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

0.7 Mbps

Short answer

0.7 Mbps corresponds to the 34^th percentile.

Step-by-step solution

Given information 

A group of 50 airports was sampled for data speeds, measured in Mbps.

Meaning of percentile 

A percentileof an observation highlights the percentage of observations less than that given value.

Mathematically,

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

Computation for percentile equivalent of 0.7 Mbps

Steps to compute the percentile:

• Tabulate the values in increasing order.
• Compute the total number of data speeds.
• Compute the number of data speeds below 0.7 Mbps.
• Compute the percentile using the formula.

The percentile corresponding to 0.7 Mbps:

$$\begin{gathered} P_{0.7}=\frac{Numberofvaluesbelow0.7}{Totalnumberofvalues}\times 100 \\ =\frac{17}{50}\times 100 \\ =34 \end{gathered}$$

Therefore, 0.7 Mbps corresponds to the 34^th percentile.