Home » date » 2011 » May » 09 »

Spreidingsmaten Australische Chocoladeproductie

*Unverified author*
R Software Module: /rwasp_variability.wasp (opens new window with default values)
Title produced by software: Variability
Date of computation: Mon, 09 May 2011 14:37:20 +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/May/09/t1304951636seqm2qavp5xv8i3.htm/, Retrieved Mon, 09 May 2011 16:33:56 +0200
 
Original text written by user:
 
IsPrivate?
No (this computation is public)
 
User-defined keywords:
KDGP2W83
 
Dataseries X:
» Textbox « » Textfile « » CSV «
7992 6114 5965 8460 8323 6333 5675 10090 9035 6976 6459 10896 9978 7466 7199 10977 9412 6341 7784 11911 10079 7721 8197 12038 11963 8033 8618 13625 11734 8895 8727 13974 12583 9525 9662 15490 13839 10047 9788 14978 13045 9489 8741 13149 14106 9998 10034 15081 13266 9997 9027 14324 13149 11209 10332 15354 13800 11786 10550 16114 13255 11403 10269 14009 15847 12967 11328 15814 18626 13219 13818 18062 15722 12111 11702 15589 14852 13612 12380 15501 16322 12157 11124 14621 14035 11159 10944 15824 14378 11816 12233 17344 16812 12181 13275 18458 17375 14609 13323 18327 16053 15070 13806 18245 17461 14999 16022 20564 16372 15854 15115 18207 19488 16644 18631 21093 22212 19762 19403 21227 23176 20823 20647 21336 23458 22003 21647 26416 25226 24723 19945 24040 25034 24885 21168 23541 26019 24657 20599 24534 28717 26138 22968 26577 28660 30430 27356 25454 30194
 
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'RServer@AstonUniversity' @ vre.aston.ac.uk


Variability - Ungrouped Data
Absolute range24755
Relative range (unbiased)4.23479510875427
Relative range (biased)4.24907776349702
Variance (unbiased)34171264.9473064
Variance (biased)33941927.5986667
Standard Deviation (unbiased)5845.61929544735
Standard Deviation (biased)5825.97009936257
Coefficient of Variation (unbiased)0.385660672903226
Coefficient of Variation (biased)0.384364330839013
Mean Squared Error (MSE versus 0)263689190.651007
Mean Squared Error (MSE versus Mean)33941927.5986667
Mean Absolute Deviation from Mean (MAD Mean)4703.76109184271
Mean Absolute Deviation from Median (MAD Median)4619.26174496644
Median Absolute Deviation from Mean4213.41610738255
Median Absolute Deviation from Median3962
Mean Squared Deviation from Mean33941927.5986667
Mean Squared Deviation from Median35260787.1543624
Interquartile Difference (Weighted Average at Xnp)7947.5
Interquartile Difference (Weighted Average at X(n+1)p)7905.5
Interquartile Difference (Empirical Distribution Function)7730
Interquartile Difference (Empirical Distribution Function - Averaging)7730
Interquartile Difference (Empirical Distribution Function - Interpolation)7730
Interquartile Difference (Closest Observation)8076
Interquartile Difference (True Basic - Statistics Graphics Toolkit)7905.5
Interquartile Difference (MS Excel (old versions))7905.5
Semi Interquartile Difference (Weighted Average at Xnp)3973.75
Semi Interquartile Difference (Weighted Average at X(n+1)p)3952.75
Semi Interquartile Difference (Empirical Distribution Function)3865
Semi Interquartile Difference (Empirical Distribution Function - Averaging)3865
Semi Interquartile Difference (Empirical Distribution Function - Interpolation)3865
Semi Interquartile Difference (Closest Observation)4038
Semi Interquartile Difference (True Basic - Statistics Graphics Toolkit)3952.75
Semi Interquartile Difference (MS Excel (old versions))3952.75
Coefficient of Quartile Variation (Weighted Average at Xnp)0.271983710066563
Coefficient of Quartile Variation (Weighted Average at X(n+1)p)0.269338875355604
Coefficient of Quartile Variation (Empirical Distribution Function)0.261838628819186
Coefficient of Quartile Variation (Empirical Distribution Function - Averaging)0.261838628819186
Coefficient of Quartile Variation (Empirical Distribution Function - Interpolation)0.261838628819186
Coefficient of Quartile Variation (Closest Observation)0.276802851658898
Coefficient of Quartile Variation (True Basic - Statistics Graphics Toolkit)0.269338875355604
Coefficient of Quartile Variation (MS Excel (old versions))0.269338875355604
Number of all Pairs of Observations11026
Squared Differences between all Pairs of Observations68342529.8946127
Mean Absolute Differences between all Pairs of Observations6576.2535824415
Gini Mean Difference6576.2535824415
Leik Measure of Dispersion0.487619777380698
Index of Diversity0.992297074236098
Index of Qualitative Variation0.999001784197153
Coefficient of Dispersion0.335767084862782
Observations149
 
