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Central_Tendency_Eigen_Reeks

*Unverified author*
R Software Module: /rwasp_centraltendency.wasp (opens new window with default values)
Title produced by software: Central Tendency
Date of computation: Tue, 24 May 2011 14:18:37 +0000
 
Cite this page as follows:
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2011/May/24/t13062469296ga0r6fnp6im9bf.htm/, Retrieved Tue, 24 May 2011 16:22:10 +0200
 
Original text written by user:
 
IsPrivate?
No (this computation is public)
 
User-defined keywords:
KDGP1W52
 
Dataseries X:
» Textbox « » Textfile « » CSV «
476 475 470 461 455 456 517 525 523 519 509 512 519 517 510 509 501 507 569 580 578 565 547 555 562 561 555 544 537 543 594 611 613 611 594 595 591 589 584 573 567 569 621 629 628 612 595 597 593 590 580 574 573 573 620 626 620 588 566 577 561 549 532 526 511 499 555 565 542 527 510 514 517 508 493 490 469 478 528 534 518 506 502 516 528 533 536 537 524 536 587 597 581 564 558 575 580 575 563 552 537 545 601 604 586 564 549 551 556
 
Output produced by software:


Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'RServer@AstonUniversity' @ vre.aston.ac.uk


Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean550.2660550458724.00022600028034137.558741682922
Geometric Mean548.670601930839
Harmonic Mean547.05000426805
Quadratic Mean551.834147734176
Winsorized Mean ( 1 / 36 )550.2660550458723.996550547187137.685248453365
Winsorized Mean ( 2 / 36 )550.3211009174313.97043270142588138.604817736817
Winsorized Mean ( 3 / 36 )550.4036697247713.90254887795497141.036970179652
Winsorized Mean ( 4 / 36 )550.4036697247713.88937930356269141.514526294876
Winsorized Mean ( 5 / 36 )550.6330275229363.8465437520324143.150075241442
Winsorized Mean ( 6 / 36 )550.3027522935783.77469228317756145.787447296321
Winsorized Mean ( 7 / 36 )550.3669724770643.74164968019907147.092063532731
Winsorized Mean ( 8 / 36 )551.1743119266053.58167277828479153.887400118822
Winsorized Mean ( 9 / 36 )551.4220183486243.54317320786054155.629427634329
Winsorized Mean ( 10 / 36 )551.3302752293583.36483723787986163.850503383261
Winsorized Mean ( 11 / 36 )551.2293577981653.29291584646804167.398556021227
Winsorized Mean ( 12 / 36 )550.8990825688073.21734872462654171.227656595651
Winsorized Mean ( 13 / 36 )551.3761467889913.15196676598186174.930825013706
Winsorized Mean ( 14 / 36 )551.2477064220183.10092321162707177.76889938941
Winsorized Mean ( 15 / 36 )551.3853211009173.08286585587191178.854788654102
Winsorized Mean ( 16 / 36 )551.3853211009173.04471457214592181.095898494124
Winsorized Mean ( 17 / 36 )551.3853211009173.04471457214592181.095898494124
Winsorized Mean ( 18 / 36 )551.3853211009173.0022335172156183.658372321516
Winsorized Mean ( 19 / 36 )551.0366972477062.95805214254236186.283632165492
Winsorized Mean ( 20 / 36 )551.0366972477062.91174192082805189.246407212835
Winsorized Mean ( 21 / 36 )551.0366972477062.86355610242469192.430906725075
Winsorized Mean ( 22 / 36 )551.2385321100922.7884067516173197.689426691557
Winsorized Mean ( 23 / 36 )551.4495412844042.71106911110743203.406670462615
Winsorized Mean ( 24 / 36 )551.4495412844042.65790757692667207.475062741663
Winsorized Mean ( 25 / 36 )550.9908256880732.6033674647361211.645429679642
Winsorized Mean ( 26 / 36 )550.2752293577982.52095773939684218.280227692137
Winsorized Mean ( 27 / 36 )550.2752293577982.46297322318712223.419087214328
Winsorized Mean ( 28 / 36 )550.5321100917432.43196828228034226.373063375455
Winsorized Mean ( 29 / 36 )550.5321100917432.43196828228034226.373063375455
Winsorized Mean ( 30 / 36 )551.082568807342.24039947624932245.97513731342
Winsorized Mean ( 31 / 36 )551.082568807342.17600233075552253.254585722802
Winsorized Mean ( 32 / 36 )550.7889908256882.07815660176275265.037288507754
Winsorized Mean ( 33 / 36 )551.0917431192662.04355152481927269.673524952107
