Home » date » 2010 » Oct » 03 »

Task 9: mediaan tijdreeks

*Unverified author*

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

Title produced by software: Central Tendency

Date of computation: Sun, 03 Oct 2010 16:26:48 +0000

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2010/Oct/03/t12861231412rxefoctndiji18.htm/, Retrieved Wed, 19 Jun 2013 06:54:36 +0000

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

System-generated keywords (parent):

t1204472634kobk5s74i81tzo2 (pk = 9574)

Estimated Impact

Dataseries X:

» Textfile « » CSV « » Stem and Leaf « » Histogram « » Kernel Density « » Harrell-Davis Quantiles « » Central Tendency « » Variability «

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	'George Udny Yule' @ 72.249.76.132

Central Tendency - Ungrouped Data
Measure	Value	S.E.	Value/S.E.
Arithmetic Mean	16750.2857142857	227.180590759787	73.7311477986115
Geometric Mean	16623.1754136431
Harmonic Mean	16497.0390487161
Quadratic Mean	16877.6712326700
Winsorized Mean ( 1 / 28 )	16743.0714285714	224.744336027652	74.4983020462478
Winsorized Mean ( 2 / 28 )	16727.4523809524	217.842184322602	76.7870209939723
Winsorized Mean ( 3 / 28 )	16731.4166666667	216.596338739475	77.2469967130491
Winsorized Mean ( 4 / 28 )	16731.6547619048	215.718998502654	77.5622679413605
Winsorized Mean ( 5 / 28 )	16731.2976190476	212.498426155801	78.7361013524893
Winsorized Mean ( 6 / 28 )	16751.7261904762	208.090499911759	80.5021190183108
Winsorized Mean ( 7 / 28 )	16716.4761904762	201.585801776728	82.9248689299606
Winsorized Mean ( 8 / 28 )	16713.1428571429	200.930045757858	83.1789133083856
Winsorized Mean ( 9 / 28 )	16708.6428571429	198.533144678927	84.160470455271
Winsorized Mean ( 10 / 28 )	16729.3571428571	195.08020008291	85.7563050260718
Winsorized Mean ( 11 / 28 )	16718.0952380952	189.558931551628	88.1947112765928
Winsorized Mean ( 12 / 28 )	16714.3809523810	183.941369454132	90.8679814768308
Winsorized Mean ( 13 / 28 )	16708.8095238095	182.980121186258	91.3148893742476
Winsorized Mean ( 14 / 28 )	16713.8095238095	181.680587988067	91.9955715076577
Winsorized Mean ( 15 / 28 )	16736.6666666667	170.199875187572	98.33536392563
Winsorized Mean ( 16 / 28 )	16758	166.879663667344	100.419665474669
Winsorized Mean ( 17 / 28 )	16757.3928571429	165.851009576273	101.038835397841
Winsorized Mean ( 18 / 28 )	16765.1071428571	164.691548315605	101.797009708898
Winsorized Mean ( 19 / 28 )	16742.9404761905	153.658430232897	108.962068991682
Winsorized Mean ( 20 / 28 )	16716.0357142857	148.536903939802	112.537930109680
Winsorized Mean ( 21 / 28 )	16756.2857142857	138.328354538653	121.134136021285
Winsorized Mean ( 22 / 28 )	16699.7142857143	122.598179855146	136.215026238118
Winsorized Mean ( 23 / 28 )	16701.0833333333	117.560599732180	142.063611204611
Winsorized Mean ( 24 / 28 )	16670.2261904762	110.171874995066	151.311087255461
Winsorized Mean ( 25 / 28 )	16690.7619047619	104.635569001931	159.513271289745
Winsorized Mean ( 26 / 28 )	16685.5	99.9560380992349	166.928384890915
Winsorized Mean ( 27 / 28 )	16583.2857142857	86.131987822671	192.533414512939
Winsorized Mean ( 28 / 28 )	16591.2857142857	84.5556635168089	196.217320333457