Charts produced by software:
 
Parameters (Session):
 
Parameters (R input):
 
R code (references can be found in the software module):
num <- 50
res <- array(NA,dim=c(num,3))
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]
}
}
}
}
iqd <- 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)
}
iqdiff <- qvalue3 - qvalue1
return(c(iqdiff,iqdiff/2,iqdiff/(qvalue3 + qvalue1)))
}
range <- max(x) - min(x)
lx <- length(x)
biasf <- (lx-1)/lx
varx <- var(x)
bvarx <- varx*biasf
sdx <- sqrt(varx)
mx <- mean(x)
bsdx <- sqrt(bvarx)
x2 <- x*x
mse0 <- sum(x2)/lx
xmm <- x-mx
xmm2 <- xmm*xmm
msem <- sum(xmm2)/lx
axmm <- abs(x - mx)
medx <- median(x)
axmmed <- abs(x - medx)
xmmed <- x - medx
xmmed2 <- xmmed*xmmed
msemed <- sum(xmmed2)/lx
qarr <- array(NA,dim=c(8,3))
for (j in 1:8) {
qarr[j,] <- iqd(x,j)
}
sdpo <- 0
adpo <- 0
for (i in 1:(lx-1)) {
for (j in (i+1):lx) {
ldi <- x[i]-x[j]
aldi <- abs(ldi)
sdpo = sdpo + ldi * ldi
adpo = adpo + aldi
}
}
denom <- (lx*(lx-1)/2)
sdpo = sdpo / denom
adpo = adpo / denom
gmd <- 0
for (i in 1:lx) {
for (j in 1:lx) {
ldi <- abs(x[i]-x[j])
gmd = gmd + ldi
}
}
gmd <- gmd / (lx*(lx-1))
sumx <- sum(x)
pk <- x / sumx
ck <- cumsum(pk)
dk <- array(NA,dim=lx)
for (i in 1:lx) {
if (ck[i] <= 0.5) dk[i] <- ck[i] else dk[i] <- 1 - ck[i]
}
bigd <- sum(dk) * 2 / (lx-1)
iod <- 1 - sum(pk*pk)
res[1,] <- c('Absolute range','http://www.xycoon.com/absolute.htm', range)
res[2,] <- c('Relative range (unbiased)','http://www.xycoon.com/relative.htm', range/sd(x))
res[3,] <- c('Relative range (biased)','http://www.xycoon.com/relative.htm', range/sqrt(varx*biasf))
res[4,] <- c('Variance (unbiased)','http://www.xycoon.com/unbiased.htm', varx)
res[5,] <- c('Variance (biased)','http://www.xycoon.com/biased.htm', bvarx)
res[6,] <- c('Standard Deviation (unbiased)','http://www.xycoon.com/unbiased1.htm', sdx)
res[7,] <- c('Standard Deviation (biased)','http://www.xycoon.com/biased1.htm', bsdx)
res[8,] <- c('Coefficient of Variation (unbiased)','http://www.xycoon.com/variation.htm', sdx/mx)
res[9,] <- c('Coefficient of Variation (biased)','http://www.xycoon.com/variation.htm', bsdx/mx)
res[10,] <- c('Mean Squared Error (MSE versus 0)','http://www.xycoon.com/mse.htm', mse0)
res[11,] <- c('Mean Squared Error (MSE versus Mean)','http://www.xycoon.com/mse.htm', msem)
res[12,] <- c('Mean Absolute Deviation from Mean (MAD Mean)', 'http://www.xycoon.com/mean2.htm', sum(axmm)/lx)
res[13,] <- c('Mean Absolute Deviation from Median (MAD Median)', 'http://www.xycoon.com/median1.htm', sum(axmmed)/lx)
res[14,] <- c('Median Absolute Deviation from Mean', 'http://www.xycoon.com/mean3.htm', median(axmm))
res[15,] <- c('Median Absolute Deviation from Median', 'http://www.xycoon.com/median2.htm', median(axmmed))
res[16,] <- c('Mean Squared Deviation from Mean', 'http://www.xycoon.com/mean1.htm', msem)
