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.

Q1

The sample given comprises a set of 50 airport data speeds (in Mbps).

The first quartileis the same as the 25^th percentile, that is,

$Q_1=P_{25}$

Therefore, the 25^th percentile value is required to becomputedto obtain the first quartile.

A percentile can be converted to a value in the following steps:

Here, L is the locator of the value;

k is the percentile of the value;

n is the total number of values.

• Arrange the data values in ascending order.
• Find the total number of values.
• Apply the formula mentioned above to calculate the locator for k=25.

$$\begin{gathered} L=\frac{k}{100}\times n \\ =\frac{25}{100}\times 50 \\ =12.5 \\ \approx 13\left(\text{rounded}\text{to}\text{the}\text{next}\text{whole}\text{number}\right) \end{gathered}$$

The data value corresponding to the 13^th observation from the arranged values is obtained as 0.5 Mbps.

Therefore,the data speed corresponding to the first quartile is equal to 0.5 Mbps.