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.

P60

Short answer

The data speed corresponding to the 60^th percentile is 2.45 Mbps.

Step-by-step solution

Given information 

The data given contains a set of 50 airport data speeds (in Mbps).

Steps to obtain the value corresponding to the given percentile 

The percentileof a value indicates the location of the value relative to all the other observations.

The data value corresponding to a given percentile is calculated in the following steps:

• Compute $L=\frac{k}{100}\times n$.

Here, L is the locator of the value;

k is the percentile of the value;

n is the total number of values.

• If L turns out to be a whole number, compute the average of the $L^{th}$observation and the${\left(L+1\right)}^{th}$ observation from the sorted data. This average is treated as the data value corresponding to the given percentile.

• If L contains decimals, the value of L is rounded to the next whole number.

• Now, the ${\left(L\right)}^{th}$value is the data value corresponding to the given percentile.

Step 3: Follow the steps to find the value corresponding to the 60th percentile

Sort the values from the smallest to the largest, andenumerate the total number of observations.

$$\begin{gathered} L=\frac{k}{100}\times n \\ =\frac{60}{100}\times 50 \\ =30 \end{gathered}$$

As L =30 is a whole number, locate the 30^th and the 31^st observation from the sorted data, and divide their sum by 2, which is 2.4 and 2.5, respectively.

The data value (x) is computed as follows:

$$\begin{gathered} x=\frac{{30}^{th}obs+{31}^{st}obs}{2} \\ =\frac{2.4+2.5}{2} \\ =2.45 \end{gathered}$$

Therefore,the data speed corresponding to the 60^th percentile is 2.45 Mbps.