WS8 - Central tendency - Machines
| Summary of compuational transaction | |
| Raw Input | view raw input (R code) |
| Raw Output | view raw output of R engine |
| Computing time | 2 seconds |
| R Server | 'Gwilym Jenkins' @ 72.249.127.135 |
| Central Tendency - Ungrouped Data | |||
| Measure | Value | S.E. | Value/S.E. |
| Arithmetic Mean | 5.44628782954777 | 3.90017597062776 | 1.39642105139968 |
| Geometric Mean | NaN | ||
| Harmonic Mean | -39.3416462537721 | ||
| Quadratic Mean | 32.3855525728225 | ||
| Winsorized Mean ( 1 / 22 ) | 4.81598855003934 | 3.68259448830151 | 1.30777053116717 |
| Winsorized Mean ( 2 / 22 ) | 4.81360958482815 | 3.60543774660992 | 1.33509712915005 |
| Winsorized Mean ( 3 / 22 ) | 4.71893645768683 | 3.5832721642285 | 1.3169349804895 |
| Winsorized Mean ( 4 / 22 ) | 4.94304235888525 | 3.44084344714489 | 1.43657868624823 |
| Winsorized Mean ( 5 / 22 ) | 4.96942761001516 | 3.40488420813525 | 1.4594997380944 |
| Winsorized Mean ( 6 / 22 ) | 4.71005742790334 | 3.34452177342605 | 1.40829025701886 |
| Winsorized Mean ( 7 / 22 ) | 4.7898609230858 | 3.30782705186991 | 1.44803850019247 |
| Winsorized Mean ( 8 / 22 ) | 4.80992610185888 | 3.26698626523072 | 1.47228231506483 |
| Winsorized Mean ( 9 / 22 ) | 4.83558073659271 | 3.25373955775553 | 1.48616096978836 |
| Winsorized Mean ( 10 / 22 ) | 4.58871037883093 | 3.14128744347354 | 1.46077379463144 |
| Winsorized Mean ( 11 / 22 ) | 4.9627157140051 | 3.06141520121112 | 1.62105280983834 |
| Winsorized Mean ( 12 / 22 ) | 4.71374105726731 | 2.99531480663792 | 1.57370472272937 |
| Winsorized Mean ( 13 / 22 ) | 4.72991831250282 | 2.99211889691024 | 1.58079223301824 |
| Winsorized Mean ( 14 / 22 ) | 4.17030635828353 | 2.74380025905574 | 1.51990158340414 |
| Winsorized Mean ( 15 / 22 ) | 3.32834060456271 | 2.57352897485576 | 1.29329828305091 |
| Winsorized Mean ( 16 / 22 ) | 2.56547279519003 | 2.43740860476340 | 1.05254112510161 |
| Winsorized Mean ( 17 / 22 ) | 2.23826362151740 | 2.34962723810532 | 0.952603708885448 |
| Winsorized Mean ( 18 / 22 ) | 1.95921920705687 | 2.17446260413652 | 0.901013061033938 |
| Winsorized Mean ( 19 / 22 ) | 2.92902020375054 | 2.03219391823596 | 1.44130940333345 |
| Winsorized Mean ( 20 / 22 ) | 0.201046219238596 | 1.55676333329996 | 0.129143727205103 |
| Winsorized Mean ( 21 / 22 ) | 0.160675058700280 | 1.48441194476370 | 0.108241556036426 |
| Winsorized Mean ( 22 / 22 ) | -0.299005426774177 | 1.39866888148196 | -0.213778565272264 |
| Trimmed Mean ( 1 / 22 ) | 4.64850461520335 | 3.59249507578397 | 1.29394877853491 |
| Trimmed Mean ( 2 / 22 ) | 4.47055293444011 | 3.48407378000166 | 1.28313957072344 |
| Trimmed Mean ( 3 / 22 ) | 4.28242509390474 | 3.40299393767609 | 1.25842865792151 |
| Trimmed Mean ( 4 / 22 ) | 4.11752080092039 | 3.31451812935292 | 1.24226829971337 |
| Trimmed Mean ( 5 / 22 ) | 3.87555758565483 | 3.25899207346034 | 1.18918901865871 |
| Trimmed Mean ( 6 / 22 ) | 3.6099034368816 | 3.20063738395797 | 1.12787017203977 |
| Trimmed Mean ( 7 / 22 ) | 3.37900692024741 | 3.14455072994617 | 1.07455951912891 |
| Trimmed Mean ( 8 / 22 ) | 3.11544078784903 | 3.08247871253345 | 1.01069336673164 |
| Trimmed Mean ( 9 / 22 ) | 2.82737828446736 | 3.01298587685419 | 0.93839745688399 |
| Trimmed Mean ( 10 / 22 ) | 2.51127234292911 | 2.92625152607063 | 0.858187452635435 |
| Trimmed Mean ( 11 / 22 ) | 2.20417280718710 | 2.84209287693468 | 0.775545663927913 |
| Trimmed Mean ( 12 / 22 ) | 1.8166089277168 | 2.74968521025013 | 0.660660689792758 |
| Trimmed Mean ( 13 / 22 ) | 1.42572602134887 | 2.64385648797780 | 0.539259989273989 |
| Trimmed Mean ( 14 / 22 ) | 0.99363933712105 | 2.50134123148635 | 0.397242617126096 |
| Trimmed Mean ( 15 / 22 ) | 0.587599191558929 | 2.37824294435758 | 0.247072820273899 |
| Trimmed Mean ( 16 / 22 ) | 0.242468791402897 | 2.25947185995983 | 0.107312153649574 |
| Trimmed Mean ( 17 / 22 ) | -0.0479067090704942 | 2.13558137680993 | -0.0224326310346721 |
| Trimmed Mean ( 18 / 22 ) | -0.333678000393981 | 1.98660859338906 | -0.167963634862136 |
| Trimmed Mean ( 19 / 22 ) | -0.6224132042952 | 1.82995467655026 | -0.340124928923674 |
| Trimmed Mean ( 20 / 22 ) | -1.07635582036120 | 1.63685241093371 | -0.65757658611824 |
| Trimmed Mean ( 21 / 22 ) | -1.24340070246271 | 1.55339209725963 | -0.800442273818834 |
| Trimmed Mean ( 22 / 22 ) | -1.43283949563549 | 1.44830081984348 | -0.989324507729228 |
| Median | -1.95225364021973 | ||
| Midrange | 31.7731339029136 | ||
| Midmean - Weighted Average at Xnp | -0.616803189028742 | ||
| Midmean - Weighted Average at X(n+1)p | -0.0479067090704957 | ||
| Midmean - Empirical Distribution Function | -0.616803189028742 | ||
| Midmean - Empirical Distribution Function - Averaging | -0.0479067090704957 | ||
| Midmean - Empirical Distribution Function - Interpolation | -0.0479067090704957 | ||
| Midmean - Closest Observation | -0.616803189028742 | ||
| Midmean - True Basic - Statistics Graphics Toolkit | -0.0479067090704957 | ||
| Midmean - MS Excel (old versions) | 0.242468791402895 | ||
| Number of observations | 68 | ||
 |
| http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/30/t1196432023kjbvlynhcorp0me/1pwbi1196432649.png (open in new window) |
| http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/30/t1196432023kjbvlynhcorp0me/1pwbi1196432649.ps (open in new window) |
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| http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/30/t1196432023kjbvlynhcorp0me/2hs6m1196432649.png (open in new window) |
| http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/30/t1196432023kjbvlynhcorp0me/2hs6m1196432649.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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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.