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.

P50

Short answer

The data speed equal to 1.6 Mbps is in the 50^th percentile.

Step-by-step solution

Given information 

The data is recorded for 50 airport data speeds (in Mbps).

Method to find observation corresponding to the percentile value

• For $k^{th}$percentile and sample size equal to n, the locator (L) of the data value is calculated using the expression written below:

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

• If the calculated value of L is a whole number, the sum of the$L^{th}$ and the ${\left(L+1\right)}^{th}$values are obtained from the data when it is arranged in increasing order. The average of two values is the required data value.

• If the calculated value of L is a decimal number, it is first rounded to the subsequent whole number, and the ${\left(L\right)}^{th}$observation is the required data value.

Computation using the above methods

For k equal to 50 and n equal to 50, the L value is calculated as follows:

$$\begin{gathered} L=\frac{k}{100}\times n \\ =\frac{50}{100}\times 50 \\ =25 \end{gathered}$$

As L = 25 is a whole number, choose the 25^th and the 26^th values after arranging the values from the lowest to the greatest.

The corresponding values are 1.6 and 1.6, respectively.

The following computation is done to calculate the data speed (x):

$$\begin{gathered} x=\frac{{25}^{th}obs+{26}^{th}obs}{2} \\ =\frac{1.6+1.6}{2} \\ =1.6 \end{gathered}$$

Therefore,the data speed equal to 1.6 Mbpsis equivalent to the 50^th percentile.