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central tendancy, vrouwen

R Software Module: rwasp_centraltendency.wasp (opens new window with default values)
Title produced by software: Central Tendency
Date of computation: Sun, 25 Nov 2007 14:12:37 -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/25/t1196024616ty88b11isw8dzma.htm/, Retrieved Sun, 25 Nov 2007 22:03:38 +0100
 
User-defined keywords:
 
Dataseries X:
» Textbox « » Textfile « » CSV «
8,7 8,5 8,2 8,3 8 8,1 8,7 9,3 8,9 8,8 8,4 8,4 7,3 7,2 7 7 6,9 6,9 7,1 7,5 7,4 8,9 8,3 8,3 9 8,9 8,8 7,8 7,8 7,8 9,2 9,3 9,2 8,6 8,5 8,5 9 9 8,8 8 7,9 8,1 9,3 9,4 9,4 9,3 9 9,1 9,7 9,7 9,6 8,3 8,2 8,4 10,6 10,9 10,9 9,6 9,3 9,3 9,6 9,5 9,5 9 8,9 9 10,1 10,2 10,2 9,5 9,3 9,3 9,4 9,3 9,1 9 8,9 9 9,8 10 9,8 9,4 9 8,9 9,3 9,1 8,8 8,9 8,7 8,6 9,1 9,3 8,9
 
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 time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135


Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean8.846236559139780.0871146646445433101.547042570104
Geometric Mean8.8055188260725
Harmonic Mean8.76338191212069
Quadratic Mean8.88561117883882
Winsorized Mean ( 1 / 31 )8.846236559139780.0871146646445433101.547042570104
Winsorized Mean ( 2 / 31 )8.841935483870970.0850476667028924103.964468710936
Winsorized Mean ( 3 / 31 )8.829032258064520.082427247663984107.113030075397
Winsorized Mean ( 4 / 31 )8.833333333333330.081410734252619108.503300141273
Winsorized Mean ( 5 / 31 )8.833333333333330.0792280033542793111.492565246581
Winsorized Mean ( 6 / 31 )8.833333333333330.0767096450463397115.152838055725
Winsorized Mean ( 7 / 31 )8.82580645161290.0727459029755943121.323759697833
Winsorized Mean ( 8 / 31 )8.834408602150540.0709498539514126124.516233792397
Winsorized Mean ( 9 / 31 )8.853763440860210.0639504969363283138.447140601196
Winsorized Mean ( 10 / 31 )8.853763440860210.0639504969363283138.447140601196
Winsorized Mean ( 11 / 31 )8.841935483870970.0623170080469544141.886392832095
Winsorized Mean ( 12 / 31 )8.854838709677420.060027968567665147.511883559678
Winsorized Mean ( 13 / 31 )8.868817204301080.0576738280411099153.775421287787
Winsorized Mean ( 14 / 31 )8.853763440860210.0556856018622118158.995559799603
Winsorized Mean ( 15 / 31 )8.869892473118280.053068202305379167.141378222628
Winsorized Mean ( 16 / 31 )8.869892473118280.053068202305379167.141378222628
Winsorized Mean ( 17 / 31 )8.869892473118280.0479545363389657184.964617537361
Winsorized Mean ( 18 / 31 )8.869892473118280.0479545363389657184.964617537361
Winsorized Mean ( 19 / 31 )8.890322580645160.0449420310256366197.817552472735
Winsorized Mean ( 20 / 31 )8.890322580645160.0449420310256366197.817552472735
Winsorized Mean ( 21 / 31 )8.867741935483870.0422917937259207209.679967535849
Winsorized Mean ( 22 / 31 )8.867741935483870.0422917937259207209.679967535849
Winsorized Mean ( 23 / 31 )8.892473118279570.0387761752864464229.328268004498
Winsorized Mean ( 24 / 31 )8.892473118279570.0387761752864464229.328268004498
Winsorized Mean ( 25 / 31 )8.892473118279570.0387761752864464229.328268004498
Winsorized Mean ( 26 / 31 )8.920430107526880.0350168309155775254.746928099612
Winsorized Mean ( 27 / 31 )8.920430107526880.0350168309155775254.746928099612
Winsorized Mean ( 28 / 31 )8.920430107526880.0350168309155775254.746928099612
Winsorized Mean ( 29 / 31 )8.95161290322580.0310563929011770288.237366512920
Winsorized Mean ( 30 / 31 )8.95161290322580.0310563929011770288.237366512920
Winsorized Mean ( 31 / 31 )8.984946236559140.0270898905598560331.671559052872
Trimmed Mean ( 1 / 31 )8.845054945054950.083370156498228106.093778836111
Trimmed Mean ( 2 / 31 )8.84382022471910.0790319858732003111.901784157470
Trimmed Mean ( 3 / 31 )8.84482758620690.0753102576831022117.445190845383
Trimmed Mean ( 4 / 31 )8.850588235294120.0721736066311682122.629152794368
Trimmed Mean ( 5 / 31 )8.855421686746990.0688952539397472128.534567772862
Trimmed Mean ( 6 / 31 )8.86049382716050.0657501587179627134.760037084745
Trimmed Mean ( 7 / 31 )8.865822784810130.0627686973492701141.245926062113
Trimmed Mean ( 8 / 31 )8.872727272727270.0602636144369441147.231913578816
Trimmed Mean ( 9 / 31 )8.878666666666670.0577441805759714153.758639885545
Trimmed Mean ( 10 / 31 )8.882191780821920.0563117567549924157.732457530451
Trimmed Mean ( 11 / 31 )8.885915492957750.0546175941260714162.693279247101
Trimmed Mean ( 12 / 31 )8.891304347826090.0529093520369517168.047878220403
Trimmed Mean ( 13 / 31 )8.891304347826090.0513249522880171173.235511217454
Trimmed Mean ( 14 / 31 )8.898461538461540.0498792921660106178.399916118401
Trimmed Mean ( 15 / 31 )8.90317460317460.04847749853964183.655817056948
Trimmed Mean ( 16 / 31 )8.906557377049180.0472679174955509188.427116085398
Trimmed Mean ( 17 / 31 )8.910169491525420.0457865167429707194.602475255848
Trimmed Mean ( 18 / 31 )8.91403508771930.0448779042938135198.628595251675
Trimmed Mean ( 19 / 31 )8.918181818181820.0437386567567898203.897021067008
Trimmed Mean ( 20 / 31 )8.920754716981130.0428788493611966208.04557141531
Trimmed Mean ( 21 / 31 )8.92352941176470.041782652868603213.570197177934
Trimmed Mean ( 22 / 31 )8.928571428571430.0408248290463863218.704441319927
Trimmed Mean ( 23 / 31 )8.934042553191490.0395717823086721225.768010232726
Trimmed Mean ( 24 / 31 )8.937777777777780.0387022940474364230.936640779561
Trimmed Mean ( 25 / 31 )8.941860465116280.0375366278321488238.216935871312
Trimmed Mean ( 26 / 31 )8.941860465116280.0359704419603723248.589118670471
Trimmed Mean ( 27 / 31 )8.948717948717950.0348259204488832256.955676501148
Trimmed Mean ( 28 / 31 )8.951351351351350.0332480037608035269.229738294971
Trimmed Mean ( 29 / 31 )8.954285714285710.0310442506464447288.436200836795
Trimmed Mean ( 30 / 31 )8.954545454545460.0292231841242211306.419225792841
Trimmed Mean ( 31 / 31 )8.954838709677420.0265745895597106336.969972369911
Median9
Midrange8.9
Midmean - Weighted Average at Xnp8.94897959183674
Midmean - Weighted Average at X(n+1)p8.94897959183674
Midmean - Empirical Distribution Function8.94897959183674
Midmean - Empirical Distribution Function - Averaging8.94897959183674
Midmean - Empirical Distribution Function - Interpolation8.94897959183674
Midmean - Closest Observation8.9
Midmean - True Basic - Statistics Graphics Toolkit8.94897959183674
Midmean - MS Excel (old versions)8.94897959183674
Number of observations93
 
Charts produced by software:
http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/25/t1196024616ty88b11isw8dzma/1xhgi1196025154.png (open in new window)
http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/25/t1196024616ty88b11isw8dzma/1xhgi1196025154.ps (open in new window)


http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/25/t1196024616ty88b11isw8dzma/28goc1196025154.png (open in new window)
http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/25/t1196024616ty88b11isw8dzma/28goc1196025154.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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