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s 0650692 paper

R Software Module: rwasp_centraltendency.wasp (opens new window with default values)
Title produced by software: Central Tendency
Date of computation: Wed, 09 Jan 2008 09:40:34 -0700
 
Cite this page as follows:
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2008/Jan/09/t1199896757fe7fk927yw503xn.htm/, Retrieved Wed, 09 Jan 2008 17:39:20 +0100
 
User-defined keywords:
residuals mul.regre.
 
Dataseries X:
» Textbox « » Textfile « » CSV «
0.0640061800725882 0.055543390675083 0.032601938563982 0.0408184280409284 0.0462166153670518 -0.0137516738094333 -0.00063153303605741 -0.00233761316721433 0.0483117836462727 0.0729374241986308 0.0573703673438476 0.0732313798761501 0.0182045786194426 0.0203594752119119 0.0227844996034191 -0.0378014755630382 -0.0646039043977659 -0.0373526591017259 -0.0233447045393399 -0.0482940754041509 0.00826205351002031 -0.0234440266211367 -0.0252275371441901 -0.0430726405517209 -0.125589104079991 -0.112546393698512 -0.099426252925136 0.000565864129830549 0.0438787023103477 0.0542958079481452 0.0126671582088848 0.0115787640677000 0.0285598815647022 0.0626452665189847 0.0379660234532115 0.00888554806573639 0.0313105724572436 0.00713374836619783 0.0321843775013869 -0.00380766793622727 -0.0143558064793364 -0.0633588514749149 -0.0538295596261275 -0.0658057675563223 -0.0597898942402267 -0.0415734047632801 -0.0616191243316618 -0.0630550766637809 -0.0515952964531803 -0.0327611209862616 0.00676817086252592 -0.0325050019320905 -0.0721257329176413 -0.0613610690889093 -0.0588586143055058 0.00260116590509487 0.0317828995629480 -0.0113512499552947 -0.00444756285018907 0.00956039171219682 -0.0324932466098945 -0.0454346987209958 -0.0467157902693218 0.0301878968357837 0.0413001188554499 0.0635324458398158 0.0644519704523407 0.0643288204920626 0.0764837170845318 0.150066683064087 0.0873953587520234 0.0134886624600154
 
