Chapter 2.1, Problem 4E

(a)

To determine

Sunny’s percentile who sent 42 text messages.

Answer to Problem 4E

Percentile that corresponds 42 text messages is 72^nd percentile.

Explanation of Solution

Given information:

Data values:

  

Let

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

N , Total number of data values

Now,

Sort all the data values in ascending order:

0, 0, 0, 1, 1, 3, 3, 5, 5, 7, 8, 8, 9, 14, 25, 25, 26, 29, 42, 44, 52, 72, 92, 98, 118.

Note that

18 of the 25 data values are smaller than 42.

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.

  $\begin{array}{l}\text{Percentile}=\frac{n}{N}\times 100\%\\ =\frac{18}{25}\times 100\%\\ =0.72\times 100\%\\ =72\%\end{array}$

Thus,

The percentile that corresponds with 42 text messages is 72^nd percentile.

(b)

To determine

Number of text messages sent by Joelle.

Answer to Problem 4E

Joelle sent only 1 text message.

Explanation of Solution

Given information:

Data values:

  

Let

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

N , Total number of data values

Now,

Sort all the data values in ascending order:

0, 0, 0, 1, 1, 3, 3, 5, 5, 7, 8, 8, 9, 14, 25, 25, 26, 29, 42, 44, 52, 72, 92, 98, 118.

Note that

The data set consists of 25 data values.

Such that

  $N=25$

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

Then

16^th percentile has 16% of the 25 data values below it.

Calculate 16% of 25 data values:

  $n=16\%\times N=\frac{16}{100}\times 25=\frac{4}{25}\times 25=4$

We have

4 out of 25 data values are smaller than 16^th percentile.

16^th percentile needs to be the 5^th data value in the ascending order, and that is 1.

Thus,

The 16^th percentile is 1 text message.