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

13.0 Mbps

Short answer

The value of data speed equal to 13.0 Mbps is in the 90^th percentile.

Step-by-step solution

Given information 

A sample of 50 data speeds is listed.

Define percentile

A percentileof a data point is the proportion of values in the dataset lower than the specific data point.

The formula for the percentile of value x:

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

For example,if a value is in the 26^th percentile, it shows that 26% of observations lie below that value.

Compute the value of percentile corresponding to 13 Mbps

Steps to be followed to find the percentile measure:

• Sort the data speeds in ascending order.
• Calculate the total number of observations.
• Calculate the number of observations below 13.0.
• Calculate the percentile as shown below:

The percentile corresponding to 13 Mbps data speed is as follows:

$$\begin{gathered} P_{13.0}=\frac{Numberofvaluesbelow13.0}{Totalnumberofvalues}\times 100 \\ =\frac{45}{50}\times 100 \\ =90 \end{gathered}$$

Therefore, 13.0 Mbps corresponds to the 90^th percentile.