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.

P25

Short answer

The data speed corresponding to the 25^th percentile is 0.5 Mbps.

Step-by-step solution

Given information 

Sprint airport data speeds are provided.

The sample size is equal to 50.

Mapping method of percentile to value 

• Convert percentile and count of observations to a locator value L as follows:

$L=\frac{k}{100}\times n$

Here, L is the locator of the value;

k is the percentile of the value;

n is the total number of values.

• When L is a whole number, the mid-value corresponding to the $L^{th}$value and the ${\left(L+1\right)}^{th}$ is calculated and used as observation corresponding to kth percentile.

• When L contains decimals, the location of the data value in the sample is the rounded L value (to the next whole number) to obtain the observation corresponding kth percentile.

Calculation to obtain the observation

The locator value for the 25^th percentile in a data set of 50 observations is as follows:

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

The data value corresponding to the 13^th observation from the sample is 0.5 Mbps.

Therefore,the data speed corresponding to the 25^th percentile is 0.5 Mbps.