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central tendency: Dow Jones Industrial

*The author of this computation has been verified*
R Software Module: rwasp_centraltendency.wasp (opens new window with default values)
Title produced by software: Central Tendency
Date of computation: Fri, 12 Dec 2008 06:03:18 -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/Dec/12/t1229087113imbfuv1ygxweffd.htm/, Retrieved Fri, 12 Dec 2008 14:05:15 +0100
 
BibTeX entries for LaTeX users:
@Manual{KEY,
    author = {{YOUR NAME}},
    publisher = {Office for Research Development and Education},
    title = {Statistical Computations at FreeStatistics.org, URL http://www.freestatistics.org/blog/date/2008/Dec/12/t1229087113imbfuv1ygxweffd.htm/},
    year = {2008},
}
@Manual{R,
    title = {R: A Language and Environment for Statistical Computing},
    author = {{R Development Core Team}},
    organization = {R Foundation for Statistical Computing},
    address = {Vienna, Austria},
    year = {2008},
    note = {{ISBN} 3-900051-07-0},
    url = {http://www.R-project.org},
}
 
 
Original text written by user:
 
IsPrivate?
No (this computation is public)
 
User-defined keywords:
 
Dataseries X:
» Textbox « » Textfile « » CSV «
10967,87 10433,56 10665,78 10666,71 10682,74 10777,22 10052,6 10213,97 10546,82 10767,2 10444,5 10314,68 9042,56 9220,75 9721,84 9978,53 9923,81 9892,56 10500,98 10179,35 10080,48 9492,44 8616,49 8685,4 8160,67 8048,1 8641,21 8526,63 8474,21 7916,13 7977,64 8334,59 8623,36 9098,03 9154,34 9284,73 9492,49 9682,35 9762,12 10124,63 10540,05 10601,61 10323,73 10418,4 10092,96 10364,91 10152,09 10032,8 10204,59 10001,6 10411,75 10673,38 10539,51 10723,78 10682,06 10283,19 10377,18 10486,64 10545,38 10554,27 10532,54 10324,31 10695,25 10827,81 10872,48 10971,19 11145,65 11234,68 11333,88 10997,97 11036,89 11257,35 11533,59 11963,12 12185,15 12377,62 12512,89 12631,48 12268,53 12754,8 13407,75 13480,21 13673,28 13239,71 13557,69 13901,28 13200,58 13406,97 12538,12 12419,57 12193,88 12656,63 12812,48 12056,67 11322,38 11530,75 11114,08 9181,73 8614,55
 
Output produced by software:


Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'George Udny Yule' @ 72.249.76.132


Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean10656.0145454545142.33186801150574.8673834913289
Geometric Mean10563.6685769862
Harmonic Mean10471.9894508114
Quadratic Mean10748.7657587651
Winsorized Mean ( 1 / 33 )10654.3328282828141.69265682113775.1932603094044
Winsorized Mean ( 2 / 33 )10653.4211111111140.92178590234675.5981131156937
Winsorized Mean ( 3 / 33 )10654.4844444444139.8004959438176.2120647177589
Winsorized Mean ( 4 / 33 )10658.5838383838137.95714170557477.2601092383549
Winsorized Mean ( 5 / 33 )10665.5959595960136.76646212124177.9840012980745
Winsorized Mean ( 6 / 33 )10658.6359595960134.21759692446879.4131038241893
Winsorized Mean ( 7 / 33 )10662.0857575758132.68270246314380.3577675133464
Winsorized Mean ( 8 / 33 )10630.8809090909126.83727402530683.8151165797674
Winsorized Mean ( 9 / 33 )10626.2618181818125.82317709359584.4539302188922
Winsorized Mean ( 10 / 33 )10618.1486868687123.84106147880585.740129808932
Winsorized Mean ( 11 / 33 )10620.2642424242122.57709060930086.6415101682831
Winsorized Mean ( 12 / 33 )10652.24114.05835582290493.3928945682816
Winsorized Mean ( 13 / 33 )10656.2109090909112.46035662905094.7552651308082
Winsorized Mean ( 14 / 33 )10650.9771717172109.13720242721797.5925434667458
Winsorized Mean ( 15 / 33 )10648.7711111111107.51088322044899.0483083398738
Winsorized Mean ( 16 / 33 )10637.4466666667103.771640600349102.508224839907
Winsorized Mean ( 17 / 33 )10635.6144444444100.205352200732106.138187340923
Winsorized Mean ( 18 / 33 )10671.792626262694.9542306158324112.388806239069
Winsorized Mean ( 19 / 33 )10647.144444444490.9980816450784117.004053843373
Winsorized Mean ( 20 / 33 )10666.601010101083.1965566068746128.209645268175
Winsorized Mean ( 21 / 33 )10583.865252525368.3774798739577154.785834049965
Winsorized Mean ( 22 / 33 )10592.185252525367.1473558737174157.745381254412
Winsorized Mean ( 23 / 33 )10576.752020202057.0010814883966185.553532389645
Winsorized Mean ( 24 / 33 )10581.539898989955.7025494891732189.965091293471
Winsorized Mean ( 25 / 33 )10578.936363636451.8416067657268204.062663633147
Winsorized Mean ( 26 / 33 )10579.041414141450.3357288215938210.169628250283
Winsorized Mean ( 27 / 33 )10563.269595959646.1600638370766228.840012727084
Winsorized Mean ( 28 / 33 )10559.940707070744.3610017376182238.045587192317
Winsorized Mean ( 29 / 33 )10545.496363636440.566419611445259.956300423939
Winsorized Mean ( 30 / 33 )10537.484242424238.6779014749308272.441984714557
Winsorized Mean ( 31 / 33 )10539.015454545536.5059135153307288.693377036561
Winsorized Mean ( 32 / 33 )10546.818282828335.356136212889298.302343313845
Winsorized Mean ( 33 / 33 )10524.108282828330.5261606877371344.757023016524
Trimmed Mean ( 1 / 33 )10650.8044329897138.45353018707176.926925724457
Trimmed Mean ( 2 / 33 )10647.1274736842134.78148534723578.9954751296457
Trimmed Mean ( 3 / 33 )10643.7776344086131.07400335034881.2043377202635
Trimmed Mean ( 4 / 33 )10639.8949450549127.32953130721583.5618794463592
Trimmed Mean ( 5 / 33 )10634.6977528090123.68049925631385.985242756579
Trimmed Mean ( 6 / 33 )10627.6657471264119.83658061102688.6846544931255
Trimmed Mean ( 7 / 33 )10621.6538823529116.07936552651891.5033764543314
Trimmed Mean ( 8 / 33 )10614.7644578313112.09809978750794.6917430175238
Trimmed Mean ( 9 / 33 )10612.3022222222108.79569527868797.543401832565
Trimmed Mean ( 10 / 33 )10610.3584810127105.168336254340100.889287202875
Trimmed Mean ( 11 / 33 )10609.3568831169101.331873032720104.699109624582
Trimmed Mean ( 12 / 33 )10608.04897.0729125994504109.279177022036
Trimmed Mean ( 13 / 33 )10603.053698630193.6742926737857113.190645971084
Trimmed Mean ( 14 / 33 )10597.352112676189.9428098530516117.823227114986
Trimmed Mean ( 15 / 33 )10591.856376811686.1225558044187122.98585751293
Trimmed Mean ( 16 / 33 )10586.249850746381.8453686096197129.344519190082
Trimmed Mean ( 17 / 33 )10581.376307692377.4057951441775136.700053115962
Trimmed Mean ( 18 / 33 )10576.362698412772.6963154833475145.486915369671
Trimmed Mean ( 19 / 33 )10567.758360655767.9011036037777155.634559672574
Trimmed Mean ( 20 / 33 )10560.747457627162.8066741333915168.146898452189
Trimmed Mean ( 21 / 33 )10551.554912280758.0479278966132181.773153575329
Trimmed Mean ( 22 / 33 )10548.785454545555.3604658346444190.547266817687
Trimmed Mean ( 23 / 33 )10545.100566037752.2310080888812201.893491086620
Trimmed Mean ( 24 / 33 )10542.429215686350.3720954815599209.291059164803
Trimmed Mean ( 25 / 33 )10539.136734693948.2636135102168218.36609338136
Trimmed Mean ( 26 / 33 )10535.783404255346.3668682693372227.226547694676
Trimmed Mean ( 27 / 33 )10535.783404255344.2310468190536238.198825529871
Trimmed Mean ( 28 / 33 )10529.467209302342.4055276533860248.304119580070
Trimmed Mean ( 29 / 33 )10526.839268292740.4105725214455260.497157339362
Trimmed Mean ( 30 / 33 )10525.206153846238.6919318824429272.025862803251
Trimmed Mean ( 31 / 33 )10524.111081081136.8450253237622285.631804798729
Trimmed Mean ( 32 / 33 )10522.751142857134.891609149439301.584002554561
Trimmed Mean ( 33 / 33 )10520.494848484832.4656949575392324.049581019111
Median10539.51
Midrange10908.705
Midmean - Weighted Average at Xnp10526.8302
Midmean - Weighted Average at X(n+1)p10542.4292156863
Midmean - Empirical Distribution Function10542.4292156863
Midmean - Empirical Distribution Function - Averaging10542.4292156863
Midmean - Empirical Distribution Function - Interpolation10539.1367346939
Midmean - Closest Observation10526.8302
Midmean - True Basic - Statistics Graphics Toolkit10542.4292156863
Midmean - MS Excel (old versions)10542.4292156863
Number of observations99
 
Charts produced by software:
http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/12/t1229087113imbfuv1ygxweffd/13zbn1229086996.png (open in new window)
http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/12/t1229087113imbfuv1ygxweffd/13zbn1229086996.ps (open in new window)


http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/12/t1229087113imbfuv1ygxweffd/2algi1229086996.png (open in new window)
http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/12/t1229087113imbfuv1ygxweffd/2algi1229086996.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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