Central tendency
| Summary of compuational transaction | |
| Raw Input | view raw input (R code) |
| Raw Output | view raw output of R engine |
| Computing time | 3 seconds |
| R Server | 'Herman Ole Andreas Wold' @ 193.190.124.10:1001 |
| Central Tendency - Ungrouped Data | |||
| Measure | Value | S.E. | Value/S.E. |
| Arithmetic Mean | 102.01625 | 0.842388564072274 | 121.103555236829 |
| Geometric Mean | 101.740724187079 | ||
| Harmonic Mean | 101.464710451030 | ||
| Quadratic Mean | 102.290640456495 | ||
| Winsorized Mean ( 1 / 26 ) | 102.0225 | 0.83546957727793 | 122.113961746402 |
| Winsorized Mean ( 2 / 26 ) | 102.02 | 0.827659503156073 | 123.263249695040 |
| Winsorized Mean ( 3 / 26 ) | 102.035 | 0.808616767046892 | 126.184620648712 |
| Winsorized Mean ( 4 / 26 ) | 101.985 | 0.795716578574131 | 128.167494238652 |
| Winsorized Mean ( 5 / 26 ) | 101.99125 | 0.792345088780886 | 128.720744842282 |
| Winsorized Mean ( 6 / 26 ) | 101.99875 | 0.788339654337688 | 129.384269126602 |
| Winsorized Mean ( 7 / 26 ) | 101.9725 | 0.78073110616049 | 130.611550116767 |
| Winsorized Mean ( 8 / 26 ) | 101.9525 | 0.767011657611143 | 132.921708540299 |
| Winsorized Mean ( 9 / 26 ) | 102.0875 | 0.722095611941251 | 141.376707338731 |
| Winsorized Mean ( 10 / 26 ) | 102.125 | 0.716250124262697 | 142.582872296360 |
| Winsorized Mean ( 11 / 26 ) | 102.11125 | 0.705321081722916 | 144.772717909649 |
| Winsorized Mean ( 12 / 26 ) | 102.11125 | 0.691290743185473 | 147.711004387923 |
| Winsorized Mean ( 13 / 26 ) | 102.17625 | 0.681649720150322 | 149.895535756205 |
| Winsorized Mean ( 14 / 26 ) | 102.36875 | 0.64938041002973 | 157.640650101092 |
| Winsorized Mean ( 15 / 26 ) | 102.2375 | 0.628455951448781 | 162.680454794503 |
| Winsorized Mean ( 16 / 26 ) | 101.9375 | 0.572360134371465 | 178.100279663856 |
| Winsorized Mean ( 17 / 26 ) | 101.9375 | 0.566455152570279 | 179.956876616729 |
| Winsorized Mean ( 18 / 26 ) | 101.8925 | 0.554015191378793 | 183.916436923719 |
| Winsorized Mean ( 19 / 26 ) | 101.8925 | 0.54751965169055 | 186.098343110410 |
| Winsorized Mean ( 20 / 26 ) | 101.8425 | 0.533962898132706 | 190.729543861845 |
| Winsorized Mean ( 21 / 26 ) | 101.8425 | 0.526884126645881 | 193.292025418045 |
| Winsorized Mean ( 22 / 26 ) | 101.7875 | 0.519585932391592 | 195.901185260125 |
| Winsorized Mean ( 23 / 26 ) | 101.96 | 0.488881440935467 | 208.557722716782 |
| Winsorized Mean ( 24 / 26 ) | 102.41 | 0.432828495283194 | 236.606418283516 |
| Winsorized Mean ( 25 / 26 ) | 102.37875 | 0.420633540220259 | 243.391789314734 |
| Winsorized Mean ( 26 / 26 ) | 102.41125 | 0.416856051369404 | 245.675334839379 |
| Trimmed Mean ( 1 / 26 ) | 102.019230769231 | 0.817778350701958 | 124.751689356487 |
| Trimmed Mean ( 2 / 26 ) | 102.015789473684 | 0.79711552934838 | 127.981184304713 |
| Trimmed Mean ( 3 / 26 ) | 102.013513513514 | 0.777786101231013 | 131.158828053182 |
| Trimmed Mean ( 4 / 26 ) | 102.005555555556 | 0.7634779802495 | 133.606414584767 |
| Trimmed Mean ( 5 / 26 ) | 102.011428571429 | 0.751025641996603 | 135.829488191949 |
| Trimmed Mean ( 6 / 26 ) | 102.016176470588 | 0.737139103209674 | 138.394742629154 |
| Trimmed Mean ( 7 / 26 ) | 102.019696969697 | 0.721560145016558 | 141.387655172329 |
| Trimmed Mean ( 8 / 26 ) | 102.028125 | 0.70470171540056 | 144.782001760853 |
