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.

P75

Short answer

The data speed corresponding to the 75^th percentile is 3.8 Mbps.

Step-by-step solution

Given information 

50 airport data speeds (in Mbps) are provided.

Steps to obtain the observation corresponding to the percentile 

The observation corresponding to a percentile is obtained by the given formula:

• $L=\frac{k}{100}\times n$
  

Here, L is the locator of the value;

k is the percentile of the value;

n is the total number of values.

• The sum of the observation at place L^th and (L+1)^th place is divided by 2 if the computed value of L is a whole number. The value obtained is the value for the given percentile.

• The computed value of L is rounded to the next whole number if it is in decimal form.

• The whole number value of L corresponds to the position of the required value.

Step 3: Computation for the 75th percentile

The value for L is as follows:

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

Thus, the 38^th observation from the sorted data is 3.8 Mbps.

Therefore,the data speed corresponding to the 75^th percentile is 3.8 Mbps.