res[17,] <- c('Mean Squared Deviation from Median', 'http://www.xycoon.com/median.htm', msemed)
load(file='createtable')
mylink1 <- hyperlink('http://www.xycoon.com/difference.htm','Interquartile Difference','')
mylink2 <- paste(mylink1,hyperlink('http://www.xycoon.com/method_1.htm','(Weighted Average at Xnp)',''),sep=' ')
res[18,] <- c('', mylink2, qarr[1,1])
mylink2 <- paste(mylink1,hyperlink('http://www.xycoon.com/method_2.htm','(Weighted Average at X(n+1)p)',''),sep=' ')
res[19,] <- c('', mylink2, qarr[2,1])
mylink2 <- paste(mylink1,hyperlink('http://www.xycoon.com/method_3.htm','(Empirical Distribution Function)',''),sep=' ')
res[20,] <- c('', mylink2, qarr[3,1])
mylink2 <- paste(mylink1,hyperlink('http://www.xycoon.com/method_4.htm','(Empirical Distribution Function - Averaging)',''),sep=' ')
res[21,] <- c('', mylink2, qarr[4,1])
mylink2 <- paste(mylink1,hyperlink('http://www.xycoon.com/method_5.htm','(Empirical Distribution Function - Interpolation)',''),sep=' ')
res[22,] <- c('', mylink2, qarr[5,1])
mylink2 <- paste(mylink1,hyperlink('http://www.xycoon.com/method_6.htm','(Closest Observation)',''),sep=' ')
res[23,] <- c('', mylink2, qarr[6,1])
mylink2 <- paste(mylink1,hyperlink('http://www.xycoon.com/method_7.htm','(True Basic - Statistics Graphics Toolkit)',''),sep=' ')
res[24,] <- c('', mylink2, qarr[7,1])
mylink2 <- paste(mylink1,hyperlink('http://www.xycoon.com/method_8.htm','(MS Excel (old versions))',''),sep=' ')
res[25,] <- c('', mylink2, qarr[8,1])
mylink1 <- hyperlink('http://www.xycoon.com/deviation.htm','Semi Interquartile Difference','')
mylink2 <- paste(mylink1,hyperlink('http://www.xycoon.com/method_1.htm','(Weighted Average at Xnp)',''),sep=' ')
res[26,] <- c('', mylink2, qarr[1,2])
mylink2 <- paste(mylink1,hyperlink('http://www.xycoon.com/method_2.htm','(Weighted Average at X(n+1)p)',''),sep=' ')
res[27,] <- c('', mylink2, qarr[2,2])
mylink2 <- paste(mylink1,hyperlink('http://www.xycoon.com/method_3.htm','(Empirical Distribution Function)',''),sep=' ')
res[28,] <- c('', mylink2, qarr[3,2])
mylink2 <- paste(mylink1,hyperlink('http://www.xycoon.com/method_4.htm','(Empirical Distribution Function - Averaging)',''),sep=' ')
res[29,] <- c('', mylink2, qarr[4,2])
mylink2 <- paste(mylink1,hyperlink('http://www.xycoon.com/method_5.htm','(Empirical Distribution Function - Interpolation)',''),sep=' ')
res[30,] <- c('', mylink2, qarr[5,2])
mylink2 <- paste(mylink1,hyperlink('http://www.xycoon.com/method_6.htm','(Closest Observation)',''),sep=' ')
res[31,] <- c('', mylink2, qarr[6,2])
mylink2 <- paste(mylink1,hyperlink('http://www.xycoon.com/method_7.htm','(True Basic - Statistics Graphics Toolkit)',''),sep=' ')
res[32,] <- c('', mylink2, qarr[7,2])
