267902 | 44.4452419658598 |
| Trimmed Mean ( 13 / 24 ) | 24715.6956521739 | 538.829254116151 | 45.8692535035341 |
| Trimmed Mean ( 14 / 24 ) | 24702.9318181818 | 522.170738884592 | 47.3081503397715 |
| Trimmed Mean ( 15 / 24 ) | 24710.3571428571 | 510.147385755623 | 48.4376825851151 |
| Trimmed Mean ( 16 / 24 ) | 24711.35 | 498.186685673203 | 49.6025901748204 |
| Trimmed Mean ( 17 / 24 ) | 24705.3947368421 | 487.613228692411 | 50.6659649146361 |
| Trimmed Mean ( 18 / 24 ) | 24702.1388888889 | 475.354330920677 | 51.9657385703108 |
| Trimmed Mean ( 19 / 24 ) | 24689.6764705882 | 465.616465459045 | 53.0257804483933 |
| Trimmed Mean ( 20 / 24 ) | 24673.75 | 453.158251838888 | 54.4484181847631 |
| Trimmed Mean ( 21 / 24 ) | 24655.4333333333 | 440.125976436406 | 56.0190369424737 |
| Trimmed Mean ( 22 / 24 ) | 24613.75 | 427.317542439717 | 57.6006074065455 |
| Trimmed Mean ( 23 / 24 ) | 24564.3846153846 | 415.000771368785 | 59.1911782100178 |
| Trimmed Mean ( 24 / 24 ) | 24524.875 | 402.665634802732 | 60.9063026002079 |
| Median | 24440 | ||
| Midrange | 26913.5 | ||
| Midmean - Weighted Average at Xnp | 24569.2432432432 | ||
| Midmean - Weighted Average at X(n+1)p | 24702.1388888889 | ||
| Midmean - Empirical Distribution Function | 24569.2432432432 | ||
| Midmean - Empirical Distribution Function - Averaging | 24702.1388888889 | ||
| Midmean - Empirical Distribution Function - Interpolation | 24702.1388888889 | ||
| Midmean - Closest Observation | 24569.2432432432 | ||
| Midmean - True Basic - Statistics Graphics Toolkit | 24702.1388888889 | ||
| Midmean - MS Excel (old versions) | 24705.3947368421 | ||
| Number of observations | 72 | ||
 |
| http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/30/t1196431882tp68hhe8g1ax7fa/1yymq1196432512.png (open in new window) |
| http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/30/t1196431882tp68hhe8g1ax7fa/1yymq1196432512.ps (open in new window) |
 |
| http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/30/t1196431882tp68hhe8g1ax7fa/2fsdw1196432512.png (open in new window) |
| http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/30/t1196431882tp68hhe8g1ax7fa/2fsdw1196432512.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')
Copyright
This work is licensed under a
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As a general rule, we do not log on-line behavior of individuals (other than normal logging of webserver 'hits'). However, in cases of abuse, hacking, unauthorized access, Denial of Service attacks, illegal copying, hotlinking, non-compliance with international webstandards (such as robots.txt), or any other harmful behavior, our system engineers are empowered to log, track, identify, publish, and ban misbehaving individuals - even if this leads to ban entire blocks of IP addresses, or disclosing user's identity.