Trimmed Mean ( 1 / 28 )	16733.9024390244	218.643550765635	76.5350836117801
Trimmed Mean ( 2 / 28 )	16724.275	211.561156863339	79.0517278689456
Trimmed Mean ( 3 / 28 )	16722.5641025641	207.612960550458	80.5468216349618
Trimmed Mean ( 4 / 28 )	16719.3026315789	203.538382965618	82.1432419181752
Trimmed Mean ( 5 / 28 )	16715.7972972973	199.062745554764	83.9725045020974
Trimmed Mean ( 6 / 28 )	16712.1805555556	194.757940655854	85.8100085638447
Trimmed Mean ( 7 / 28 )	16704.2714285714	190.822363193069	87.5383322429066
Trimmed Mean ( 8 / 28 )	16702.1176470588	187.706182252359	88.9801148083865
Trimmed Mean ( 9 / 28 )	16700.3636363636	184.102070397497	90.7125248526845
Trimmed Mean ( 10 / 28 )	16699.15625	180.267124622373	92.6356166438098
Trimmed Mean ( 11 / 28 )	16695.0645161290	176.326104775386	94.6828862203704
Trimmed Mean ( 12 / 28 )	16692.1333333333	172.630108906128	96.6930591604394
Trimmed Mean ( 13 / 28 )	16689.4482758621	169.181637897206	98.6481067525929
Trimmed Mean ( 14 / 28 )	16687.2142857143	165.090920865242	101.078933948981
Trimmed Mean ( 15 / 28 )	16684.2592592593	160.252816476993	104.112112511012
Trimmed Mean ( 16 / 28 )	16678.6153846154	156.456674243764	106.602134202531
Trimmed Mean ( 17 / 28 )	16670.28	152.266077640425	109.481246633060
Trimmed Mean ( 18 / 28 )	16661.3125	147.109002610846	113.258279264356
Trimmed Mean ( 19 / 28 )	16650.7826086957	140.690907015877	118.350097826980
Trimmed Mean ( 20 / 28 )	16641.5227272727	134.888276879695	123.37263928514
Trimmed Mean ( 21 / 28 )	16634.0714285714	128.488480631091	129.459632076514
Trimmed Mean ( 22 / 28 )	16621.85	122.381044021929	135.820462497620
Trimmed Mean ( 23 / 28 )	16614.0263157895	118.182065866699	140.579928045334
Trimmed Mean ( 24 / 28 )	16605.1944444444	113.639333534223	146.121892200677
Trimmed Mean ( 25 / 28 )	16598.5	109.312885978727	151.843946405643
Trimmed Mean ( 26 / 28 )	16588.8125	104.623253034901	158.557605683186
Trimmed Mean ( 27 / 28 )	16578.4	99.2121446959615	167.100510232946
Trimmed Mean ( 28 / 28 )	16577.8571428571	95.9831984068943	172.716240112982
Median	16441.5
Midrange	17422
Midmean - Weighted Average at Xnp	16597.7906976744
Midmean - Weighted Average at X(n+1)p	16634.0714285714
Midmean - Empirical Distribution Function	16597.7906976744
Midmean - Empirical Distribution Function - Averaging	16634.0714285714
Midmean - Empirical Distribution Function - Interpolation	16634.0714285714
Midmean - Closest Observation	16597.7906976744
Midmean - True Basic - Statistics Graphics Toolkit	16634.0714285714
Midmean - MS Excel (old versions)	16641.5227272727
Number of observations	84

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Oct/03/t12861231412rxefoctndiji18/1nzye1286123206.png (opens in new window)

http://www.freestatistics.org/blog/date/2010/Oct/03/t12861231412rxefoctndiji18/1nzye1286123206.ps (opens in new window)

Click here to open pdf file.

http://www.freestatistics.org/blog/date/2010/Oct/03/t12861231412rxefoctndiji18/2nzye1286123206.png (opens in new window)

http://www.freestatistics.org/blog/date/2010/Oct/03/t12861231412rxefoctndiji18/2nzye1286123206.ps (opens in new window)

Click here to open pdf file.

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')