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Opgave 5 oef 2 stap1 - Sophie Berns - centrummaten

*Unverified author*
R Software Module: /rwasp_centraltendency.wasp (opens new window with default values)
Title produced by software: Central Tendency
Date of computation: Mon, 04 Apr 2011 14:33:25 +0000
 
Cite this page as follows:
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2011/Apr/04/t1301927594uz3e8tklc331te2.htm/, Retrieved Mon, 04 Apr 2011 16:33:15 +0200
 
Original text written by user:
 
IsPrivate?
No (this computation is public)
 
User-defined keywords:
KDGP1W52
 
Dataseries X:
» Textbox « » Textfile « » CSV «
41 39 50 40 43 38 44 35 39 35 29 49 50 59 63 32 39 47 53 60 57 52 70 90 74 62 55 84 94 70 108 139 120 97 126 149 158 124 140 109 114 77 120 133 110 92 97 78 99 107 112 90 98 125 155 190 236 189 174 178 136 161 171 149 184 155 276 224 213 279 268 287 238 213 257 293 212 246 353 339 308 247 257 322 298 273 312 249 286 279 309 401 309 328 353 354 327 324 285 243 241 287 355 460 364 487 452 391 500 451 375 372 302 316 398 394 431 431
 
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' @ www.wessa.org


Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean196.2881355932211.787369041110516.6524128419693
Geometric Mean150.591705333384
Harmonic Mean109.547926428759
Quadratic Mean234.062500707158
Winsorized Mean ( 1 / 39 )196.20338983050811.76053723394516.6831995790292
Winsorized Mean ( 2 / 39 )195.79661016949211.661826520179616.7895320540642
Winsorized Mean ( 3 / 39 )195.59322033898311.622959273840116.8281773798525
Winsorized Mean ( 4 / 39 )195.66101694915311.604666823999816.860545840446
Winsorized Mean ( 5 / 39 )194.8559322033911.445297059284917.0249781367898
Winsorized Mean ( 6 / 39 )194.8559322033911.445297059284917.0249781367898
Winsorized Mean ( 7 / 39 )193.07627118644111.146309171131117.3219913625317
Winsorized Mean ( 8 / 39 )192.94067796610211.106051746400517.3725714927121
Winsorized Mean ( 9 / 39 )192.7118644067811.049262832434417.4411512631491
Winsorized Mean ( 10 / 39 )192.62711864406810.990051185642417.5274086890258
Winsorized Mean ( 11 / 39 )191.22881355932210.755142967377317.7802205083987
Winsorized Mean ( 12 / 39 )191.22881355932210.675323865012717.9131627271801
Winsorized Mean ( 13 / 39 )190.56779661016910.524073235118718.1077984115738
Winsorized Mean ( 14 / 39 )189.61864406779710.362374686321918.2987635370962
Winsorized Mean ( 15 / 39 )189.49152542372910.345065928828618.3170921023975
Winsorized Mean ( 16 / 39 )189.62711864406810.295537251491618.4183801206289
Winsorized Mean ( 17 / 39 )189.77118644067810.279115103141418.461821327663
Winsorized Mean ( 18 / 39 )187.9406779661029.9609355219761118.8677737699899
Winsorized Mean ( 19 / 39 )186.4915254237299.6989132740019819.2280846477534
Winsorized Mean ( 20 / 39 )186.6610169491539.6392725807344719.3646372571954
Winsorized Mean ( 21 / 39 )186.3050847457639.5530382666352719.5021813527585
Winsorized Mean ( 22 / 39 )186.3050847457639.4652280253802319.6831058106789
Winsorized Mean ( 23 / 39 )185.3305084745769.301460876077319.9248817947762
Winsorized Mean ( 24 / 39 )185.9406779661029.0461361327787720.5547070303689
Winsorized Mean ( 25 / 39 )185.3050847457638.970831000946420.6564012549354
Winsorized Mean ( 26 / 39 )186.1864406779668.8748028169760520.9792199914371
Winsorized Mean ( 27 / 39 )186.644067796618.7740029041897721.2723964004484
Winsorized Mean ( 28 / 39 )185.4576271186448.5818370747495321.6104810081188
Winsorized Mean ( 29 / 39 )185.9491525423738.3119224941897322.3713770998655
Winsorized Mean ( 30 / 39 )186.2033898305088.00792342050223.2523939169783
Winsorized Mean ( 31 / 39 )184.6271186440687.8299950038380523.5794682568212
Winsorized Mean ( 32 / 39 )185.1694915254247.774204748055523.8184479990366
Winsorized Mean ( 33 / 39 )185.4491525423737.6858271752653124.128717483941
Winsorized Mean ( 34 / 39 )186.0254237288147.5661883291975524.5864120261123
Winsorized Mean ( 35 / 39 )184.2457627118647.3688832174636525.0032138214943
Winsorized Mean ( 36 / 39 )184.5508474576277.3380688500753825.1497841227984