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 Mean9.28670453284529e-180.006162310387835831.50701667854591e-15
Geometric MeanNaN
Harmonic Mean0.194012254920243
Quadratic Mean0.0519245502767052
Winsorized Mean ( 1 / 24 )-0.0006892863045914440.00586929293702535-0.117439410843376
Winsorized Mean ( 2 / 24 )-0.0006279391072057650.005715073174175-0.109874202493726
Winsorized Mean ( 3 / 24 )0.0003740685094239430.005443471524102850.068718740929869
Winsorized Mean ( 4 / 24 )0.0007088468251905930.005376853786036260.131833011161932
Winsorized Mean ( 5 / 24 )0.0002030419232646420.005255804693565770.0386319384190987
Winsorized Mean ( 6 / 24 )0.0002965338368123820.005236145061362730.0566320897028791
Winsorized Mean ( 7 / 24 )0.0002946996804459540.005225700709817740.056394289839885
Winsorized Mean ( 8 / 24 )0.0004016128025955880.005189622346936820.0773876740438812
Winsorized Mean ( 9 / 24 )0.0003229722928357630.005165271390972380.0625276521578787
Winsorized Mean ( 10 / 24 )-0.0001914338636162500.00500701738752295-0.0382331134086504
Winsorized Mean ( 11 / 24 )-0.0003282764202062580.00493837644523508-0.0664745638261344
Winsorized Mean ( 12 / 24 )0.0003019689052004910.004768207599551910.063329647230307
Winsorized Mean ( 13 / 24 )-0.0003750712986332450.00453593014391821-0.0826889495060107
Winsorized Mean ( 14 / 24 )-0.0001405610378371470.00437388578799629-0.0321364216283159
Winsorized Mean ( 15 / 24 )-0.000298816854894440.00425109810481671-0.0702916864129449
Winsorized Mean ( 16 / 24 )-0.0005871483896881720.00412447478293364-0.142357129231991
Winsorized Mean ( 17 / 24 )-0.0001431727642602850.00402356644833597-0.0355835466118614
Winsorized Mean ( 18 / 24 )-0.0004814649640793110.00386626159018038-0.124529846946246
Winsorized Mean ( 19 / 24 )-0.0009016171597843720.00352421694338952-0.255834749752158
Winsorized Mean ( 20 / 24 )-0.0008929351045851530.00349034678633231-0.255829910105711
Winsorized Mean ( 21 / 24 )0.0003291657803805900.003280890577100950.100328180000275
Winsorized Mean ( 22 / 24 )0.0002631022090787490.003250323833426330.080946460279744
Winsorized Mean ( 23 / 24 )-9.17751087416615e-050.00320177839636933-0.0286637916121022
Winsorized Mean ( 24 / 24 )0.001787456289465970.002790796852540450.640482408398467
Trimmed Mean ( 1 / 24 )-0.0003496796997727900.00567990629573073-0.0615643430659455
Trimmed Mean ( 2 / 24 )9.90376415284239e-060.005454057534178120.00181585252645026
Trimmed Mean ( 3 / 24 )0.0003578180576211740.005284061036926290.0677164883449784
Trimmed Mean ( 4 / 24 )0.0003517241381951360.005204592893046180.067579567782347
Trimmed Mean ( 5 / 24 )0.0002480433580996800.005131063666667850.0483415085474395
Trimmed Mean ( 6 / 24 )0.0002588437024600890.005076918732110590.050984409268352
Trimmed Mean ( 7 / 24 )0.0002510457436285810.005013342479243920.0500755224020606
Trimmed Mean ( 8 / 24 )0.00024302767360090.004935272759733590.0492430075159653
Trimmed Mean ( 9 / 24 )0.0002165968187684520.004845148970857710.0447038512275318
Trimmed Mean ( 10 / 24 )0.0002002313612196350.004736560304226190.04227358005787
Trimmed Mean ( 11 / 24 )0.0002566311535960020.004634838378993870.0553700329140089
Trimmed Mean ( 12 / 24 )0.0003363912772963100.004519397087308160.0744327773810802
Trimmed Mean ( 13 / 24 )0.0003408811519175040.004408660638893610.077320796459183
Trimmed Mean ( 14 / 24 )0.0004310010407980180.004315404953902170.0998749932861547
Trimmed Mean ( 15 / 24 )0.0005009882341002830.004226700484056970.118529390949276
Trimmed Mean ( 16 / 24 )0.000596964844779650.004133362238197520.144425968588704
Trimmed Mean ( 17 / 24 )0.0007371887804403130.004033615692509820.182761283334262
Trimmed Mean ( 18 / 24 )0.0008407607268756780.003918768944009750.214547154702976
Trimmed Mean ( 19 / 24 )0.0009963166905174410.003796451546962470.262433664223791
Trimmed Mean ( 20 / 24 )0.001221072014895290.003711582142238810.328989624397412
Trimmed Mean ( 21 / 24 )0.001474752869232940.003590704093925250.410714119196824
Trimmed Mean ( 22 / 24 )0.001615028839296490.003474361089302880.464841965985908
Trimmed Mean ( 23 / 24 )0.001785201422121100.00330013079158230.54094868805644
Trimmed Mean ( 24 / 24 )0.002030024447885810.003038371000315370.668129220452377
Median0.00468466838381040
Midrange0.012238789492048
Midmean - Weighted Average at Xnp-0.000346087956329635
Midmean - Weighted Average at X(n+1)p0.00084076072687568
Midmean - Empirical Distribution Function-0.000346087956329635
Midmean - Empirical Distribution Function - Averaging0.00084076072687568
Midmean - Empirical Distribution Function - Interpolation0.00084076072687568
Midmean - Closest Observation-0.000346087956329635
Midmean - True Basic - Statistics Graphics Toolkit0.00084076072687568
Midmean - MS Excel (old versions)0.000737188780440314
Number of observations72
 
Charts produced by software:
http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Jan/09/t1199896757fe7fk927yw503xn/1x32a1199896831.png (open in new window)
http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Jan/09/t1199896757fe7fk927yw503xn/1x32a1199896831.ps (open in new window)


http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Jan/09/t1199896757fe7fk927yw503xn/2bk7l1199896831.png (open in new window)
http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Jan/09/t1199896757fe7fk927yw503xn/2bk7l1199896831.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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