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R Software Module: rwasp_centraltendency.wasp (opens new window with default values)
Title produced by software: Central Tendency
Date of computation: Fri, 30 Nov 2007 08:06:40 -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/30/t1196434677ovhncmeo4pqur1m.htm/, Retrieved Fri, 30 Nov 2007 15:57:57 +0100
 
User-defined keywords:
 
Dataseries X:
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0.00463569519292025 0 0.00143923460172335 0.00144853054504027 -0.00162948785000958 0.00126792818850945 0.00234811866264784 0.000540524400251635 -0.000270568209359912 0.00206931662322303 0.00286676786841799 0.00187581043598554 0.00176070152375519 -0.000265784295388790 0.00243491709541981 -0.000161830926563079 0.00409488594184309 0.000567568947962611 -8.62318787957905e-05 0.00338400851898412 0.00205249103249761 3.09799421278379e-05 -0.000592916602392861 0.000405795936844418 0.000781413303939543 0.00252397900894133 0.00290919488973382 -0.00107510474861822 -0.00350707915903945 9.89132513938052e-05 -1.89306660423649e-05 0.000639485643732569 0.00263583378053166 -0.00121439777818397 0.00105472150930439 -0.00127092158767014 -0.00148950401692806 0.00385464616352799 -0.000223456361577770 0.000768236994111173 -0.00386435457822765 0.00119889404368548 0.00179114278704465 -0.000972899385449658 -0.0018621951901171 0.000901096765850996 -0.00108950772866412 0.00158624372277465 0.00037245345943365 0.00312515160034284 7.61954697028127e-06 -0.000918699155153142 -0.0063070273548383 -0.000158493786046726 0.00156746782611579 0.00187755099080337 -7.78210268363866e-05 -0.000402478951780790 -0.000686610555711077 0.000627079511179277 0.00103812971298083 6.29695604751267e-05 0.00144113835067093 0.000157148599393572 0.00516738774839585 -0.000275128215104696 9.78943043732883e-06 -0.00215536805984324 -0.000474302520938954 0.00272873858269233 0.000731914959171474 0.00061088221663088
 
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 time6 seconds
R Server'Herman Ole Andreas Wold' @ 193.190.124.10:1001


Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean0.0005894638726269140.0002240683016690562.63073298737962
Geometric MeanNaN
Harmonic Mean0
Quadratic Mean0.00197791216383464
Winsorized Mean ( 1 / 24 )0.0006160052645871230.0002094663776116452.94083122843327
Winsorized Mean ( 2 / 24 )0.0006109071025902070.0002026983874578763.01387253372780
Winsorized Mean ( 3 / 24 )0.000657218407626920.0001861368389834573.5308346870838
Winsorized Mean ( 4 / 24 )0.000647359253470380.0001767504894967213.66255989057608
Winsorized Mean ( 5 / 24 )0.0006455433105166460.0001697970558242133.8018522016363
Winsorized Mean ( 6 / 24 )0.0006392122373893550.0001640232390148443.89708337201845
Winsorized Mean ( 7 / 24 )0.0006563384576059470.0001594657616881174.11585816703157
Winsorized Mean ( 8 / 24 )0.0006472822935793370.0001554576769662924.16372035277286
Winsorized Mean ( 9 / 24 )0.0006512804494992340.0001506981550812294.32175463029513
Winsorized Mean ( 10 / 24 )0.0006377454784513970.0001475319225377414.32276260948374
Winsorized Mean ( 11 / 24 )0.0006397535054808060.0001425790653788714.48700869079769
Winsorized Mean ( 12 / 24 )0.0006343204717348970.0001386039713131884.57649564962027
Winsorized Mean ( 13 / 24 )0.0006258861006269010.000123617631732095.06308114673602
Winsorized Mean ( 14 / 24 )0.0006408327266866120.0001204010093210825.32248633379524
Winsorized Mean ( 15 / 24 )0.0006290981516365420.0001109841181411685.66836194379047
Winsorized Mean ( 16 / 24 )0.0006446721548232830.0001087222261767495.92953416696271
Winsorized Mean ( 17 / 24 )0.0006547501060940950.0001015708107097856.44624278883517
Winsorized Mean ( 18 / 24 )0.0006482797917079260.0001002292416212506.46797063633055
Winsorized Mean ( 19 / 24 )0.0006035047381915529.30353309738259e-056.48683389282873
Winsorized Mean ( 20 / 24 )0.0006100469707338199.0725222885202e-056.72411652827499
Winsorized Mean ( 21 / 24 )0.0005933310156327448.33261884638094e-057.12058269520442
Winsorized Mean ( 22 / 24 )0.0005920919713998878.2869845630621e-057.14484221485148
Winsorized Mean ( 23 / 24 )0.0006145674941912367.98824012396425e-057.69340286038185
Winsorized Mean ( 24 / 24 )0.0005602689737730717.13859000777649e-057.84845429087168
Trimmed Mean ( 1 / 24 )0.0006225862633654320.0001973218115033633.15518217992247
Trimmed Mean ( 2 / 24 )0.0006295543797189360.0001825457721127413.44874807251148
Trimmed Mean ( 3 / 24 )0.0006397256217891520.0001691141825950343.78280290850034
Trimmed Mean ( 4 / 24 )0.0006331658270999880.0001610214297803863.93218361036511
Trimmed Mean ( 5 / 24 )0.0006290451549279390.0001549007984551664.06095488984849
Trimmed Mean ( 6 / 24 )0.000625085597586650.0001497774450071614.17342943429676
Trimmed Mean ( 7 / 24 )0.0006221628445240210.0001452251542442474.28412589927525
Trimmed Mean ( 8 / 24 )0.000615885691100810.0001408467609852784.37273592088628
Trimmed Mean ( 9 / 24 )0.0006106529240210560.0001364480169267514.47535213610962
Trimmed Mean ( 10 / 24 )0.0006044025354859510.0001321177948316584.57472467093528
Trimmed Mean ( 11 / 24 )0.0005996011516989270.0001274303091472384.7053260382985
Trimmed Mean ( 12 / 24 )0.0005941258307286710.0001226583928362184.84374380742121
Trimmed Mean ( 13 / 24 )0.000588883051466990.0001174925402206035.01208885569508
Trimmed Mean ( 14 / 24 )0.0005842253249993080.0001143872977396625.10743182629392
Trimmed Mean ( 15 / 24 )0.0005772938064253530.0001109883313962455.20139188654281
Trimmed Mean ( 16 / 24 )0.000571077285000010.0001086461916189355.25630283482927
Trimmed Mean ( 17 / 24 )0.0005623621030472540.0001058771044692835.31146092317255
Trimmed Mean ( 18 / 24 )0.0005514929262182140.0001036847347295575.31894041737852
Trimmed Mean ( 19 / 24 )0.00054010623616060.0001008134572163825.35748154139121
Trimmed Mean ( 20 / 24 )0.000532598518814839.8668634021593e-055.39785033102084
Trimmed Mean ( 21 / 24 )0.0005233047045845519.59672515390353e-055.45295083679346
Trimmed Mean ( 22 / 24 )0.0005147300542521199.40346261482086e-055.47383528106817
Trimmed Mean ( 23 / 24 )0.0005049921905551979.0901553723455e-055.55537468690039
Trimmed Mean ( 24 / 24 )0.0004906997596461498.66417824794731e-055.66354645072548
Median0.000554046674107123
Midrange-0.000569819803221225
Midmean - Weighted Average at Xnp0.000529151814290567
Midmean - Weighted Average at X(n+1)p0.000551492926218213
Midmean - Empirical Distribution Function0.000529151814290567
Midmean - Empirical Distribution Function - Averaging0.000551492926218213
Midmean - Empirical Distribution Function - Interpolation0.000551492926218213
Midmean - Closest Observation0.000529151814290567
Midmean - True Basic - Statistics Graphics Toolkit0.000551492926218213
Midmean - MS Excel (old versions)0.000562362103047254
Number of observations72
 
Charts produced by software:
http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/30/t1196434677ovhncmeo4pqur1m/1tfl61196435192.png (open in new window)
http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/30/t1196434677ovhncmeo4pqur1m/1tfl61196435192.ps (open in new window)


http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/30/t1196434677ovhncmeo4pqur1m/2aw5s1196435192.png (open in new window)
http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/30/t1196434677ovhncmeo4pqur1m/2aw5s1196435192.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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