mylink2 <- paste(mylink1,hyperlink('http://www.xycoon.com/method_8.htm','(MS Excel (old versions))',''),sep=' ')
res[33,] <- c('', mylink2, qarr[8,2])
mylink1 <- hyperlink('http://www.xycoon.com/variation1.htm','Coefficient of Quartile Variation','')
mylink2 <- paste(mylink1,hyperlink('http://www.xycoon.com/method_1.htm','(Weighted Average at Xnp)',''),sep=' ')
res[34,] <- c('', mylink2, qarr[1,3])
mylink2 <- paste(mylink1,hyperlink('http://www.xycoon.com/method_2.htm','(Weighted Average at X(n+1)p)',''),sep=' ')
res[35,] <- c('', mylink2, qarr[2,3])
mylink2 <- paste(mylink1,hyperlink('http://www.xycoon.com/method_3.htm','(Empirical Distribution Function)',''),sep=' ')
res[36,] <- c('', mylink2, qarr[3,3])
mylink2 <- paste(mylink1,hyperlink('http://www.xycoon.com/method_4.htm','(Empirical Distribution Function - Averaging)',''),sep=' ')
res[37,] <- c('', mylink2, qarr[4,3])
mylink2 <- paste(mylink1,hyperlink('http://www.xycoon.com/method_5.htm','(Empirical Distribution Function - Interpolation)',''),sep=' ')
res[38,] <- c('', mylink2, qarr[5,3])
mylink2 <- paste(mylink1,hyperlink('http://www.xycoon.com/method_6.htm','(Closest Observation)',''),sep=' ')
res[39,] <- c('', mylink2, qarr[6,3])
mylink2 <- paste(mylink1,hyperlink('http://www.xycoon.com/method_7.htm','(True Basic - Statistics Graphics Toolkit)',''),sep=' ')
res[40,] <- c('', mylink2, qarr[7,3])
mylink2 <- paste(mylink1,hyperlink('http://www.xycoon.com/method_8.htm','(MS Excel (old versions))',''),sep=' ')
res[41,] <- c('', mylink2, qarr[8,3])
res[42,] <- c('Number of all Pairs of Observations', 'http://www.xycoon.com/pair_numbers.htm', lx*(lx-1)/2)
res[43,] <- c('Squared Differences between all Pairs of Observations', 'http://www.xycoon.com/squared_differences.htm', sdpo)
res[44,] <- c('Mean Absolute Differences between all Pairs of Observations', 'http://www.xycoon.com/mean_abs_differences.htm', adpo)
res[45,] <- c('Gini Mean Difference', 'http://www.xycoon.com/gini_mean_difference.htm', gmd)
res[46,] <- c('Leik Measure of Dispersion', 'http://www.xycoon.com/leiks_d.htm', bigd)
res[47,] <- c('Index of Diversity', 'http://www.xycoon.com/diversity.htm', iod)
res[48,] <- c('Index of Qualitative Variation', 'http://www.xycoon.com/qualitative_variation.htm', iod*lx/(lx-1))
res[49,] <- c('Coefficient of Dispersion', 'http://www.xycoon.com/dispersion.htm', sum(axmm)/lx/medx)
res[50,] <- c('Observations', '', lx)
res
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Variability - Ungrouped Data',2,TRUE)
a<-table.row.end(a)
for (i in 1:num) {
a<-table.row.start(a)
if (res[i,1] != '') {
a<-table.element(a,hyperlink(res[i,2],res[i,1],''),header=TRUE)
} else {
a<-table.element(a,res[i,2],header=TRUE)
}
a<-table.element(a,res[i,3])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable.tab')
 





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