Question

32. Gas Prices for Rental Cars The first column of these data represents the prebuy gas price of a rental car, and the second column represents the price charged if the car is returned without refilling the gas tank for a selected car rental company. Draw two boxplots for the data and compare the distributions. (Note: The data were collected several years ago.)

Prebuy cost                     No prebuy cost

$1.55                                $3.80

1.54                                  3.99

1.62                                  3.99

1.65                                  3.85

1.72                                  3.99

1.63                                  3.95

1.65                                  3.94

1.72                                  4.19

1.45                                  3.84

1.52                                  3.94

Answer 1

Solution-:

Let, x=Prebuy cost and y= No prebuy cost

By using R-Software:

> x=c(1.55,1.54,1.62,1.65,1.72,1.63,1.65,1.72,1.45,1.52);x
[1] 1.55 1.54 1.62 1.65 1.72 1.63 1.65 1.72 1.45 1.52
> boxplot(x,main="Prebuy cost")
> f1=fivenum(x);f1
[1] 1.450 1.540 1.625 1.650 1.720
> text(rep(1.3,5),f1,labels=c("Min=1.450","Q1=1.540","Med=1.625","Q3=1.650","Max=1.720"))

> Q1=1.540;Q2=1.625;Q3=1.650
> a1=Q3-Q2;a1
[1] 0.025
> a2=Q2-Q1;a2
[1] 0.085
> # Here, a1=Q3-Q2=0.025 < a2=Q2-Q1=0.085, hence distribution is negatively skewed.

R-Code:

x=c(1.55,1.54,1.62,1.65,1.72,1.63,1.65,1.72,1.45,1.52);x
boxplot(x,main="Prebuy cost")
f1=fivenum(x);f1
text(rep(1.3,5),f1,labels=c("Min=1.450","Q1=1.540","Med=1.625","Q3=1.650","Max=1.720"))
Q1=1.540;Q2=1.625;Q3=1.650
a1=Q3-Q2;a1
a2=Q2-Q1;a2
# Here, a1=Q3-Q2=0.025 < a2=Q2-Q1=0.085, hence distribution is negatively skewed.

> y=c(3.80,3.99,3.99,3.85,3.99,3.95,3.94,4.19,3.84,3.94);y
[1] 3.80 3.99 3.99 3.85 3.99 3.95 3.94 4.19 3.84 3.94
> boxplot(y,main="No prebuy cost")
> f2=fivenum(y);f2
[1] 3.800 3.850 3.945 3.990 4.190
> text(rep(1.3,5),f2,labels=c("Min=3.800","Q1=3.850","Med=3.945","Q3=3.990","Max=4.190"))

> Q1=3.850;Q2=3.945;Q3=3.990
> b1=Q3-Q2;b1
[1] 0.045
> b2=Q2-Q1;b2
[1] 0.095
> # Here, b1=Q3-Q2=0.045 <b2=Q2-Q1=0.095, hence distribution is negatively skewed.

R-Code:
boxplot(y,main="No prebuy cost")
f2=fivenum(y);f2
text(rep(1.3,5),f2,labels=c("Min=3.800","Q1=3.850","Med=3.945","Q3=3.990","Max=4.190"))
Q1=3.850;Q2=3.945;Q3=3.990
b1=Q3-Q2;b1
b2=Q2-Q1;b2
# Here, b1=Q3-Q2=0.045 <b2=Q2-Q1=0.095, hence distribution is negatively skewed.

From these two boxplot we seen that both data are said negatively skewed distribution.