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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: Tue, 16 Mar 2010 13:32:12 -0600

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2010/Mar/16/t1268767969v9pexrjkgkqvrvr.htm/, Retrieved Tue, 16 Mar 2010 20:32:51 +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/2010/Mar/16/t1268767969v9pexrjkgkqvrvr.htm/},
    year = {2010},
}
@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 = {2010},
    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:

KDGP1W52

Dataseries X:

» Textbox « » Textfile « » CSV «

104,9 110,9 104,8 94,1 95,8 99,3 101,1 104 99 105,4 107,1 110,7 117,1 118,7 126,5 127,5 134,6 131,8 135,9 142,7 141,7 153,4 145 137,7 148,3 152,2 169,4 168,6 161,1 174,1 179 190,6 190 181,6 174,8 180,5 196,8 193,8 197 216,3 221,4 217,9 229,7 227,4 204,2 196,6 198,8 207,5 190,7 201,6 210,5 223,5 223,8 231,2 244 234,7 250,2 265,7 287,6 283,3 295,4 312,3 333,8 347,7 383,2 407,1 413,6 362,7 321,9 239,4 191 159,7 163,4 157,6 166,2 176,7 198,3 226,2 216,2 235,9 226,9 242,3 253,1 250 259,4

Output produced by software:

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	2 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Central Tendency - Ungrouped Data
Measure	Value	S.E.	Value/S.E.
Arithmetic Mean	197.812941176471	7.96360801572441	24.8396129977621
Geometric Mean	185.261493209033
Harmonic Mean	173.555377200228
Quadratic Mean	210.848666388116
Winsorized Mean ( 1 / 28 )	197.756470588235	7.93618674652979	24.9183237371156
Winsorized Mean ( 2 / 28 )	197.269411764706	7.75611713469344	25.4340423615202
Winsorized Mean ( 3 / 28 )	196.556470588235	7.55646317439893	26.0117023072597
Winsorized Mean ( 4 / 28 )	195.935294117647	7.36443697435522	26.6056040400565
Winsorized Mean ( 5 / 28 )	195.288235294118	7.14362861050539	27.3374003523822
Winsorized Mean ( 6 / 28 )	194.504705882353	6.94627117306505	28.0013119321582
Winsorized Mean ( 7 / 28 )	193.722352941176	6.77629257858321	28.5882509786317
Winsorized Mean ( 8 / 28 )	192.178823529412	6.45134691474076	29.788945792126
Winsorized Mean ( 9 / 28 )	191.532941176471	6.26846122501453	30.5550173002828
Winsorized Mean ( 10 / 28 )	191.450588235294	6.10974943521801	31.3352601878775
Winsorized Mean ( 11 / 28 )	189.198823529412	5.71972298944274	33.0783193309585
Winsorized Mean ( 12 / 28 )	189.184705882353	5.44010486230144	34.7759299996872
Winsorized Mean ( 13 / 28 )	188.465882352941	5.2568721337015	35.8513347023789
Winsorized Mean ( 14 / 28 )	189.272941176471	4.98935516405077	37.9353513536614
Winsorized Mean ( 15 / 28 )	189.414117647059	4.95788881408533	38.2045916618652
Winsorized Mean ( 16 / 28 )	189.094117647059	4.67751620535684	40.4261811921682
Winsorized Mean ( 17 / 28 )	189.314117647059	4.54925615027816	41.6143016337920
Winsorized Mean ( 18 / 28 )	188.975294117647	4.42565759119663	42.699935596814
Winsorized Mean ( 19 / 28 )	188.595294117647	4.26359118823542	44.2339065335439
Winsorized Mean ( 20 / 28 )	189.254117647059	4.09430928187326	46.2236984599438
Winsorized Mean ( 21 / 28 )	188.636470588235	3.94745702174705	47.7868332825443
Winsorized Mean ( 22 / 28 )	188.843529411765	3.8158362509786	49.4894217128249
Winsorized Mean ( 23 / 28 )	189.114117647059	3.61584172120081	52.3015475313048
Winsorized Mean ( 24 / 28 )	190.074117647059	3.45203271134144	55.0615053625019
Winsorized Mean ( 25 / 28 )	190.221176470588	3.37997650287593	56.2788458170446
Winsorized Mean ( 26 / 28 )	190.771764705882	3.12260692091307	61.0937494015736
