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

50 airport data speeds (in Mbps) are provided.

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:

Here, L is the locator of the value;

k is the percentile of the value;

n is the total number of values.

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.