Home » date » 2010 » May » 16 »

Hoeveel champagn central tendency

*Unverified author*

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

Title produced by software: Central Tendency

Date of computation: Sun, 16 May 2010 09:41:43 +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/May/16/t1274002998r86gz5ppbzjasti.htm/, Retrieved Sun, 16 May 2010 11:43:21 +0200

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/May/16/t1274002998r86gz5ppbzjasti.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 «

2851 2672 2755 2721 2946 3036 2282 2212 2922 4301 5764 7132 2541 2475 3031 3266 3776 3230 3028 1759 3595 4474 6838 8357 3113 3006 4047 3523 3937 3986 3260 1573 3528 5211 7614 9254 5375 3088 3718 4514 4520 4539 3663 1643 4739 5428 8314 10651 3633 4292 4154 4121 4647 4753 3965 1723 5048 6922 9858 11331 4016 3975 4510 4276 4968 4677 3523 1821 5222 6873 10803 13916 2639 2899 3370 3740 2927 3986 4217 1738 5221 6424 9842 13076 3934 3162 4286 4676 5010 4874 4633 1659 5951 6981 9851 12670

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	3 seconds
R Server	'George Udny Yule' @ 72.249.76.132

Central Tendency - Ungrouped Data
Measure	Value	S.E.	Value/S.E.
Arithmetic Mean	4802.09375	269.477407703775	17.8200235445293
Geometric Mean	4243.18893576555
Harmonic Mean	3795.02956676872
Quadratic Mean	5473.46520439748
Winsorized Mean ( 1 / 32 )	4794.07291666667	266.396048916353	17.9960361130280
Winsorized Mean ( 2 / 32 )	4785.94791666667	263.638933698717	18.1534185771514
Winsorized Mean ( 3 / 32 )	4746.10416666667	251.004008267764	18.9084795873206
Winsorized Mean ( 4 / 32 )	4724.72916666667	245.012144560782	19.2836529598825
Winsorized Mean ( 5 / 32 )	4717.90625	242.819996899608	19.4296446348716
Winsorized Mean ( 6 / 32 )	4672.21875	230.051569925629	20.3094408419400
Winsorized Mean ( 7 / 32 )	4700.21875	226.41945975351	20.7588992355907
Winsorized Mean ( 8 / 32 )	4705.30208333333	225.572538669291	20.8593745989254
Winsorized Mean ( 9 / 32 )	4668.27083333333	210.623192104879	22.1640873765164
Winsorized Mean ( 10 / 32 )	4581.70833333333	189.2940004915	24.2041920052245
Winsorized Mean ( 11 / 32 )	4588.01041666667	187.006898675869	24.5339099741923
Winsorized Mean ( 12 / 32 )	4504.63541666667	168.853949218314	26.6777024613298
Winsorized Mean ( 13 / 32 )	4446	155.824890473981	28.5320271137452
Winsorized Mean ( 14 / 32 )	4428.9375	151.2938270651	29.2737488760482
Winsorized Mean ( 15 / 32 )	4434.71875	147.940664005792	29.9763339566082
Winsorized Mean ( 16 / 32 )	4434.55208333333	145.603312984792	30.4563954791091
Winsorized Mean ( 17 / 32 )	4432.42708333333	144.061463296716	30.767611142503
Winsorized Mean ( 18 / 32 )	4355.73958333333	130.648794521123	33.3393017463249
Winsorized Mean ( 19 / 32 )	4265.88541666667	115.159322197508	37.0433355742605
Winsorized Mean ( 20 / 32 )	4239.42708333333	107.747175793158	39.3460622250717
Winsorized Mean ( 21 / 32 )	4170.73958333333	96.627230966269	43.1631905584593
Winsorized Mean ( 22 / 32 )	4159.28125	94.8905379333567	43.8324130159441
Winsorized Mean ( 23 / 32 )	4123.82291666667	89.9079585333231	45.8671621949711
Winsorized Mean ( 24 / 32 )	4136.57291666667	88.234621373617	46.8815171671779
Winsorized Mean ( 25 / 32 )	4140.47916666667	87.0861818293047	47.5446170643043
Winsorized Mean ( 26 / 32 )	4109.60416666667	79.8408937001259	51.4724219157906
Winsorized Mean ( 27 / 32 )	4118.04166666667	76.1518809547947	54.0766900966139
Winsorized Mean ( 28 / 32 )	4114.54166666667	73.576769367084	55.9217495149683
Winsorized Mean ( 29 / 32 )	4087.95833333333	69.9392796116913	58.4501063784188
Winsorized Mean ( 30 / 32 )	4082.64583333333	61.5371660254909	66.3443914794867