| Trimmed Mean ( 9 / 26 ) | 102.040322580645 | 0.687535238950428 | 148.414680149947 |
| Trimmed Mean ( 10 / 26 ) | 102.033333333333 | 0.676530141246542 | 150.818606759089 |
| Trimmed Mean ( 11 / 26 ) | 102.020689655172 | 0.664080397598688 | 153.62701568075 |
| Trimmed Mean ( 12 / 26 ) | 102.008928571429 | 0.650825034768379 | 156.737868277812 |
| Trimmed Mean ( 13 / 26 ) | 101.996296296296 | 0.637068117162288 | 160.102653936947 |
| Trimmed Mean ( 14 / 26 ) | 101.975 | 0.621630434166274 | 164.044413521626 |
| Trimmed Mean ( 15 / 26 ) | 101.93 | 0.608324899764484 | 167.558487314037 |
| Trimmed Mean ( 16 / 26 ) | 101.895833333333 | 0.595535684222224 | 171.099458912207 |
| Trimmed Mean ( 17 / 26 ) | 101.891304347826 | 0.590061210997823 | 172.679210984777 |
| Trimmed Mean ( 18 / 26 ) | 101.886363636364 | 0.583336170517432 | 174.661488153543 |
| Trimmed Mean ( 19 / 26 ) | 101.885714285714 | 0.576248545273636 | 176.808627321277 |
| Trimmed Mean ( 20 / 26 ) | 101.885 | 0.567377570663758 | 179.571779478008 |
| Trimmed Mean ( 21 / 26 ) | 101.889473684211 | 0.557628965923619 | 182.719119541159 |
| Trimmed Mean ( 22 / 26 ) | 101.894444444444 | 0.545150983082908 | 186.910502973353 |
| Trimmed Mean ( 23 / 26 ) | 101.905882352941 | 0.528913411708417 | 192.670255843542 |
| Trimmed Mean ( 24 / 26 ) | 101.9 | 0.513762214359158 | 198.340783249514 |
| Trimmed Mean ( 25 / 26 ) | 101.843333333333 | 0.505661813598576 | 201.406019981138 |
| Trimmed Mean ( 26 / 26 ) | 101.782142857143 | 0.495483665458515 | 205.419774560993 |
| Median | 100.9 | ||
| Midrange | 101.9 | ||
| Midmean - Weighted Average at Xnp | 101.741463414634 | ||
| Midmean - Weighted Average at X(n+1)p | 101.885 | ||
| Midmean - Empirical Distribution Function | 101.741463414634 | ||
| Midmean - Empirical Distribution Function - Averaging | 101.885 | ||
| Midmean - Empirical Distribution Function - Interpolation | 101.885 | ||
| Midmean - Closest Observation | 101.741463414634 | ||
| Midmean - True Basic - Statistics Graphics Toolkit | 101.885 | ||
| Midmean - MS Excel (old versions) | 101.885714285714 | ||
| Number of observations | 80 | ||
 |
| http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/12/t1194891139vxuhatez400q72j/1x9k91194891396.png (open in new window) |
| http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/12/t1194891139vxuhatez400q72j/1x9k91194891396.ps (open in new window) |
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| http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/12/t1194891139vxuhatez400q72j/2zvns1194891396.png (open in new window) |
| http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/12/t1194891139vxuhatez400q72j/2zvns1194891396.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
Creative Commons Attribution-Noncommercial-Share Alike 3.0 License.
Software written by Ed van Stee & Patrick Wessa
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FreeStatistics.org is safe. There is no need to download any software to use the applications and services contained in this website. Hence, your system's security is not compromised by their use, and your personal data - other than data you submit in the account application form, and the user-agent information that is transmitted by your browser - is never transmitted to our servers.
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.