Winsorized Mean ( 27 / 28 )	191.343529411765	3.0268821017456	63.2147282186568
Winsorized Mean ( 28 / 28 )	191.112941176471	2.88258014882233	66.2992636144216
Trimmed Mean ( 1 / 28 )	196.462650602410	7.62148426260263	25.777479009754
Trimmed Mean ( 2 / 28 )	195.104938271605	7.25090349866968	26.9076727207031
Trimmed Mean ( 3 / 28 )	193.940506329114	6.93043832627572	27.9838730537169
Trimmed Mean ( 4 / 28 )	192.977922077922	6.64574409972411	29.037820172151
Trimmed Mean ( 5 / 28 )	192.14	6.38164315590972	30.1082331471431
Trimmed Mean ( 6 / 28 )	191.406849315068	6.14001935082373	31.1736557132169
Trimmed Mean ( 7 / 28 )	190.788732394366	5.91002304832847	32.2822315300999
Trimmed Mean ( 8 / 28 )	190.272463768116	5.68109887400971	33.4921936737605
Trimmed Mean ( 9 / 28 )	189.970149253731	5.487795354358	34.6168428279438
Trimmed Mean ( 10 / 28 )	189.743076923077	5.29808790310184	35.8135010957423
Trimmed Mean ( 11 / 28 )	189.512698412698	5.10428998010908	37.1281214725674
Trimmed Mean ( 12 / 28 )	189.552459016393	4.95282367250386	38.2715944580693
Trimmed Mean ( 13 / 28 )	189.596610169492	4.82460753929796	39.2978306784888
Trimmed Mean ( 14 / 28 )	189.726315789474	4.70273511729422	40.3438235531827
Trimmed Mean ( 15 / 28 )	189.776363636364	4.60341694468086	41.2251086349338
Trimmed Mean ( 16 / 28 )	189.815094339623	4.48482718326605	42.3238369246128
Trimmed Mean ( 17 / 28 )	189.890196078431	4.38943674523367	43.2607204750419
Trimmed Mean ( 18 / 28 )	189.948979591837	4.29202325555988	44.2562792141858
Trimmed Mean ( 19 / 28 )	190.046808510638	4.19021243057633	45.3549340658365
Trimmed Mean ( 20 / 28 )	190.191111111111	4.08968253716226	46.5051038516747
Trimmed Mean ( 21 / 28 )	190.283720930233	3.9922196345578	47.6636403676496
Trimmed Mean ( 22 / 28 )	190.446341463415	3.89216395006149	48.9307089595766
Trimmed Mean ( 23 / 28 )	190.605128205128	3.78549855473946	50.3513937329311
Trimmed Mean ( 24 / 28 )	190.754054054054	3.68552194280672	51.7576769353826
Trimmed Mean ( 25 / 28 )	190.822857142857	3.5856321260131	53.2187492850905
Trimmed Mean ( 26 / 28 )	190.884848484848	3.46073790413817	55.1572681238294
Trimmed Mean ( 27 / 28 )	190.896774193548	3.35307749469009	56.931810999254
Trimmed Mean ( 28 / 28 )	190.848275862069	3.22013225522253	59.2672166034623
Median	191
Midrange	253.85
Midmean - Weighted Average at Xnp	189.309523809524
Midmean - Weighted Average at X(n+1)p	190.283720930233
Midmean - Empirical Distribution Function	190.283720930233
Midmean - Empirical Distribution Function - Averaging	190.283720930233
Midmean - Empirical Distribution Function - Interpolation	190.283720930233
Midmean - Closest Observation	189.179545454545
Midmean - True Basic - Statistics Graphics Toolkit	190.283720930233
Midmean - MS Excel (old versions)	190.283720930233
Number of observations	85

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Mar/16/t1268767969v9pexrjkgkqvrvr/1nnt51268767930.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Mar/16/t1268767969v9pexrjkgkqvrvr/1nnt51268767930.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Mar/16/t1268767969v9pexrjkgkqvrvr/2nfq81268767930.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Mar/16/t1268767969v9pexrjkgkqvrvr/2nfq81268767930.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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Software written by Ed van Stee & Patrick Wessa

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