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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: Sat, 01 Dec 2007 10:20:45 -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/01/t1196529109d78k72117mlwgq1.htm/, Retrieved Sat, 01 Dec 2007 18:11:51 +0100
 
User-defined keywords:
 
Dataseries X:
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-0.380048863112299 0.128827241934028 -1.78018273712276 -0.460516984026575 -0.414395956192115 2.87998200286135 4.10576012559306 -0.101868322578922 -4.50361041132808 -1.53993720789598 3.51665337212412 -1.38122140031529 1.58237986405844 -0.123133033866621 3.66314326329599 -0.511985315223507 -1.21002566320509 3.78892726266821 4.44243460770059 1.43121012327424 4.03419450689848 -2.88800419871577 -2.12212207474709 -2.20759757657912 1.35729583200525 3.21471063721915 -7.39784817169113 4.48946358236397 -2.48469296334684 -0.80915061937459 -4.66725063202075 3.21201658875771 0.90173525205496 4.93111155690056 1.39625263166861 1.31760343456557 4.67803724476682 0.0166432457321966 9.9711302420896 -4.95336140821711 -3.49883659301842 -2.8922251076851 -7.33406116929741 -5.36264801495136 -0.776909114605922 -0.515872655929886 5.6036762018959 1.21825585712809 -2.82140643233298 5.22942650705011 6.05880445164751 -6.39478899720465 2.61221750394062 1.02267740860387 0.0251629689553848 -3.46316632792863 -4.78972833107371 4.71190593449837 -1.88725722568947 6.30417057732905 3.41423076008627 0.00169494032452635 -5.24002783490566 2.60442929601493 -0.7916626640232 -1.04274305225078 3.22300022326394 -5.07492117142369 1.41997038497602 5.10318758819723 8.2142423987708 -1.63523249951777 -3.17446784606862 3.14387866951378 -3.58644038899541 -2.60628124121237 2.65287546541382 10.9564683830469 -2.06296715376449 2.82384224419473 9.37573300874498
 
