Question

In Exercises 17–20, use the following cell phone airport data speeds (Mbps) from Sprint. Find the percentile corresponding to the given data speed.

0.2 0.3 0.3 0.3 0.3 0.3 0.3 0.4 0.4 0.4 0.5 0.5 0.5 0.5 0.5 0.6 0.6 0.7 0.8 1.0 1.1 1.1 1.2 1.2 1.6 1.6 2.1 2.1 2.3 2.4 2.5 2.7 2.7 2.7 3.2 3.4 3.6 3.8 4.0 4.0 5.0 5.6 8.2 9.6 10.6 13.0 14.1 15.1 15.2 30.4

2.4 Mbps

Short answer

The value of data speed equal to 2.4 Mbps is in the 58^th percentile.

Step-by-step solution

Given information 

A list of 50 sprint data speeds is provided.

The formula for percentile 

A percentileof a value is the percentage of values that lie below that value in a sorted data set.

It is computed as follows for a value x of the data set:

$P_x=\frac{Numberofvaluesbelowx}{Totalnumberofvalues}\times 100$

Computation to determine percentile for 2.4 Mbps

Steps to follow to compute the percentile.

• Arrange the data speeds in ascending order.
• Count the total number of values.
• Count the number of values less than 2.4.
• Perform the calculation as shown below:

Thus, the percentile for 2.4 Mbps speed is computed as follows:

$$\begin{gathered} P_{2.4}=\frac{Numberofvaluesbelow2.4}{Totalnumberofvalues}\times 100 \\ =\frac{29}{50}\times 100 \\ =58 \end{gathered}$$

Therefore, a value of 2.4 Mbps lies in the 58^th percentile.