Winsorized Mean ( 37 / 39 )183.9237288135597.2033355060967625.5331337347663
Winsorized Mean ( 38 / 39 )185.5338983050856.8415108022269627.1188489894209
Winsorized Mean ( 39 / 39 )184.211864406786.6295014876411727.7866842250795
Trimmed Mean ( 1 / 39 )195.11206896551711.609099023726516.8068226971577
Trimmed Mean ( 2 / 39 )193.98245614035111.439946562000616.9565876107054
Trimmed Mean ( 3 / 39 )193.02678571428611.308228827929317.0695861086171
Trimmed Mean ( 4 / 39 )192.10909090909111.176134359657317.1892252479132
Trimmed Mean ( 5 / 39 )191.13888888888911.033269320678217.3238668733176
Trimmed Mean ( 6 / 39 )190.31132075471710.914989349061517.4357770464596
Trimmed Mean ( 7 / 39 )189.45192307692310.781157668870617.5725027771316
Trimmed Mean ( 8 / 39 )188.85294117647110.69179054158917.6633596067815
Trimmed Mean ( 9 / 39 )188.2510.596982370162517.7644911942146
Trimmed Mean ( 10 / 39 )187.6530612244910.498215031080317.8747587726997
Trimmed Mean ( 11 / 39 )187.04166666666710.394466694616817.9943495093918
Trimmed Mean ( 12 / 39 )186.56382978723410.31176735517918.0923233972627
Trimmed Mean ( 13 / 39 )186.06521739130410.227182944785118.1932031915182
Trimmed Mean ( 14 / 39 )185.61111111111110.149970258124418.2868625612515
Trimmed Mean ( 15 / 39 )185.22727272727310.081366043042818.373231557751
Trimmed Mean ( 16 / 39 )184.83720930232610.002227665214918.4796042930657
Trimmed Mean ( 17 / 39 )184.4166666666679.91491641458118.5999214673622
Trimmed Mean ( 18 / 39 )183.9634146341469.8136727976619318.7456234202117
Trimmed Mean ( 19 / 39 )183.63759.7354442427878118.8627755878774
Trimmed Mean ( 20 / 39 )183.4102564102569.67435882873218.9583888356036
Trimmed Mean ( 21 / 39 )183.1578947368429.6064680811178719.066101421484
Trimmed Mean ( 22 / 39 )182.9189189189199.5338551209825319.1862490669008
Trimmed Mean ( 23 / 39 )182.6666666666679.4554593780565919.3186453839127
Trimmed Mean ( 24 / 39 )182.4714285714299.3797438554813219.4537752184774
Trimmed Mean ( 25 / 39 )182.2205882352949.3172276543254219.5573828391646
Trimmed Mean ( 26 / 39 )1829.2471881948238519.6816584853194
Trimmed Mean ( 27 / 39 )181.7031259.16993122841619.8151022591025
Trimmed Mean ( 28 / 39 )181.3548387096779.0844820581314819.9631456751403
Trimmed Mean ( 29 / 39 )181.0666666666679.0021612805637220.1136883714361
Trimmed Mean ( 30 / 39 )180.7241379310348.9323529194284620.2325344241546
Trimmed Mean ( 31 / 39 )180.3392857142868.8810785580558820.3060117682106
Trimmed Mean ( 32 / 39 )180.0370370370378.8347656353499520.3782470829409
Trimmed Mean ( 33 / 39 )179.6730769230778.7746515984449320.4763773133647
Trimmed Mean ( 34 / 39 )179.268.7022310064601220.599315263744
Trimmed Mean ( 35 / 39 )178.7708333333338.6186051215114720.7424323092763
Trimmed Mean ( 36 / 39 )178.3695652173918.5362743287741820.8954818399101
Trimmed Mean ( 37 / 39 )177.9090909090918.4233152079707321.1210297271959
Trimmed Mean ( 38 / 39 )177.4523809523818.2914535838443821.4018421689221
Trimmed Mean ( 39 / 39 )176.8258.1757840916220721.6278950151334
Median166
Midrange264.5
Midmean - Weighted Average at Xnp179.084745762712
Midmean - Weighted Average at X(n+1)p181.066666666667
Midmean - Empirical Distribution Function181.066666666667
Midmean - Empirical Distribution Function - Averaging181.066666666667
Midmean - Empirical Distribution Function - Interpolation180.724137931034
Midmean - Closest Observation181.066666666667
Midmean - True Basic - Statistics Graphics Toolkit181.066666666667
Midmean - MS Excel (old versions)181.066666666667
Number of observations118
 
Charts produced by software:
http://www.freestatistics.org/blog/date/2011/Apr/04/t1301927594uz3e8tklc331te2/10vqd1301927603.png (open in new window)
http://www.freestatistics.org/blog/date/2011/Apr/04/t1301927594uz3e8tklc331te2/10vqd1301927603.ps (open in new window)


http://www.freestatistics.org/blog/date/2011/Apr/04/t1301927594uz3e8tklc331te2/2k2qw1301927603.png (open in new window)
http://www.freestatistics.org/blog/date/2011/Apr/04/t1301927594uz3e8tklc331te2/2k2qw1301927603.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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