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 Mean0.5665526670455630.4365922388487031.29767003769826
Geometric MeanNaN
Harmonic Mean0.121281437610936
Quadratic Mean3.94588451001423
Winsorized Mean ( 1 / 27 )0.5551754924953950.4329492775281541.28231070314996
Winsorized Mean ( 2 / 27 )0.5636662317237440.4240177872303831.32934572251207
Winsorized Mean ( 3 / 27 )0.5588755047711180.4059328635088591.37676831567721
Winsorized Mean ( 4 / 27 )0.4706062879120540.3847035484089541.22329593750402
Winsorized Mean ( 5 / 27 )0.4656520001219570.3800001019460931.22539967157171
Winsorized Mean ( 6 / 27 )0.4409432233408440.3723393703014571.18425087033865
Winsorized Mean ( 7 / 27 )0.4227417872431070.3643230057259231.16034886789755
Winsorized Mean ( 8 / 27 )0.4223703087443490.3601317422226101.17282166281046
Winsorized Mean ( 9 / 27 )0.4214329964550160.353867602616261.19093410456120
Winsorized Mean ( 10 / 27 )0.5076014408908770.3309214801633611.53390296888645
Winsorized Mean ( 11 / 27 )0.5148988009982830.3283629800495461.56807810953778
Winsorized Mean ( 12 / 27 )0.4922464458407920.3231813028437991.52312785891177
Winsorized Mean ( 13 / 27 )0.531032909958770.3150602315490511.68549647585749
Winsorized Mean ( 14 / 27 )0.5216249542533860.2991146240428931.74389652770232
Winsorized Mean ( 15 / 27 )0.5091537117116730.2970274334644131.71416392678986
Winsorized Mean ( 16 / 27 )0.4738609753467380.2880667368711651.64496942789569
Winsorized Mean ( 17 / 27 )0.4926115958371410.2779093141909841.77256238162141
Winsorized Mean ( 18 / 27 )0.4870779039912880.2695557905776191.80696509226365
Winsorized Mean ( 19 / 27 )0.5280505301624920.2573842108353272.05160420854384
Winsorized Mean ( 20 / 27 )0.5019381758438990.2480386584489322.02362881247095
Winsorized Mean ( 21 / 27 )0.515125484901850.2457239731258682.0963582769272
Winsorized Mean ( 22 / 27 )0.5621174522043040.2394414883442032.34761927054282
Winsorized Mean ( 23 / 27 )0.5731735150984270.2329041993080332.46098403034959
Winsorized Mean ( 24 / 27 )0.5379301287140.2168238630076332.48095445423857
Winsorized Mean ( 25 / 27 )0.5500151697495460.2108210139509162.60892004758881
Winsorized Mean ( 26 / 27 )0.5460827592408340.1971857293004152.76938275999106
Winsorized Mean ( 27 / 27 )0.5895953511198340.1884785968065063.12818198516789
Trimmed Mean ( 1 / 27 )0.5358499470801870.4154814694704861.28970841410354
Trimmed Mean ( 2 / 27 )0.5155204772278260.3949273569886661.30535519534196
Trimmed Mean ( 3 / 27 )0.489521769800030.3764260712105801.30044597661830
Trimmed Mean ( 4 / 27 )0.4638703883723680.3629661818529751.27799891991113
Trimmed Mean ( 5 / 27 )0.4619492339261890.3548471492130471.30182596915507
Trimmed Mean ( 6 / 27 )0.4610798888193570.3466510179049821.33009818233316
Trimmed Mean ( 7 / 27 )0.4651372766396540.3389596358510681.37224975319488
Trimmed Mean ( 8 / 27 )0.4726846055212370.3317146182209341.42497369593285
Trimmed Mean ( 9 / 27 )0.4807708317889520.323937972644721.48414472024939
Trimmed Mean ( 10 / 27 )0.4895255943792050.3158927889258651.54965738864678
Trimmed Mean ( 11 / 27 )0.4870439951123480.3109076154702491.56652320778856
Trimmed Mean ( 12 / 27 )0.4834455273663180.3052025117779341.58401555921032
Trimmed Mean ( 13 / 27 )0.482365414644450.2991043058054351.61269966791527
Trimmed Mean ( 14 / 27 )0.4766439819587320.2930310192439471.62659906513832
Trimmed Mean ( 15 / 27 )0.4715410985471540.2884229276801611.63489464010315
Trimmed Mean ( 16 / 27 )0.4673960350555540.2828344195426741.65254298190194
Trimmed Mean ( 17 / 27 )0.4666996784550410.2773438108546991.68274776717316
Trimmed Mean ( 18 / 27 )0.4639560636734060.2721401806287591.70484219787564
Trimmed Mean ( 19 / 27 )0.4615363361982790.2668731273267261.72942229448689
Trimmed Mean ( 20 / 27 )0.4546202261711920.2622382146624211.73361547155293
Trimmed Mean ( 21 / 27 )0.4497064390897950.2577758272134231.74456404214141
Trimmed Mean ( 22 / 27 )0.442886693001280.2518937243505051.75822837247430
Trimmed Mean ( 23 / 27 )0.4303442365136890.2449709984569921.75671503657296
Trimmed Mean ( 24 / 27 )0.4151015862299420.2366821532774321.75383559969294
Trimmed Mean ( 25 / 27 )0.4017291239433710.229235347856661.75247459739312
Trimmed Mean ( 26 / 27 )0.3851619933084740.219789884663941.75241000693635
Trimmed Mean ( 27 / 27 )0.3665942126239710.2099851526751481.74581015825962
Median0.0166432457321966
Midrange1.77931010567788
Midmean - Weighted Average at Xnp0.385410726243873
Midmean - Weighted Average at X(n+1)p0.454620226171192
Midmean - Empirical Distribution Function0.454620226171192
Midmean - Empirical Distribution Function - Averaging0.454620226171192
Midmean - Empirical Distribution Function - Interpolation0.454620226171192
Midmean - Closest Observation0.39123408801047
Midmean - True Basic - Statistics Graphics Toolkit0.454620226171192
Midmean - MS Excel (old versions)0.454620226171192
Number of observations81
 
Charts produced by software:
http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Dec/01/t1196529109d78k72117mlwgq1/1uh3c1196529642.png (open in new window)
http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Dec/01/t1196529109d78k72117mlwgq1/1uh3c1196529642.ps (open in new window)


http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Dec/01/t1196529109d78k72117mlwgq1/21go11196529642.png (open in new window)
http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Dec/01/t1196529109d78k72117mlwgq1/21go11196529642.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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