Measures of Dispersion. Range, Coefficient of range, Quartile Deviation, Mean deviation, Variance and Coeff. Of variation. Experiment :1 For ungrouped data. Experiment :2 For grouped data without class intervals. Experiment :3 For grouped data with class intervals.

 #Measure of Dispersion

#Program-1

#Range
x=c(25,29,30,17,19,30,18,28,31,33,26,28)
r=range(x)
r
diff(r)

#Coeffient of Range
x=c(25,29,30,17,19,30,18,28,31,33,26,28)
r=range(x)
crange=(max(x)-min(x))/(max(x)+min(x))
crange

#Quartile Deviation
x=c(25,29,30,17,19,30,18,28,31,33,26,28)
qd=((quantile(x,0.75)-quantile(x,0.25)))/2
qd

#Mean deviation from Median
x=c(25,29,30,17,19,30,18,28,31,33,26,28)
mad(x)

#Coeff. of Mean deviation from Median
x=c(25,29,30,17,19,30,18,28,31,33,26,28)
cmd=mad(x)/median(x)
cmd

#Variance
x=c(25,29,30,17,19,30,18,28,31,33,26,28)
n=12
var(x)
var(x)*(n-1)/n
#Standard Deviation
x=c(25,29,30,17,19,30,18,28,31,33,26,28)
sd(x)

#Program 2
#Range
grp=seq(0,15,1)
f=c(5,14,21,23,60,80,86,125,112,93,56,43,32,24,22,16)
data=rep(grp,f)
r=range(data)
diff(r)

#Coeffient of Range
grp=seq(0,15,1)
f=c(5,14,21,23,60,80,86,125,112,93,56,43,32,24,22,16)
data=rep(grp,f)
crange=(max(data)-min(data))/(max(data)+min(data))
print(crange)

#Quartile Deviation
grp=seq(0,15,1)
f=c(5,14,21,23,60,80,86,125,112,93,56,43,32,24,22,16)
data=rep(grp,f)
qd=(quantile(data,0.75)-quantile(data,0.25))/2
qd

#Mean Deviation From median
grp=seq(0,15,1)
f=c(5,14,21,23,60,80,86,125,112,93,56,43,32,24,22,16)
data=rep(grp,f)
mad(data)

#Coeff. of Mean deviation from Median
grp=seq(0,15,1)
f=c(5,14,21,23,60,80,86,125,112,93,56,43,32,24,22,16)
data=rep(grp,f)
cmd=(mad(data))/median(data)
cmd

#Variance
grp=seq(0,15,1)
f=c(5,14,21,23,60,80,86,125,112,93,56,43,32,24,22,16)
data=rep(grp,f)
var(data)

#Standard Deviation
grp=seq(0,15,1)
f=c(5,14,21,23,60,80,86,125,112,93,56,43,32,24,22,16)
data=rep(grp,f)
sd(data)

#Program 3
#Range
ub=c(30,40,50,60,70)
lb=c(20,30,40,50,60)
range=ub[length(ub)]-lb[1]
range

#Quartile Deviation
ub=c(30,40,50,60,70)
lb=c(20,30,40,50,60)
h=10
midx=(ub+lb)/2
f=c(25,42,28,15,10)
cf=cumsum(f)
l=min(which(cf>= sum(f)/4))
l1=lb[l]
l2=ub[l]
h=l2-l1
first_quart=l1+(h* (sum(f)/4 - cf[l - 1])/f[l])
first_quart

b = min(which(cf>= 3*sum(f)/4))
b1 = lb[b]
b2 = ub[b]
h = b2-b1
third_quart =b1+(h*(3*sum(f)/4 - cf[b - 1])/f[b])
third_quart
qd=(third_quart-first_quart)/2
qd

#Mean Deviation From Median
ub = c(30,40,50,60,70)
lb = c(20,30,40,50,60)
h=10
x=(ub+lb)/2
f=c(25,42,28,15,10)
n=sum(f)
cf=cumsum(f)
medc=min(which(cf>n/2))
med=lb[medc]+(n/2-cf[medc-1])*h/f[medc]
med
modxminsum=abs(x-med)
z=f*modxminsum
mdaboutmedian=sum(z)/n
mdaboutmedian

#Variance
ub = c(30,40,50,60,70)
lb = c(20,30,40,50,60)
h=10
midx=(ub+lb)/2
f=c(25,42,28,15,10)
cf=cumsum(f)
x_bar=sum(f*midx)/sum(f)
dev_mean=f*(midx-x_bar)^2
variance=sum(dev_mean)/(sum(f)-1)
variance


#Standard Deviation
ub = c(30,40,50,60,70)
lb = c(20,30,40,50,60)
h=10
midx=(ub+lb)/2
f=c(25,42,28,15,10)
cf=cumsum(f)
x_bar=sum(f*midx)/sum(f)
dev_mean=f*(midx-x_bar)^2
variance=sum(dev_mean)/(sum(f)-1)
sqrt(variance)





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