Winsorized Mean ( 31 / 32 )	4127.53125	55.1434949343986	74.850737243084
Winsorized Mean ( 32 / 32 )	4106.86458333333	52.7612954976078	77.8385849816659
Trimmed Mean ( 1 / 32 )	4739.48936170213	254.993165534208	18.5867309493294
Trimmed Mean ( 2 / 32 )	4682.53260869565	241.687897429220	19.3742949419591
Trimmed Mean ( 3 / 32 )	4627.37777777778	227.843058529976	20.3094964035035
Trimmed Mean ( 4 / 32 )	4584.20454545455	217.531274345706	21.0737723081106
Trimmed Mean ( 5 / 32 )	4544.98837209302	207.708576952387	21.8815632882356
Trimmed Mean ( 6 / 32 )	4505.46428571429	196.862191509457	22.8863869246211
Trimmed Mean ( 7 / 32 )	4472.92682926829	187.799795682002	23.8175276656968
Trimmed Mean ( 8 / 32 )	4433.9625	177.935686934159	24.9189051190203
Trimmed Mean ( 9 / 32 )	4392.21794871795	166.292189003838	26.4126533845590
Trimmed Mean ( 10 / 32 )	4353.47368421053	155.967684994989	27.9126646288966
Trimmed Mean ( 11 / 32 )	4323.86486486487	148.595534417070	29.0982153792648
Trimmed Mean ( 12 / 32 )	4291.84722222222	140.174983787064	30.6177829044151
Trimmed Mean ( 13 / 32 )	4267.52857142857	134.012622194418	31.8442285625713
Trimmed Mean ( 14 / 32 )	4248.14705882353	129.259157815417	32.8653468784773
Trimmed Mean ( 15 / 32 )	4229.36363636364	124.410094547606	33.9953413888392
Trimmed Mean ( 16 / 32 )	4208.828125	119.130971082982	35.3294201057782
Trimmed Mean ( 17 / 32 )	4186.98387096774	113.102323752664	37.0194327759699
Trimmed Mean ( 18 / 32 )	4163.88333333333	105.925792412031	39.309437659306
Trimmed Mean ( 19 / 32 )	4146.24137931035	100.005608766922	41.4600883933799
Trimmed Mean ( 20 / 32 )	4135.44642857143	95.9563108095745	43.0971803071736
Trimmed Mean ( 21 / 32 )	4126.2037037037	92.384743687841	44.6632586614706
Trimmed Mean ( 22 / 32 )	4122.28846153846	90.092709650843	45.7560714680967
Trimmed Mean ( 23 / 32 )	4119.06	87.5162044936799	47.0662550304894
Trimmed Mean ( 24 / 32 )	4118.64583333333	85.1970415860826	48.342592144727
Trimmed Mean ( 25 / 32 )	4117.08695652174	82.5257379034513	49.8885203709225
Trimmed Mean ( 26 / 32 )	4115.04545454545	79.2829583099537	51.903278362266
Trimmed Mean ( 27 / 32 )	4115.52380952381	76.638132129364	53.7007321965633
Trimmed Mean ( 28 / 32 )	4115.3	73.9445322262157	55.6538783342387
Trimmed Mean ( 29 / 32 )	4115.36842105263	70.9171919185006	58.0306172554335
Trimmed Mean ( 30 / 32 )	4117.88888888889	67.6941391308224	60.8308036967699
Trimmed Mean ( 31 / 32 )	4121.20588235294	65.4809953163096	62.9374349373468
Trimmed Mean ( 32 / 32 )	4120.59375	64.0637890802641	64.3201691494926
Median	4084
Midrange	7744.5
Midmean - Weighted Average at Xnp	4096.55102040816
Midmean - Weighted Average at X(n+1)p	4118.64583333333
Midmean - Empirical Distribution Function	4096.55102040816
Midmean - Empirical Distribution Function - Averaging	4118.64583333333
Midmean - Empirical Distribution Function - Interpolation	4118.64583333333
Midmean - Closest Observation	4096.55102040816
Midmean - True Basic - Statistics Graphics Toolkit	4118.64583333333
Midmean - MS Excel (old versions)	4119.06
Number of observations	96

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/May/16/t1274002998r86gz5ppbzjasti/11sk11274002899.png (open in new window)

http://www.freestatistics.org/blog/date/2010/May/16/t1274002998r86gz5ppbzjasti/11sk11274002899.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/May/16/t1274002998r86gz5ppbzjasti/21sk11274002899.png (open in new window)

http://www.freestatistics.org/blog/date/2010/May/16/t1274002998r86gz5ppbzjasti/21sk11274002899.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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