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Q7 Central tendency

R Software Module: rwasp_centraltendency.wasp (opens new window with default values)
Title produced by software: Central Tendency
Date of computation: Mon, 22 Oct 2007 02:27:10 -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/Oct/22/39wu00pebpx3d7m1193045139.htm/, Retrieved Mon, 22 Oct 2007 11:25:39 +0200
 
User-defined keywords:
Q7, central tendancy, associations, own data, indexcijfer der consumptieprijzen
 
Dataseries X:
» Textbox « » Textfile « » CSV «
1,79 1,95 2,26 2,04 2,16 2,75 2,79 2,88 3,36 2,97 3,1 2,49 2,2 2,25 2,09 2,79 3,14 2,93 2,65 2,67 2,26 2,35 2,13 2,18 2,9 2,63 2,67 1,81 1,33 0,88 1,28 1,26 1,26 1,29 1,1 1,37 1,21 1,74 1,76 1,48 1,04 1,62 1,49 1,79 1,8 1,58 1,86 1,74 1,59 1,26 1,13 1,92 2,61 2,26 2,41 2,26 2,03 2,86 2,55 2,27 2,26 2,57 3,07 2,76 2,51 2,87 3,14 3,11 3,16 2,47 2,57 2,89 2,63 2,38 1,69 1,96 2,19 1,87 1,6 1,63 1,22 1,21 1,49 1,64 1,66 1,77 1,82 1,78 1,28 1,29 1,37 1,12 1,51
 
Text written by user:
 
Output produced by software:


Summary of compuational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Herman Ole Andreas Wold' @ 193.190.124.10:1001


Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean2.072150537634410.065040327954718631.8594724657146
Geometric Mean1.97378769351537
Harmonic Mean1.87330851159682
Quadratic Mean2.1640217934625
Winsorized Mean ( 1 / 31 )2.071720430107530.064289300489698532.2249645637301
Winsorized Mean ( 2 / 31 )2.072580645161290.06399160315303532.3883219522528
Winsorized Mean ( 3 / 31 )2.073225806451610.06388599470945832.4519609639057
Winsorized Mean ( 4 / 31 )2.072365591397850.06358493082477332.5920869067053
Winsorized Mean ( 5 / 31 )2.076129032258060.062820758447083933.0484553765275
Winsorized Mean ( 6 / 31 )2.074193548387100.062481661186201733.1968374241169
Winsorized Mean ( 7 / 31 )2.067419354838710.061111701777195433.8301715500613
Winsorized Mean ( 8 / 31 )2.067419354838710.06005605594505634.4248273101741
Winsorized Mean ( 9 / 31 )2.064516129032260.059608257561705334.6347337345855
Winsorized Mean ( 10 / 31 )2.063440860215050.05944509148709234.7117114061993
Winsorized Mean ( 11 / 31 )2.064623655913980.05892177505782635.0400790520610
Winsorized Mean ( 12 / 31 )2.063333333333330.05872840900809535.133479148889
Winsorized Mean ( 13 / 31 )2.063333333333330.058318204142386135.3806047987285
Winsorized Mean ( 14 / 31 )2.052795698924730.056791937049821836.1459003788492
Winsorized Mean ( 15 / 31 )2.059247311827960.055863161087547836.8623484911772
Winsorized Mean ( 16 / 31 )2.060967741935480.054168685440741138.0472172283029
Winsorized Mean ( 17 / 31 )2.059139784946240.053913176246853438.1936277602716
Winsorized Mean ( 18 / 31 )2.064946236559140.048925247494051942.2061479977222
Winsorized Mean ( 19 / 31 )2.066989247311830.04866083806274442.477469143598
Winsorized Mean ( 20 / 31 )2.062688172043010.048085638255863242.8961379501187
Winsorized Mean ( 21 / 31 )2.062688172043010.046907431691025343.9735900620127
Winsorized Mean ( 22 / 31 )2.079247311827960.044843824508178746.3664135392542
Winsorized Mean ( 23 / 31 )2.076774193548390.043888315396985647.3195239954693
Winsorized Mean ( 24 / 31 )2.069032258064520.042229549386942848.9948931045012
Winsorized Mean ( 25 / 31 )2.074408602150540.041585698524568949.8827403590438
Winsorized Mean ( 26 / 31 )2.071612903225810.040533287713557751.1089284902218
Winsorized Mean ( 27 / 31 )2.062903225806450.03871491705227753.2844542330002
Winsorized Mean ( 28 / 31 )2.062903225806450.037250206109404455.3796459473989
Winsorized Mean ( 29 / 31 )2.066021505376340.035384133847239558.388358869989
Winsorized Mean ( 30 / 31 )2.062795698924730.031168743105609766.1815489939814
Winsorized Mean ( 31 / 31 )2.052795698924730.029969739137020368.4956145110054
Trimmed Mean ( 1 / 31 )2.07109890109890.063586432874096932.5713962473684
Trimmed Mean ( 2 / 31 )2.070449438202250.062776642117230232.9812071556146
Trimmed Mean ( 3 / 31 )2.069310344827590.06201999166858833.3652148146878
Trimmed Mean ( 4 / 31 )2.067882352941180.061187614800514233.7957666708034
Trimmed Mean ( 5 / 31 )2.066626506024100.060322689201118334.2595221365858
Trimmed Mean ( 6 / 31 )2.064444444444440.059529793350021834.6791804282937
Trimmed Mean ( 7 / 31 )2.062531645569620.058686108602374235.1451424313075
Trimmed Mean ( 8 / 31 )2.061688311688310.058004054645733835.5438654121734
Trimmed Mean ( 9 / 31 )2.06080.057409783515035535.8963206934978
Trimmed Mean ( 10 / 31 )2.060273972602740.056782373343130736.2836889566537
Trimmed Mean ( 11 / 31 )2.059859154929580.056057060954055536.7457572671860
Trimmed Mean ( 12 / 31 )2.059275362318840.055277459814440437.2534369204297
Trimmed Mean ( 13 / 31 )2.059275362318840.054370923330831137.8745703799944
Trimmed Mean ( 14 / 31 )2.058307692307690.053347810689150538.5827959145528
Trimmed Mean ( 15 / 31 )2.058888888888890.052372347972094439.3125183156945
Trimmed Mean ( 16 / 31 )2.058852459016390.051342149388791440.1006284997072
Trimmed Mean ( 17 / 31 )2.058644067796610.050368865929302140.8713603098813
Trimmed Mean ( 18 / 31 )2.058596491228070.049208929159791141.8337998078236
Trimmed Mean ( 19 / 31 )2.0580.048620290619582542.3280069652877
Trimmed Mean ( 20 / 31 )2.057169811320750.04790106622016242.9462217368112
Trimmed Mean ( 21 / 31 )2.056666666666670.047073298427416443.6907277665681
Trimmed Mean ( 22 / 31 )2.056122448979590.046212699912560744.4925843517041
Trimmed Mean ( 23 / 31 )2.054042553191490.045453475796939345.1899996024023
Trimmed Mean ( 24 / 31 )2.0520.044620283470297445.9880538716426
Trimmed Mean ( 25 / 31 )2.050465116279070.043829622673940446.7826321831013
Trimmed Mean ( 26 / 31 )2.050465116279070.042869487754915247.8304086114015
Trimmed Mean ( 27 / 31 )2.046153846153850.041781539978129748.9726766228553
Trimmed Mean ( 28 / 31 )2.044594594594590.040704373662106850.2303416229196
Trimmed Mean ( 29 / 31 )2.042857142857140.039540578940541351.6648263023428
Trimmed Mean ( 30 / 31 )2.040606060606060.038353764467808953.2048441377582
Trimmed Mean ( 31 / 31 )2.038387096774190.037765822787201553.9743860013288
Median2.04
Midrange2.12
Midmean - Weighted Average at Xnp2.04195652173913
Midmean - Weighted Average at X(n+1)p2.05404255319149
Midmean - Empirical Distribution Function2.05404255319149
Midmean - Empirical Distribution Function - Averaging2.05404255319149
Midmean - Empirical Distribution Function - Interpolation2.05404255319149
Midmean - Closest Observation2.04416666666667
Midmean - True Basic - Statistics Graphics Toolkit2.05404255319149
Midmean - MS Excel (old versions)2.05404255319149
Number of observations93
 
Charts produced by software:
http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Oct/22/39wu00pebpx3d7m1193045139/1gofm1193045225.png (open in new window)
http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Oct/22/39wu00pebpx3d7m1193045139/1gofm1193045225.ps (open in new window)


http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Oct/22/39wu00pebpx3d7m1193045139/2sl8r1193045225.png (open in new window)
http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Oct/22/39wu00pebpx3d7m1193045139/2sl8r1193045225.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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