Winsorized Mean ( 34 / 36 )551.0917431192661.97454671780875279.097849723626
Winsorized Mean ( 35 / 36 )551.0917431192661.9040231956739289.435414637487
Winsorized Mean ( 36 / 36 )551.0917431192661.9040231956739289.435414637487
Trimmed Mean ( 1 / 36 )550.4205607476643.90659858434902140.895090412619
Trimmed Mean ( 2 / 36 )550.5809523809523.80571627488242144.67209655506
Trimmed Mean ( 3 / 36 )550.7184466019423.70793668955678148.524231320619
Trimmed Mean ( 4 / 36 )550.8316831683173.6264449303768151.893022986312
Trimmed Mean ( 5 / 36 )550.9494949494953.53891036438854155.68337093067
Trimmed Mean ( 6 / 36 )551.0206185567013.45208299652757159.619748166822
Trimmed Mean ( 7 / 36 )551.1578947368423.37135405621162163.482649863295
Trimmed Mean ( 8 / 36 )551.2903225806453.28701742530651167.717493170648
Trimmed Mean ( 9 / 36 )551.3076923076923.22386901949659171.008092752409
Trimmed Mean ( 10 / 36 )551.292134831463.15901365533035174.514008162402
Trimmed Mean ( 11 / 36 )551.2873563218393.11599284331971176.921894253939
Trimmed Mean ( 12 / 36 )551.2941176470593.07801563679255179.106990574465
Trimmed Mean ( 13 / 36 )551.337349397593.04551027840049181.032831610457
Trimmed Mean ( 14 / 36 )551.3333333333333.01708100285322182.737332147179
Trimmed Mean ( 15 / 36 )551.3417721518992.99067500627661184.353622842597
Trimmed Mean ( 16 / 36 )551.3376623376622.96162574680164186.16047720853
Trimmed Mean ( 17 / 36 )551.3333333333332.93216602490336188.029371001086
Trimmed Mean ( 18 / 36 )551.3287671232882.8967555720471190.326298995835
Trimmed Mean ( 19 / 36 )551.3239436619722.86024401654123192.754163796369
Trimmed Mean ( 20 / 36 )551.3478260869572.8224548763385195.343362513631
Trimmed Mean ( 21 / 36 )551.3731343283582.78327984312808198.10193922458
Trimmed Mean ( 22 / 36 )551.42.74254233541407201.054325718093
Trimmed Mean ( 23 / 36 )551.4126984126982.70362587894669203.953033112527
Trimmed Mean ( 24 / 36 )551.4098360655742.66687605556144206.762453363994
Trimmed Mean ( 25 / 36 )551.4067796610172.62892228954784209.746321469189
Trimmed Mean ( 26 / 36 )551.4385964912282.58950280495203212.951534725773
Trimmed Mean ( 27 / 36 )551.5272727272732.55206452973714216.110237927283
Trimmed Mean ( 28 / 36 )551.6226415094342.51327771795848219.483361336412
Trimmed Mean ( 29 / 36 )551.7058823529412.46851453587797223.497117126239
Trimmed Mean ( 30 / 36 )551.7959183673472.41064454781612228.899743376615
Trimmed Mean ( 31 / 36 )551.8510638297872.37080194697687232.769786836678
Trimmed Mean ( 32 / 36 )551.9111111111112.32939542644647236.933199423793
Trimmed Mean ( 33 / 36 )5522.29183151526288240.855401596432
Trimmed Mean ( 34 / 36 )552.0731707317072.24705504939309245.687425806866
Trimmed Mean ( 35 / 36 )552.1538461538462.1997234710083251.01057175189
Trimmed Mean ( 36 / 36 )552.2432432432432.14923878046241256.948296421688
Median555
Midrange542
Midmean - Weighted Average at Xnp551.527272727273
Midmean - Weighted Average at X(n+1)p551.527272727273
Midmean - Empirical Distribution Function551.527272727273
Midmean - Empirical Distribution Function - Averaging551.527272727273
Midmean - Empirical Distribution Function - Interpolation551.527272727273
Midmean - Closest Observation549.741379310345
Midmean - True Basic - Statistics Graphics Toolkit551.527272727273
Midmean - MS Excel (old versions)551.527272727273
Number of observations109
 
Charts produced by software:
http://www.freestatistics.org/blog/date/2011/May/24/t13062469296ga0r6fnp6im9bf/13udk1306246713.png (open in new window)
http://www.freestatistics.org/blog/date/2011/May/24/t13062469296ga0r6fnp6im9bf/13udk1306246713.ps (open in new window)


http://www.freestatistics.org/blog/date/2011/May/24/t13062469296ga0r6fnp6im9bf/2hgnr1306246713.png (open in new window)
http://www.freestatistics.org/blog/date/2011/May/24/t13062469296ga0r6fnp6im9bf/2hgnr1306246713.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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