Chapter 2.1, Problem 1E

(a)

To determine

Percentile for Jackson owing 22 pairs of shoes.

Answer to Problem 1E

Percentile for Jackson is 85^th percentile.

Explanation of Solution

Given information:

  

Let

n , Number of data values that are less than the individual’s data value

N , Total number of data values

Note that

In the dotplot, 17 of the 20 dots lie to the left of 22.

Thus,

In the sample, 17 of the 20 individuals own less than 22 pairs of shoes.

Percentile can be determined as the number of data values that are less than the individual’s data value ( n ), divided by the total number of data values ( N ), written as percentage.

  $\begin{array}{l}\text{Percentile}=\frac{n}{N}\times 100\%\\ =\frac{17}{20}\times 100\%\\ =0.85\times 100\%\\ =85\%\end{array}$

Thus,

Percentile that corresponds with 22 pairs of shoes is the 85^th percentile.

(b)

To determine

Interpretation of 45^th percentile and pairs of shoes owned by Raul.

Answer to Problem 1E

Raul owns 8 pairs of shoes and is at 45^th percentile.

Explanation of Solution

Given information:

  

Let

n , Number of data values that are less than the individual’s data value

N , Total number of data values

Now,

Write down all the data values from the dotplot in ascending order, which are shown in the form of dots in the dotplot on horizontal axis.

4, 5, 5, 5, 6, 7, 7, 7, 7, 8, 10, 10, 10, 10, 11, 12, 14, 22, 35, 38.

Note that

In the sample, there are total 20 data values.

Such that

  $N=20$

The data value represented by the x^th percentile has x% of the data values below it.

If number of shoes pairs that Raul owns is at 45^th percentile,

45^th percentile has 45% of the data values below it.

Calculate 45% of 20 data values:

  $n=45\%\times N=\frac{45}{100}\times 20=\frac{9}{20}\times 20=9$

We have

9 out of 20 data values below 45^th percentile.

45^th percentile needs to be the 10^th data value in the ascending order, and that is 8.

Thus,

Raul owns 8 pairs of shoes and is at 45^th percentile.