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.

P85

Short answer

The data speed equal to 8.2 Mbpscorresponds to the 85^th percentile

Step-by-step solution

Given information 

A sample containing sprint airport speeds is given.

The sample has 50 values.

Procedure to obtain the observation corresponding to the kth percentile 

The formula stated below is used to compute the value of the locator (L):

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

Here,

the value of the percentile is denoted by k;

the size of the sample is denoted by n.

There are two possibilities:

• L is a whole number: The mid-value of the$L^{th}$ value and the ${\left(L+1\right)}^{th}$value (from the sorted sample) is the value required.

• L is a decimal: The value is rounded to the succeeding whole number. It is used to locate the value from the sample.

Step 3: Compute the 85th percentile for the dataset

The locator value corresponding to the 85^th percentile is as follows:

$$\begin{gathered} L=\frac{k}{100}\times n \\ =\frac{85}{100}\times 50 \\ =42.5 \\ \approx 43\left(\text{rounded}\text{to}\text{the}\text{next}\text{whole}\text{number}\right) \end{gathered}$$

The 43^rd value from the sample corresponds to 8.2 Mbps.

Therefore,the data speed equal to 8.2 Mbpscorresponds to the 85^th percentile.