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trimmed mean

*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: Tue, 16 Dec 2008 14:19:25 -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/16/t12294624931cvqmkdmf8gprqn.htm/, Retrieved Tue, 16 Dec 2008 22:21:35 +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/16/t12294624931cvqmkdmf8gprqn.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 «
524 552 532 511 492 492 493 481 462 457 442 439 488 521 501 485 464 460 467 460 448 443 436 431 484 510 513 503 471 471 476 475 470 461 455 456 517 525 523 519 509 512 519 517 510 509 501 507 569 580 578 565 547 555 562 561 555 544 537 543 594 611 613 611 594 595 591 589 584 573 567 569 621 629 628 612 595 597 593 590 580 574 573 573 620 626 620 588 566 557 561 549 532 526 511 499 555 565 542 527 510 514 517 508 493 490 469 478
 
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'Gwilym Jenkins' @ 72.249.127.135


Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean530.2685185185185.03177178780895105.384055732269
Geometric Mean527.706947384403
Harmonic Mean525.144228198586
Quadratic Mean532.816859301163
Winsorized Mean ( 1 / 36 )530.3055555555565.02175017194515105.601739910957
Winsorized Mean ( 2 / 36 )530.3240740740745.00546307127795105.949053368738
Winsorized Mean ( 3 / 36 )530.2685185185184.96717516199165106.754543825247
Winsorized Mean ( 4 / 36 )530.2685185185184.95475560044476107.022134143391
Winsorized Mean ( 5 / 36 )530.54.91755320518116107.878853133925
Winsorized Mean ( 6 / 36 )530.54.79405387733043110.657913651861
Winsorized Mean ( 7 / 36 )530.54.77417514926217111.118671480242
Winsorized Mean ( 8 / 36 )530.54.75164615952593111.645518666509
Winsorized Mean ( 9 / 36 )530.754.71604797633115112.541263927704
Winsorized Mean ( 10 / 36 )529.4537037037044.52223046821205117.078001093791
Winsorized Mean ( 11 / 36 )529.3518518518524.47948894254296118.172376054877
Winsorized Mean ( 12 / 36 )529.4629629629634.46371909389175118.614758640949
Winsorized Mean ( 13 / 36 )529.5833333333334.41353069569023119.990857625725
Winsorized Mean ( 14 / 36 )529.9722222222224.36027764852912121.545521854784
Winsorized Mean ( 15 / 36 )530.1111111111114.30408560309102123.164630073901
Winsorized Mean ( 16 / 36 )529.9629629629634.24433175094762124.863699178237
Winsorized Mean ( 17 / 36 )529.9629629629634.20253360110119126.105586121690
Winsorized Mean ( 18 / 36 )529.7962962962964.180377426424126.734082178196
Winsorized Mean ( 19 / 36 )530.3240740740744.06606120272982130.426977763648
Winsorized Mean ( 20 / 36 )529.7685185185183.94579942096946134.261390911847
Winsorized Mean ( 21 / 36 )529.379629629633.79802734301216139.382785277629
Winsorized Mean ( 22 / 36 )529.9907407407413.72179587235347142.401883101021
Winsorized Mean ( 23 / 36 )530.2037037037043.59082710970893147.655035317666
Winsorized Mean ( 24 / 36 )529.5370370370373.45530794304872153.253210933730
Winsorized Mean ( 25 / 36 )5303.34489169480608158.450571306383
Winsorized Mean ( 26 / 36 )530.4814814814823.28894330422524161.292376429835
Winsorized Mean ( 27 / 36 )530.9814814814823.23200027870849164.288810548514
Winsorized Mean ( 28 / 36 )529.9444444444443.10806389115381170.506290412104
Winsorized Mean ( 29 / 36 )530.2129629629633.07757245565176172.282852996446
Winsorized Mean ( 30 / 36 )529.6574074074073.01266973979319175.809980234928
Winsorized Mean ( 31 / 36 )531.0925925925932.78851105067249190.457410044874
Winsorized Mean ( 32 / 36 )531.3888888888892.69072845427223197.48885772742
Winsorized Mean ( 33 / 36 )531.3888888888892.69072845427223197.48885772742
Winsorized Mean ( 34 / 36 )531.0740740740742.51522548543729211.143723355580
Winsorized Mean ( 35 / 36 )532.0462962962962.34551722781664226.83538197311
