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Paper - Centr. Tend. - Regress.

R Software Module: rwasp_centraltendency.wasp (opens new window with default values)
Title produced by software: Central Tendency
Date of computation: Fri, 21 Dec 2007 09:04:13 -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/Dec/21/t1198252054jxbhovk9xvu6xag.htm/, Retrieved Fri, 21 Dec 2007 16:47:36 +0100
 
User-defined keywords:
 
Dataseries X:
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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 time2 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135


Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean6.79676700596141e-1451.40381166163431.32223015886471e-15
Geometric MeanNaN
Harmonic Mean-611.289101333921
Quadratic Mean563.100543776485
Winsorized Mean ( 1 / 40 )0.11109395309411750.28515313154020.00220927940307763
Winsorized Mean ( 2 / 40 )-0.16456383190505549.755227392081-0.00330746819039254
Winsorized Mean ( 3 / 40 )-0.41054501477273849.1790186519547-0.00834797086290416
Winsorized Mean ( 4 / 40 )1.5229603417487248.34667036051390.0315008320199143
Winsorized Mean ( 5 / 40 )2.1257550390884648.21551582245420.0440886092957340
Winsorized Mean ( 6 / 40 )-5.4225181295475346.8958439787222-0.115628969850886
Winsorized Mean ( 7 / 40 )-6.0352448350902946.2348717823591-0.130534477601667
Winsorized Mean ( 8 / 40 )-7.0569308922903645.8221821129901-0.154006871058412
Winsorized Mean ( 9 / 40 )-4.5687160709033445.4045078558647-0.100622521565625
Winsorized Mean ( 10 / 40 )-9.821804362174944.2887281034489-0.221767586985865
Winsorized Mean ( 11 / 40 )-8.6867528093346443.7466491673476-0.198569558461598
Winsorized Mean ( 12 / 40 )-11.875938178516242.5211194835424-0.279295049677908
Winsorized Mean ( 13 / 40 )-12.069992024719442.4431587778793-0.284380153887370
Winsorized Mean ( 14 / 40 )-4.4909667283341741.2414884693981-0.108894389970104
Winsorized Mean ( 15 / 40 )-4.6394664334864940.7324547537251-0.113900978017098
Winsorized Mean ( 16 / 40 )-7.2574221025916740.0745897365988-0.181097851538670
Winsorized Mean ( 17 / 40 )-6.7574552840958739.999585454884-0.168938132914345
Winsorized Mean ( 18 / 40 )-1.6570759431290939.0559994314315-0.0424282048149434
Winsorized Mean ( 19 / 40 )1.1288144121368738.0977812983840.0296294002870123
Winsorized Mean ( 20 / 40 )9.2495247604995236.88646558749090.250756601728636
Winsorized Mean ( 21 / 40 )5.558647202548434.65742258649330.160388360925452
Winsorized Mean ( 22 / 40 )3.2471520138114934.38031210469420.0944480086138638
Winsorized Mean ( 23 / 40 )-4.6976320037844832.8740874791258-0.142897715617729
Winsorized Mean ( 24 / 40 )-2.9744063608335132.364368498813-0.091903735459649
Winsorized Mean ( 25 / 40 )-1.2901583085963131.531501963147-0.0409164875845179
Winsorized Mean ( 26 / 40 )2.4311270917099130.64500231200810.0793319271755214
Winsorized Mean ( 27 / 40 )2.6064768969134430.35600696587020.0858636282381918
Winsorized Mean ( 28 / 40 )3.667278699334929.72403437115720.123377555467149
Winsorized Mean ( 29 / 40 )5.7729090117824728.78874223639470.200526614340392
Winsorized Mean ( 30 / 40 )7.4515705727272628.35948244841120.262754110068209
Winsorized Mean ( 31 / 40 )9.7645061583379727.66580325355270.352944972132124
Winsorized Mean ( 32 / 40 )6.7181978472908227.29806715778500.246105257506295
Winsorized Mean ( 33 / 40 )7.9597528448509226.18793817302550.303947290247147
Winsorized Mean ( 34 / 40 )13.557684828088925.28948934713460.536099588330557
Winsorized Mean ( 35 / 40 )17.485104346307024.82275872352220.704398110663583
Winsorized Mean ( 36 / 40 )12.244195904503123.95761462079260.511077421450651
Winsorized Mean ( 37 / 40 )18.473666368521222.81973934144660.809547650483814
Winsorized Mean ( 38 / 40 )18.615448126196722.67988519962520.82079110905307
Winsorized Mean ( 39 / 40 )21.776779427978022.14044164780520.98357475313221
Winsorized Mean ( 40 / 40 )30.078769985727821.10195778839361.42540186495263
Trimmed Mean ( 1 / 40 )-0.35216247115984649.0724324811779-0.00717638098121426
Trimmed Mean ( 2 / 40 )-0.8312567218840347.7259980443493-0.0174172726804285
