data analysis time series
| 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 | 101.103913043478 | 0.420117316937905 | 240.656380889964 |
| Geometric Mean | 101.044576655596 | ||
| Harmonic Mean | 100.985291343685 | ||
| Quadratic Mean | 101.163249922008 | ||
| Winsorized Mean ( 1 / 23 ) | 101.105797101449 | 0.419618092806564 | 240.947182294299 |
| Winsorized Mean ( 2 / 23 ) | 101.107536231884 | 0.418261809664206 | 241.732651405722 |
| Winsorized Mean ( 3 / 23 ) | 101.103623188406 | 0.416147432878657 | 242.951452299085 |
| Winsorized Mean ( 4 / 23 ) | 101.097826086957 | 0.414493953402063 | 243.906636652165 |
| Winsorized Mean ( 5 / 23 ) | 101.107971014493 | 0.412552436911511 | 245.079078362539 |
| Winsorized Mean ( 6 / 23 ) | 101.079275362319 | 0.407257860571736 | 248.194780624779 |
| Winsorized Mean ( 7 / 23 ) | 101.081304347826 | 0.406583603300037 | 248.611364372295 |
| Winsorized Mean ( 8 / 23 ) | 101.027971014493 | 0.3959619589846 | 255.145649025395 |
| Winsorized Mean ( 9 / 23 ) | 101.026666666667 | 0.393662587783935 | 256.632633635269 |
| Winsorized Mean ( 10 / 23 ) | 101.023768115942 | 0.391823512596441 | 257.829775059955 |
| Winsorized Mean ( 11 / 23 ) | 101.038115942029 | 0.38847688652276 | 260.087844212346 |
| Winsorized Mean ( 12 / 23 ) | 101.067681159420 | 0.377240628924230 | 267.913033247859 |
| Winsorized Mean ( 13 / 23 ) | 101.139275362319 | 0.363473012494214 | 278.258005094474 |
| Winsorized Mean ( 14 / 23 ) | 101.153478260870 | 0.351091273176781 | 288.111627912599 |
| Winsorized Mean ( 15 / 23 ) | 101.155652173913 | 0.349496012625994 | 289.432922034972 |
| Winsorized Mean ( 16 / 23 ) | 101.153333333333 | 0.348460177918998 | 290.286637449996 |
| Winsorized Mean ( 17 / 23 ) | 101.113913043478 | 0.32893173713985 | 307.400903064846 |
| Winsorized Mean ( 18 / 23 ) | 101.004347826087 | 0.309542499789052 | 326.302035729891 |
| Winsorized Mean ( 19 / 23 ) | 101.042898550725 | 0.301030632435479 | 335.656533467176 |
| Winsorized Mean ( 20 / 23 ) | 100.996521739130 | 0.2914410521443 | 346.541851245872 |
| Winsorized Mean ( 21 / 23 ) | 100.984347826087 | 0.283115543264687 | 356.689522099731 |
| Winsorized Mean ( 22 / 23 ) | 100.981159420290 | 0.277474416555457 | 363.929621598492 |
| Winsorized Mean ( 23 / 23 ) | 101.021159420290 | 0.270164259358278 | 373.924958320710 |
| Trimmed Mean ( 1 / 23 ) | 101.1 | 0.417605383098403 | 242.094580414394 |
| Trimmed Mean ( 2 / 23 ) | 101.093846153846 | 0.414918243354807 | 243.647628835154 |
| Trimmed Mean ( 3 / 23 ) | 101.086349206349 | 0.412252954872604 | 245.204668666565 |
| Trimmed Mean ( 4 / 23 ) | 101.079836065574 | 0.409668564678113 | 246.735641395856 |
| Trimmed Mean ( 5 / 23 ) | 101.074576271186 | 0.406794953930337 | 248.465658913987 |
| Trimmed Mean ( 6 / 23 ) | 101.066491228070 | 0.403540680606075 | 250.44932539708 |
| Trimmed Mean ( 7 / 23 ) | 101.063818181818 | 0.400643883359449 | 252.253490891675 |
| Trimmed Mean ( 8 / 23 ) | 101.060566037736 | 0.396842985614978 | 254.661338869640 |
| Trimmed Mean ( 9 / 23 ) | 101.066078431373 | 0.394230258031469 | 256.363067959398 |
| Trimmed Mean ( 10 / 23 ) | 101.072244897959 | 0.390982895534908 | 258.508098569584 |
| Trimmed Mean ( 11 / 23 ) | 101.072244897959 | 0.386788217604948 | 261.31159197096 |
| Trimmed Mean ( 12 / 23 ) | 101.085111111111 | 0.38169380904179 | 264.832985803141 |
| Trimmed Mean ( 13 / 23 ) | 101.087441860465 | 0.377128524408909 | 268.045070361368 |
| Trimmed Mean ( 14 / 23 ) | 101.080731707317 | 0.373611150118889 | 270.550629110378 |
| Trimmed Mean ( 15 / 23 ) | 101.071538461538 | 0.370951386257646 | 272.465725175478 |
| Trimmed Mean ( 16 / 23 ) | 101.061081081081 | 0.366872952574728 | 275.466153533071 |
| Trimmed Mean ( 17 / 23 ) | 101.049714285714 | 0.360715555368429 | 280.136835747224 |
| Trimmed Mean ( 18 / 23 ) | 101.041818181818 | 0.356307997550514 | 283.57998943735 |
| Trimmed Mean ( 19 / 23 ) | 101.046451612903 | 0.353979997122460 | 285.458083604499 |
| Trimmed Mean ( 20 / 23 ) | 101.046896551724 | 0.351432011884814 | 287.529004571284 |
| Trimmed Mean ( 21 / 23 ) | 101.053333333333 | 0.348712732489896 | 289.789628878152 |
| Trimmed Mean ( 22 / 23 ) | 101.053333333333 | 0.345210216148557 | 292.729845775614 |
| Trimmed Mean ( 23 / 23 ) | 101.073478260870 | 0.339461098550499 | 297.746866113537 |
| Median | 100.83 | ||
| Midrange | 101.235 | ||
| Midmean - Weighted Average at Xnp | 100.951176470588 | ||
| Midmean - Weighted Average at X(n+1)p | 101.049714285714 | ||
| Midmean - Empirical Distribution Function | 101.049714285714 | ||
| Midmean - Empirical Distribution Function - Averaging | 101.049714285714 | ||
| Midmean - Empirical Distribution Function - Interpolation | 101.049714285714 | ||
| Midmean - Closest Observation | 100.958611111111 | ||
| Midmean - True Basic - Statistics Graphics Toolkit | 101.049714285714 | ||
| Midmean - MS Excel (old versions) | 101.049714285714 | ||
| Number of observations | 69 | ||
 |
| http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Oct/22/tfo5mcvvo86gc6j1193029894/18jyd1193029887.png (open in new window) |
| http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Oct/22/tfo5mcvvo86gc6j1193029894/18jyd1193029887.ps (open in new window) |
 |
| http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Oct/22/tfo5mcvvo86gc6j1193029894/25ute1193029887.png (open in new window) |
| http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Oct/22/tfo5mcvvo86gc6j1193029894/25ute1193029887.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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Software written by Ed van Stee & Patrick Wessa
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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.