Home » date » 2009 » Oct » 24 »

Berekening centrummaten (opdracht 5 eigen reeks Steffi Poppe MAR 202b)

*Unverified author*
R Software Module: rwasp_centraltendency.wasp (opens new window with default values)
Title produced by software: Central Tendency
Date of computation: Sat, 24 Oct 2009 06:54:03 -0600
 
Cite this page as follows:
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2009/Oct/24/t1256389634xgs7cz1n2smfgk1.htm/, Retrieved Sat, 24 Oct 2009 15:07:17 +0200
 
BibTeX entries for LaTeX users:
@Manual{KEY,
    author = {{YOUR NAME}},
    publisher = {Office for Research Development and Education},
    title = {Statistical Computations at FreeStatistics.org, URL http://www.freestatistics.org/blog/date/2009/Oct/24/t1256389634xgs7cz1n2smfgk1.htm/},
    year = {2009},
}
@Manual{R,
    title = {R: A Language and Environment for Statistical Computing},
    author = {{R Development Core Team}},
    organization = {R Foundation for Statistical Computing},
    address = {Vienna, Austria},
    year = {2009},
    note = {{ISBN} 3-900051-07-0},
    url = {http://www.R-project.org},
}
 
Original text written by user:
 
IsPrivate?
No (this computation is public)
 
User-defined keywords:
KDGP1W52
 
Dataseries X:
» Textbox « » Textfile « » CSV «
1,2 1,21 1,21 1,21 1,21 1,21 1,21 1,2 1,21 1,22 1,22 1,23 1,22 1,23 1,23 1,23 1,23 1,23 1,22 1,22 1,23 1,24 1,24 1,25 1,25 1,25 1,26 1,26 1,26 1,26 1,27 1,27 1,29 1,31 1,32 1,32 1,33 1,33 1,32 1,32 1,31 1,3 1,31 1,29 1,3 1,3 1,32 1,31 1,35 1,35 1,36 1,37 1,37 1,37 1,32 1,32 1,31 1,31 1,34 1,31 1,27 1,28 1,27 1,26 1,27 1,27 1,28 1,27 1,26 1,3 1,31 1,28 1,29 1,31 1,29 1,29 1,32 1,3 1,29 1,31 1,29 1,33 1,35 1,32 1,33
 
Output produced by software:


Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'George Udny Yule' @ 72.249.76.132


Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean1.279882352941180.00497470947773564257.277808617629
Geometric Mean1.27906887070120
Harmonic Mean1.27825426791863
Quadratic Mean1.28069420513205
Winsorized Mean ( 1 / 28 )1.279882352941180.00497470947773564257.277808617629
Winsorized Mean ( 2 / 28 )1.280117647058820.00493229827977242259.537759974624
Winsorized Mean ( 3 / 28 )1.279764705882350.00485929895056756263.36406113332
Winsorized Mean ( 4 / 28 )1.279294117647060.00477149635431266268.111724845139
Winsorized Mean ( 5 / 28 )1.279294117647060.00477149635431266268.111724845139
Winsorized Mean ( 6 / 28 )1.279294117647060.00477149635431266268.111724845139
Winsorized Mean ( 7 / 28 )1.278470588235290.00463365439012074275.909785365322
Winsorized Mean ( 8 / 28 )1.277529411764710.00449371139290403284.292714877515
Winsorized Mean ( 9 / 28 )1.278588235294120.00431320343161300296.435875461586
Winsorized Mean ( 10 / 28 )1.278588235294120.00431320343161300296.435875461586
Winsorized Mean ( 11 / 28 )1.278588235294120.00431320343161300296.435875461586
Winsorized Mean ( 12 / 28 )1.277176470588240.00412552268042722309.579311403998
Winsorized Mean ( 13 / 28 )1.277176470588240.00412552268042722309.579311403998
Winsorized Mean ( 14 / 28 )1.278823529411760.00386542442872324330.836510451237
Winsorized Mean ( 15 / 28 )1.278823529411760.00386542442872324330.836510451237
Winsorized Mean ( 16 / 28 )1.278823529411760.00386542442872324330.836510451237
Winsorized Mean ( 17 / 28 )1.278823529411760.00386542442872324330.836510451237
Winsorized Mean ( 18 / 28 )1.278823529411760.00386542442872324330.836510451237
Winsorized Mean ( 19 / 28 )1.278823529411760.00386542442872324330.836510451237
Winsorized Mean ( 20 / 28 )1.278823529411760.00386542442872324330.836510451237
Winsorized Mean ( 21 / 28 )1.278823529411760.00319931612399107399.71777712809
Winsorized Mean ( 22 / 28 )1.278823529411760.00319931612399107399.71777712809
Winsorized Mean ( 23 / 28 )1.281529411764710.00282300415282392453.959449716983
Winsorized Mean ( 24 / 28 )1.281529411764710.00282300415282392453.959449716983
Winsorized Mean ( 25 / 28 )1.281529411764710.00282300415282392453.959449716983
Winsorized Mean ( 26 / 28 )1.284588235294120.00243430743621647527.701725830774
Winsorized Mean ( 27 / 28 )1.284588235294120.00243430743621647527.701725830774
Winsorized Mean ( 28 / 28 )1.284588235294120.00243430743621647527.701725830774
Trimmed Mean ( 1 / 28 )1.279759036144580.0048817215124883262.153224609542
Trimmed Mean ( 2 / 28 )1.279629629629630.0047740439041658268.038932049417
Trimmed Mean ( 3 / 28 )1.279367088607590.00467489574038220273.667512530022
Trimmed Mean ( 4 / 28 )1.279220779220780.00459116746071169278.626469229786
Trimmed Mean ( 5 / 28 )1.27920.00452325323410262282.805302686924
Trimmed Mean ( 6 / 28 )1.279178082191780.0044429129885816287.914277294941
Trimmed Mean ( 7 / 28 )1.279154929577460.00434779010853755294.208068385281
Trimmed Mean ( 8 / 28 )1.279275362318840.00426787820098420299.745049430847
Trimmed Mean ( 9 / 28 )1.279552238805970.00420222010533712304.494340308554
Trimmed Mean ( 10 / 28 )1.279692307692310.00416007367936573307.612894944548
Trimmed Mean ( 11 / 28 )1.279841269841270.00410744122288941311.590890871216
Trimmed Mean ( 12 / 28 )1.280.00404212788197104316.664894673209
Trimmed Mean ( 13 / 28 )1.280338983050850.00399419583055731320.549877213257
Trimmed Mean ( 14 / 28 )1.280701754385960.00393286111648751325.641235846583
Trimmed Mean ( 15 / 28 )1.280909090909090.00390348827227214328.144726348441
Trimmed Mean ( 16 / 28 )1.281132075471700.00386323124940673331.621896998385
Trimmed Mean ( 17 / 28 )1.281372549019610.00380937551202538336.373388492311
Trimmed Mean ( 18 / 28 )1.281632653061220.00373832580547088342.835996580504
Trimmed Mean ( 19 / 28 )1.281914893617020.00364520769211103351.671290607486
Trimmed Mean ( 20 / 28 )1.282222222222220.00352321147246170363.935640038751
Trimmed Mean ( 21 / 28 )1.282558139534880.00336243700934901381.437075540397
Trimmed Mean ( 22 / 28 )1.282926829268290.00329900026318071388.883518315141
Trimmed Mean ( 23 / 28 )1.283333333333330.00320957855674555399.844811598757
Trimmed Mean ( 24 / 28 )1.283513513513510.00317687345630729404.017827957628
Trimmed Mean ( 25 / 28 )1.283714285714290.00312446874235746410.858418364494
Trimmed Mean ( 26 / 28 )1.283939393939390.00304447443900154421.72776275976
Trimmed Mean ( 27 / 28 )1.283870967741940.00302951145338681423.78812144996
Trimmed Mean ( 28 / 28 )1.283793103448280.00299481461154102428.671978058663
Median1.29
Midrange1.285
Midmean - Weighted Average at Xnp1.28255813953488
Midmean - Weighted Average at X(n+1)p1.28255813953488
Midmean - Empirical Distribution Function1.28255813953488
Midmean - Empirical Distribution Function - Averaging1.28255813953488
Midmean - Empirical Distribution Function - Interpolation1.28255813953488
Midmean - Closest Observation1.2752
Midmean - True Basic - Statistics Graphics Toolkit1.28255813953488
Midmean - MS Excel (old versions)1.28255813953488
Number of observations85
 
Charts produced by software:
http://www.freestatistics.org/blog/date/2009/Oct/24/t1256389634xgs7cz1n2smfgk1/1sv7u1256388842.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Oct/24/t1256389634xgs7cz1n2smfgk1/1sv7u1256388842.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Oct/24/t1256389634xgs7cz1n2smfgk1/21us21256388842.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Oct/24/t1256389634xgs7cz1n2smfgk1/21us21256388842.ps (open in new window)


 
Parameters (Session):
 
Parameters (R input):
 
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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