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R Software Module: rwasp_centraltendency.wasp (opens new window with default values)
Title produced by software: Central Tendency
Date of computation: Thu, 22 Nov 2007 07:24:30 -0700
 
Cite this page as follows:
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2007/Nov/22/t1195741090mqylxym2dny7rss.htm/, Retrieved Thu, 22 Nov 2007 15:18:12 +0100
 
User-defined keywords:
s0650532 Tom Steffi Jan Lennert Thomas
 
Dataseries X:
» Textbox « » Textfile « » CSV «
0.0230555555555585 0.00638888888888877 0.00472222222222195 0.00305555555555539 0.00305555555555547 0.0030555555555554 0.0127777777777777 0.0044444444444443 0.00277777777777762 0.00111111111111095 0.00111111111111097 0.00111111111111097 -0.00361111111111185 -0.0202777777777779 -0.0219444444444445 -0.0236111111111112 -0.0236111111111112 -0.0236111111111112 -0.00388888888888897 0.0277777777777777 0.0261111111111111 0.0244444444444444 0.0244444444444444 0.0244444444444444 0.0197222222222216 0.00305555555555555 0.00138888888888892 -0.000277777777777775 -0.000277777777777789 -0.000277777777777771 0.00944444444444446 0.00111111111111112 -0.000555555555555545 -0.00222222222222221 -0.00222222222222222 -0.00222222222222221 -0.00694444444444504 -0.0236111111111111 -0.0252777777777777 -0.0269444444444444 -0.0269444444444444 -0.0269444444444444 -0.0172222222222221 -0.0255555555555555 -0.0272222222222221 -0.0288888888888888 -0.0288888888888888 -0.0288888888888888 -0.0336111111111116 0.0397222222222224 0.0480555555555558 0.0463888888888891 0.0463888888888891 0.0463888888888891 -0.0122222222222221 -0.0105555555555554 -0.0122222222222221 -0.00388888888888877 -0.00388888888888877 -0.00388888888888876 0.00138888888888843 -0.00527777777777783 -0.00694444444444445 0.00138888888888886 0.00138888888888886 0.00138888888888887 0.0111111111111111 0.00277777777777776 0.0111111111111111 0.00944444444444444 0.00944444444444445 0.00944444444444444
 
Text written by user:
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Output produced by software:


Summary of compuational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135


Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean2.5207700510288e-180.002311513033848441.09052815801430e-15
Geometric MeanNaN
Harmonic Mean-0.0124823575590168
Quadratic Mean0.0194771550258562
Winsorized Mean ( 1 / 24 )4.24382716049483e-050.002292278532064420.0185135754714452
Winsorized Mean ( 2 / 24 )4.24382716049482e-050.002292278532064420.0185135754714452
Winsorized Mean ( 3 / 24 )4.24382716049484e-050.002292278532064420.0185135754714452
Winsorized Mean ( 4 / 24 )-0.0002353395061728290.00217518119894554-0.108193058255061
Winsorized Mean ( 5 / 24 )-0.001045524691358040.00197825552119854-0.528508415699808
Winsorized Mean ( 6 / 24 )-0.001184413580246920.00195031184526251-0.607294460690465
Winsorized Mean ( 7 / 24 )-0.001346450617283960.00191900021906238-0.701641721511545
Winsorized Mean ( 8 / 24 )-0.001192129629629640.00189049436508302-0.630591474721105
Winsorized Mean ( 9 / 24 )-0.001157407407407410.00188421287748006-0.614265734642112
Winsorized Mean ( 10 / 24 )-0.001118827160493440.00180639110502285-0.619371495675786
Winsorized Mean ( 11 / 24 )-0.001628086419753250.00171362639906927-0.950082480427192
Winsorized Mean ( 12 / 24 )-0.002785493827160560.00152799484142529-1.82297331878575
Winsorized Mean ( 13 / 24 )-0.003086419753086460.00148614610619311-2.07679429379429
Winsorized Mean ( 14 / 24 )-0.00276234567901240.00142386503569916-1.94003336675516
Winsorized Mean ( 15 / 24 )-0.002762345679012410.00131163250030486-2.10603631609492
Winsorized Mean ( 16 / 24 )-0.002083333333333340.00118662902728097-1.75567366500976
Winsorized Mean ( 17 / 24 )-0.0009027777777777880.000983946834043948-0.91750666452926
Winsorized Mean ( 18 / 24 )-0.0009027777777777890.000983946834043948-0.91750666452926
Winsorized Mean ( 19 / 24 )-0.001269290123456820.000797512037115934-1.59156233935602
Winsorized Mean ( 20 / 24 )-0.000729166666666950.000575793084726285-1.26636926703205
Winsorized Mean ( 21 / 24 )-0.0008101851851852590.000565084927757872-1.43374056781144
Winsorized Mean ( 22 / 24 )-0.0007253086419753540.000434351815417764-1.66986441918689
Winsorized Mean ( 23 / 24 )-0.0002816358024692160.000371041915946014-0.759040395075454
Winsorized Mean ( 24 / 24 )-0.0002816358024691730.000371041915946002-0.759040395075361
Trimmed Mean ( 1 / 24 )-0.0002063492063492000.00222315431994798-0.0928182108176948
Trimmed Mean ( 2 / 24 )-0.0004697712418300640.00214044532426064-0.219473600425805
Trimmed Mean ( 3 / 24 )-0.0007491582491582520.00204065955209521-0.367115743725634
Trimmed Mean ( 4 / 24 )-0.001046006944444450.00191882193679396-0.545129761332705
Trimmed Mean ( 5 / 24 )-0.001281362007168470.00181761269184030-0.70496977322001
Trimmed Mean ( 6 / 24 )-0.001337962962962980.00176207968896869-0.759308997963683
Trimmed Mean ( 7 / 24 )-0.001369731800766300.00170247958030190-0.804551089255003
Trimmed Mean ( 8 / 24 )-0.001374007936507950.00163780352146487-0.838933314344703
Trimmed Mean ( 9 / 24 )-0.001404320987654340.00156508057972387-0.897283504662807
Trimmed Mean ( 10 / 24 )-0.001442307692307710.00147531576976923-0.97762643215921
Trimmed Mean ( 11 / 24 )-0.001488888888888960.00138217789081011-1.07720496673283
Trimmed Mean ( 12 / 24 )-0.001469907407407470.00128776244892077-1.14144298013919
Trimmed Mean ( 13 / 24 )-0.001298309178744020.00121317512212694-1.07017458161178
Trimmed Mean ( 14 / 24 )-0.001073232323232390.00112452232313178-0.95438952269391
Trimmed Mean ( 15 / 24 )-0.0008664021164021810.00102428894746941-0.845857136838873
Trimmed Mean ( 16 / 24 )-0.0006388888888889540.000920382265023707-0.694156018828218
Trimmed Mean ( 17 / 24 )-0.0004678362573100140.000819260102222075-0.571047285277416
Trimmed Mean ( 18 / 24 )-0.0004166666666667460.000749166693641568-0.556173506114377
Trimmed Mean ( 19 / 24 )-0.0003594771241830940.000647532041559031-0.555149554171248
Trimmed Mean ( 20 / 24 )-0.0002517361111112050.000568476450046103-0.442825927249563
Trimmed Mean ( 21 / 24 )-0.0001944444444445160.000537072817762536-0.362044843852977
Trimmed Mean ( 22 / 24 )-0.0001190476190476900.000492950453195106-0.241500171621857
Trimmed Mean ( 23 / 24 )-4.27350427351173e-050.000475339711503733-0.0899042131361703
Trimmed Mean ( 24 / 24 )-1.15740740741479e-050.000470988954690493-0.0245739819562302
Median0.00111111111111096
Midrange0.0072222222222221
Midmean - Weighted Average at Xnp-0.000467836257310015
Midmean - Weighted Average at X(n+1)p-0.000467836257310015
Midmean - Empirical Distribution Function-0.000467836257310015
Midmean - Empirical Distribution Function - Averaging-0.000467836257310015
Midmean - Empirical Distribution Function - Interpolation-0.000467836257310015
Midmean - Closest Observation-0.000467836257310015
Midmean - True Basic - Statistics Graphics Toolkit-0.000467836257310015
Midmean - MS Excel (old versions)-0.000467836257310015
Number of observations72
 
Charts produced by software:
http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/22/t1195741090mqylxym2dny7rss/16f8b1195741467.png (open in new window)
http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/22/t1195741090mqylxym2dny7rss/16f8b1195741467.ps (open in new window)


http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/22/t1195741090mqylxym2dny7rss/2vr081195741467.png (open in new window)
http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/22/t1195741090mqylxym2dny7rss/2vr081195741467.ps (open in new window)


 
Parameters:
 
R code (references can be found in the software module):
geomean <- function(x) {
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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