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Central Tendency: werkelijk begonnen niet-woongebouwen

*Unverified author*

R Software Module: rwasp_centraltendency.wasp (opens new window with default values)

Title produced by software: Central Tendency

Date of computation: Mon, 20 Oct 2008 16:40:45 -0600

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2008/Oct/21/t12245424769m0cyfpcxo3gz3c.htm/, Retrieved Mon, 20 Oct 2008 22:41:18 +0000

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/Oct/21/t12245424769m0cyfpcxo3gz3c.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},
}

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

Dataseries X:

» Textbox « » Textfile « » CSV «

582 552 436 602 640 551 421 382 382 427 542 708 465 474 371 463 515 509 380 313 313 359 427 415 402 388 353 464 429 398 291 272 241 288 365 312 325 346 282 362 369 340 308 294 306 328 351 366 350 356 295 359 380 360 336 299 262 299 313 357 356 368 284 338 352 342 315 277 317 291 326 353 371 356 274 352 347 345 336 276 312 330 325 328 332 341 316 377 380 373 346 272 283 302 301 303 320

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	1 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Central Tendency - Ungrouped Data
Measure	Value	S.E.	Value/S.E.
Arithmetic Mean	365.896907216495	8.60946899063496	42.4993582780196
Geometric Mean	357.769458940421
Harmonic Mean	350.88201782416
Quadratic Mean	375.494807574571
Winsorized Mean ( 1 / 32 )	365.412371134021	8.31292715329285	43.9571241748794
Winsorized Mean ( 2 / 32 )	364.835051546392	8.03159943197161	45.4249560920684
Winsorized Mean ( 3 / 32 )	364.216494845361	7.8469879911678	46.414814863398
Winsorized Mean ( 4 / 32 )	363.061855670103	7.49521345588993	48.4391615804884
Winsorized Mean ( 5 / 32 )	363.113402061856	7.46904948663608	48.6157445752037
Winsorized Mean ( 6 / 32 )	362.618556701031	7.31748781046527	49.55506125783
Winsorized Mean ( 7 / 32 )	361.030927835052	6.79418612653836	53.1382156907434
Winsorized Mean ( 8 / 32 )	360.618556701031	6.66842400537146	54.0785283615065
Winsorized Mean ( 9 / 32 )	357.463917525773	5.94646184500968	60.113715826792
Winsorized Mean ( 10 / 32 )	356.948453608247	5.70771790021554	62.5378583610042
Winsorized Mean ( 11 / 32 )	357.175257731959	5.64316959154466	63.2933765214368
Winsorized Mean ( 12 / 32 )	357.051546391753	5.61882289952328	63.5456131607291
Winsorized Mean ( 13 / 32 )	353.835051546392	4.89421340266602	72.2966128435771
Winsorized Mean ( 14 / 32 )	352.969072164948	4.7022709109519	75.063533949705
Winsorized Mean ( 15 / 32 )	353.278350515464	4.57227051951403	77.2654087302368
Winsorized Mean ( 16 / 32 )	353.278350515464	4.57227051951403	77.2654087302368
Winsorized Mean ( 17 / 32 )	352.577319587629	4.35455668072439	80.9674429427744
Winsorized Mean ( 18 / 32 )	351.649484536082	4.15189067076576	84.696229361749
Winsorized Mean ( 19 / 32 )	349.298969072165	3.73686603044301	93.4737735381847
Winsorized Mean ( 20 / 32 )	349.092783505155	3.53769230635313	98.6781080079348
Winsorized Mean ( 21 / 32 )	347.360824742268	3.18181802941275	109.170550148142
Winsorized Mean ( 22 / 32 )	346.907216494845	2.88939443270791	120.062256841039
Winsorized Mean ( 23 / 32 )	346.907216494845	2.88939443270791	120.062256841039
Winsorized Mean ( 24 / 32 )	346.659793814433	2.79627139589283	123.972156037360
Winsorized Mean ( 25 / 32 )	346.659793814433	2.79627139589283	123.972156037360
Winsorized Mean ( 26 / 32 )	346.659793814433	2.79627139589283	123.972156037360
Winsorized Mean ( 27 / 32 )	346.381443298969	2.62404635348587	132.002791352685
Winsorized Mean ( 28 / 32 )	345.515463917526	2.45023989822672	141.012912314252
Winsorized Mean ( 29 / 32 )	345.216494845361	2.34352341077078	147.306612453178
Winsorized Mean ( 30 / 32 )	346.144329896907	2.22861109388808	155.318409230843