Trimmed Mean ( 3 / 40 )-1.1819951553077546.5418036441373-0.0253964191922039
Trimmed Mean ( 4 / 40 )-1.4573505152037345.4627304726741-0.0320559390087599
Trimmed Mean ( 5 / 40 )-2.2695523478416744.5310602695066-0.050965603201588
Trimmed Mean ( 6 / 40 )-3.2453912355821343.527300576408-0.0745599013172239
Trimmed Mean ( 7 / 40 )-2.8350604658472142.719415667803-0.0663646826982223
Trimmed Mean ( 8 / 40 )-2.3082273928153641.9545070095494-0.0550173880553518
Trimmed Mean ( 9 / 40 )-1.6109056410720641.1759871110444-0.0391224535000881
Trimmed Mean ( 10 / 40 )-1.2171817004674640.3763977231560-0.0301458715760917
Trimmed Mean ( 11 / 40 )-0.16550559736988639.6633760804966-0.00417275617269678
Trimmed Mean ( 12 / 40 )0.80082140604879738.94482992073070.0205629709432243
Trimmed Mean ( 13 / 40 )2.1463371163403538.31697204232690.0560153112821492
Trimmed Mean ( 14 / 40 )3.5691459054786737.61433363091470.094887920666106
Trimmed Mean ( 15 / 40 )4.3346668071202336.98888215665520.117188369974580
Trimmed Mean ( 16 / 40 )5.1480526663812236.34482006269620.141644742153094
Trimmed Mean ( 17 / 40 )6.2264021254657835.69594191997320.174428850747930
Trimmed Mean ( 18 / 40 )7.3136317078581434.95996942248740.209200174618968
Trimmed Mean ( 19 / 40 )8.0401749647319434.2422682551320.234802639382014
Trimmed Mean ( 20 / 40 )8.58356328628133.54271791761380.255899456548619
Trimmed Mean ( 21 / 40 )8.5325624392047732.89422334068190.259393947406326
Trimmed Mean ( 22 / 40 )8.7551003140566132.42956442489270.269972800107555
Trimmed Mean ( 23 / 40 )9.1590165227412631.9172770211520.286961087459668
Trimmed Mean ( 24 / 40 )10.157619543414031.5032356524110.322430992660167
Trimmed Mean ( 25 / 40 )11.090116688023231.07414712754960.356892069877308
Trimmed Mean ( 26 / 40 )11.958530180539730.66734626113150.389943429689453
Trimmed Mean ( 27 / 40 )12.620307318167930.29170124943460.416625900745785
Trimmed Mean ( 28 / 40 )13.310719558037929.87077593185490.445610103614449
Trimmed Mean ( 29 / 40 )13.972202746191529.44173874636320.474571249563766
Trimmed Mean ( 30 / 40 )14.533036291620329.04334076850750.500391342974528
Trimmed Mean ( 31 / 40 )14.533036291620328.60837217668670.50799941366337
Trimmed Mean ( 32 / 40 )15.376824249503128.16676432923750.545920861543255
Trimmed Mean ( 33 / 40 )15.972104814655227.66523129536180.577334945951925
Trimmed Mean ( 34 / 40 )16.526418472943627.20674037823440.607438386340647
Trimmed Mean ( 35 / 40 )16.733579240548826.76585075532980.625183910405564
Trimmed Mean ( 36 / 40 )16.680556186439926.2722108002230.634912543648528
Trimmed Mean ( 37 / 40 )16.997813629769925.78053222383320.659327491077008
Trimmed Mean ( 38 / 40 )16.890559466773625.34026894196290.66655012641966
Trimmed Mean ( 39 / 40 )16.762829033609424.77269622919800.676665506189517
Trimmed Mean ( 40 / 40 )16.383411899326424.12047213001430.679232637363664
Median49.7591290429804
Midrange20.953667034015
Midmean - Weighted Average at Xnp8.46687130395737
Midmean - Weighted Average at X(n+1)p14.5330362916203
Midmean - Empirical Distribution Function14.5330362916203
Midmean - Empirical Distribution Function - Averaging14.5330362916203
Midmean - Empirical Distribution Function - Interpolation14.5330362916203
Midmean - Closest Observation8.02313027235234
Midmean - True Basic - Statistics Graphics Toolkit14.5330362916203
Midmean - MS Excel (old versions)14.5330362916203
Number of observations121
 
Charts produced by software:
http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Dec/21/t1198252054jxbhovk9xvu6xag/1hexf1198253050.png (open in new window)
http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Dec/21/t1198252054jxbhovk9xvu6xag/1hexf1198253050.ps (open in new window)


http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Dec/21/t1198252054jxbhovk9xvu6xag/2gisg1198253050.png (open in new window)
http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Dec/21/t1198252054jxbhovk9xvu6xag/2gisg1198253050.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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