Question

The following are the FICO credit rating scores of 12 random people. Use the given data values to construct a boxplot graph and identify the Five-Number Summary. Round decimals to two places. 664 693 698 714 751 753 779 789 802 818 834 836

1) Compute the sample mean.

2) Compute the sample standard deviation.

3) Compute the coefficient of variation(CV).

4) Find the Five-Number Summary:

Answer 1

Solution-:

By using R-software:

> x=c(664,693,698,714,751,753,779,789,802,818,834,836);x
[1] 664 693 698 714 751 753 779 789 802 818 834 836
> #(1) for sample mean
> Mean=mean(x);Mean
[1] 760.9167
> round(Mean,2)
[1] 760.92
> #(2) for sample standard deviation
> n=30
> v=var(x);v
[1] 3396.992
> s=sqrt(v);s
[1] 58.28372
> round(s,2)
[1] 58.28
> #for coefficient of variation for sample (cv)
> cvs=(s/Mean)*100;cvs
[1] 7.659672
> round(cvs,2)
[1] 7.66
> #(3) for coefficient of variation for population (CV)
> var=((n-1)/n)*v;var # Variance
[1] 3283.759
> sd=sqrt(var);sd
[1] 57.3041
> CV=(sd/Mean)*100;CV
[1] 7.530929
> round(CV,2)
[1] 7.53
> #(4) for For box plot
> boxplot(x)
> f=fivenum(x);f
[1] 664 706 766 810 836
> round(f,2)
[1] 664 706 766 810 836
> text(rep(1.3,5),f,labels=c("Min=664","Q1=706","Med=766","Q3=810","Max=836"))

R-code:

x=c(664,693,698,714,751,753,779,789,802,818,834,836);x
#(1) for sample mean
Mean=mean(x);Mean
round(Mean,2)
#(2) for sample standard deviation
n=30
v=var(x);v
s=sqrt(v);s
round(s,2)
#for coefficient of variation for sample (cv)
cvs=(s/Mean)*100;cvs
round(cvs,2)
#(3) for coefficient of variation for population (CV)
var=((n-1)/n)*v;var # Variance
sd=sqrt(var);sd
CV=(sd/Mean)*100;CV
round(CV,2)
#(4) for For box plot
boxplot(x)
f=fivenum(x);f
round(f,2)
text(rep(1.3,5),f,labels=c("Min=664","Q1=706","Med=766","Q3=810","Max=836"))