Winsorized Mean ( 31 / 32 )	347.103092783505	1.96273730896520	176.846433395871
Winsorized Mean ( 32 / 32 )	346.773195876289	1.92461588274115	180.177872886716
Trimmed Mean ( 1 / 32 )	363.610526315789	7.89844974281145	46.0356827169432
Trimmed Mean ( 2 / 32 )	361.731182795699	7.41208626890103	48.8028835165368
Trimmed Mean ( 3 / 32 )	360.076923076923	7.02366887643279	51.2662156220269
Trimmed Mean ( 4 / 32 )	358.573033707865	6.65450241262751	53.884274356478
Trimmed Mean ( 5 / 32 )	357.32183908046	6.35446104358744	56.2316515325952
Trimmed Mean ( 6 / 32 )	356	6.00937642705271	59.2407555628196
Trimmed Mean ( 7 / 32 )	356	5.64485546474758	63.0662737466421
Trimmed Mean ( 8 / 32 )	353.629629629630	5.35462890912696	66.0418556787135
Trimmed Mean ( 9 / 32 )	352.556962025316	5.04081835327413	69.9404218357367
Trimmed Mean ( 10 / 32 )	351.87012987013	4.84007220227375	72.6993555395372
Trimmed Mean ( 11 / 32 )	351.213333333333	4.65340303001575	75.4745142571811
Trimmed Mean ( 12 / 32 )	350.493150684931	4.44388842407163	78.8708260059775
Trimmed Mean ( 13 / 32 )	349.746478873239	4.19733163822339	83.3259101301981
Trimmed Mean ( 14 / 32 )	349.746478873239	4.05100180992739	86.3357992129626
Trimmed Mean ( 15 / 32 )	348.925373134328	3.91244713957993	89.1834089218626
Trimmed Mean ( 16 / 32 )	348.492307692308	3.76880688354336	92.4675417076988
Trimmed Mean ( 17 / 32 )	348.031746031746	3.59431253055658	96.8284597048808
Trimmed Mean ( 18 / 32 )	347.606557377049	3.4242209188125	101.514056954479
Trimmed Mean ( 19 / 32 )	347.237288135593	3.25627919087673	106.636215072855
Trimmed Mean ( 20 / 32 )	347.052631578947	3.13275814449096	110.781814481673
Trimmed Mean ( 21 / 32 )	346.872727272727	3.01757529096951	114.950811106781
Trimmed Mean ( 22 / 32 )	346.830188679245	2.94121602482468	117.920678301730
Trimmed Mean ( 23 / 32 )	346.823529411765	2.89634060968934	119.745422293051
Trimmed Mean ( 24 / 32 )	346.816326530612	2.83783258253305	122.211693764205
Trimmed Mean ( 25 / 32 )	346.816326530612	2.77898802099749	124.799503959764
Trimmed Mean ( 26 / 32 )	346.844444444444	2.7016559746962	128.382165491462
Trimmed Mean ( 27 / 32 )	346.860465116279	2.59985121717347	133.415505789359
Trimmed Mean ( 28 / 32 )	346.860465116279	2.50409539628945	138.517272796497
Trimmed Mean ( 29 / 32 )	347.025641025641	2.41550523894317	143.665861464855
Trimmed Mean ( 30 / 32 )	347.189189189189	2.32005159342479	149.647184645872
Trimmed Mean ( 31 / 32 )	347.189189189189	2.21968709603893	156.413572799858
Trimmed Mean ( 32 / 32 )	347.303030303030	2.15299511625439	161.31157366824
Median	350
Midrange	474.5
Midmean - Weighted Average at Xnp	346.816326530612
Midmean - Weighted Average at X(n+1)p	346.816326530612
Midmean - Empirical Distribution Function	346.816326530612
Midmean - Empirical Distribution Function - Averaging	346.816326530612
Midmean - Empirical Distribution Function - Interpolation	346.816326530612
Midmean - Closest Observation	345.450980392157
Midmean - True Basic - Statistics Graphics Toolkit	346.816326530612
Midmean - MS Excel (old versions)	346.816326530612
Number of observations	97

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Oct/21/t12245424769m0cyfpcxo3gz3c/1n7ca1224542442.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Oct/21/t12245424769m0cyfpcxo3gz3c/1n7ca1224542442.ps (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Oct/21/t12245424769m0cyfpcxo3gz3c/2e1b01224542442.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Oct/21/t12245424769m0cyfpcxo3gz3c/2e1b01224542442.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')

This work is licensed under a Creative Commons Attribution-Noncommercial-Share Alike 3.0 License.

Software written by Ed van Stee & Patrick Wessa

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