Question

In Exercises 21–28, use the same list of Sprint airport data speeds (Mbps) given for Exercises 17–20. Find the indicated percentile or quartile.

Q3

Short answer

The data speed corresponding to the third quartile is equal to 3.8 Mbps.

Step-by-step solution

Given information 

50 airport data speeds (in Mbps) are provided.

Conversion of quartile to value 

The third quartileis the same as the 75^th percentile, that is,

$Q_3=P_{75}$

The value of the 75th percentile needs to be computed to compute the value corresponding to the third quartile.

A value in the given percentile is found using the given formula:

• Find $L=\frac{k}{100}\times n$.

Here, L is the locator of the value;

k is the percentile of the value;

n is the total number of values.

• When L becomes a whole number, the $L^{th}$value and the next value are added and divided by 2. The resultant is the required data value.

• When L becomes a decimal number, the value of L is rounded to the next whole number, and the resulting $L^{th}$ value is the required data value.

Calculation

List all the values in increasing order and follow the steps.

• Count the total number of values.
• For k=75, compute the value of L.

Therefore,

$$\begin{gathered} L=\frac{k}{100}\times n \\ =\frac{75}{100}\times 50 \\ =37.5 \\ \approx 38\left(\text{rounded}\text{to}\text{the}\text{next}\text{whole}\text{number}\right) \end{gathered}$$

The value corresponding to the 38^th observation from the sorted data is 3.8 Mbps.

Therefore,the data speed corresponding to the third quartile is 3.8 Mbps.