Question

Forty randomly selected car salespersons were asked the number of cars they generally sell in one week. Twelve people answered that they generally sell three cars; ten generally sell four cars; eight generally sell five cars; six generally sell six cars; four generally sell seven cars.

1.Construct the frequency table.

2.Find the sample standard deviation,

3.Construct the box plot.

4.Find the 70th percentile.

5.Find the percentile for selling five cars.

Answer 1

We solve this problem through the R software.

1. Frequency Table:

Values: 3 4 5 6 7

Frequencies: 12 10 8 6 4 (Total=40)

....................

2. The sample standard deviation is 1.71, as found in the following R session.

> x=c(rep(3,times=12),rep(4,times=10),rep(5,times=8),rep(6,times=6),rep(7,times=4))
> x
 [1] 3 3 3 3 3 3 3 3 3 3 3 3 4 4 4 4 4 4 4 4 4 4 5 5 5 5 5 5 5 5 6 6 6 6 6 6 7 7
[39] 7 7
> sd(X)
[1] 1.71981

...............

3. The box plot is given as follows.

> boxplot(x)

.......................

4. The 70-th percentile is 5.

> quantile(x,0.7)
70% 
  5