Winsorized Mean ( 36 / 36 )532.379629629632.31246107402122230.222093513495
Trimmed Mean ( 1 / 36 )530.273584905664.95243381805033107.073330888936
Trimmed Mean ( 2 / 36 )530.2403846153854.8746707667748108.774604477792
Trimmed Mean ( 3 / 36 )530.1960784313734.79686445538302110.529718603241
Trimmed Mean ( 4 / 36 )530.174.72500451605791112.205183761882
Trimmed Mean ( 5 / 36 )530.1428571428574.64787878427908114.061248528254
Trimmed Mean ( 6 / 36 )530.06254.57075976687588115.968138129101
Trimmed Mean ( 7 / 36 )529.9787234042554.51262188593083117.443636271984
Trimmed Mean ( 8 / 36 )529.8913043478264.45043458749993119.065069698170
Trimmed Mean ( 9 / 36 )529.84.38369467757704120.856957194116
Trimmed Mean ( 10 / 36 )529.6704545454554.3136475603058122.789459996566
Trimmed Mean ( 11 / 36 )529.6976744186054.26662900372034124.148988336396
Trimmed Mean ( 12 / 36 )529.7380952380954.21877748766444125.566730358980
Trimmed Mean ( 13 / 36 )529.7682926829274.1653674137108127.184048864245
Trimmed Mean ( 14 / 36 )529.78754.11060275193033128.883166769451
Trimmed Mean ( 15 / 36 )529.7692307692314.05432322615652130.66773446957
Trimmed Mean ( 16 / 36 )529.7368421052633.99633026492234132.555821713488
Trimmed Mean ( 17 / 36 )529.7162162162163.93653466544606134.564092846923
Trimmed Mean ( 18 / 36 )529.6944444444443.87170218541591136.811774014985
Trimmed Mean ( 19 / 36 )529.6857142857143.79787141304685139.469101683138
Trimmed Mean ( 20 / 36 )529.6323529411763.72672198072011142.117484395452
Trimmed Mean ( 21 / 36 )529.6212121212123.65924859824209144.734963450049
Trimmed Mean ( 22 / 36 )529.6406253.59951820984503147.142087947043
Trimmed Mean ( 23 / 36 )529.6129032258063.53791541717057149.696315704845
Trimmed Mean ( 24 / 36 )529.5666666666673.48186315040048152.092900780939
Trimmed Mean ( 25 / 36 )529.5689655172413.43270911595379154.27143624143
Trimmed Mean ( 26 / 36 )529.5357142857143.3874255908552156.323939842477
Trimmed Mean ( 27 / 36 )529.4629629629633.33801693630516158.616020549322
Trimmed Mean ( 28 / 36 )529.3461538461543.28336046899666161.220846399455
Trimmed Mean ( 29 / 36 )529.33.23390835759242163.671923094955
Trimmed Mean ( 30 / 36 )529.2291666666673.17406371733122166.735520707079
Trimmed Mean ( 31 / 36 )529.1956521739133.10751303474010170.295553472449
Trimmed Mean ( 32 / 36 )529.0454545454553.06051622472276172.861509529615
Trimmed Mean ( 33 / 36 )528.8571428571433.01382247873032175.477204310966
Trimmed Mean ( 34 / 36 )528.652.94795670218352179.327599896035
Trimmed Mean ( 35 / 36 )528.4473684210532.89520557436098182.524989969906
Trimmed Mean ( 36 / 36 )528.1388888888892.85388979269586185.059314567994
Median523.5
Midrange530
Midmean - Weighted Average at Xnp530.298245614035
Midmean - Weighted Average at X(n+1)p531.017857142857
Midmean - Empirical Distribution Function530.298245614035
Midmean - Empirical Distribution Function - Averaging531.017857142857
Midmean - Empirical Distribution Function - Interpolation531.017857142857
Midmean - Closest Observation530.298245614035
Midmean - True Basic - Statistics Graphics Toolkit531.017857142857
Midmean - MS Excel (old versions)530.298245614035
Number of observations108
 
Charts produced by software:
http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/16/t12294624931cvqmkdmf8gprqn/1uour1229462363.png (open in new window)
http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/16/t12294624931cvqmkdmf8gprqn/1uour1229462363.ps (open in new window)


http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/16/t12294624931cvqmkdmf8gprqn/2jrm51229462363.png (open in new window)
http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/16/t12294624931cvqmkdmf8gprqn/2jrm51229462363.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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