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.

P40

Short answer

The data speed corresponding to the 40^th percentile is 1.05 Mbps.

Step-by-step solution

Given information 

The data shows 50 airport data speeds (in Mbps).

Steps to convert the percentile measure to an observation 

• The given formula is used to find the locator (L) of the value corresponding to $k^{th}$percentile and total value equal to n.

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

• The mid-value of the $L^{th}$observation and the ${\left(L+1\right)}^{th}$observation (from the sorted data) is computed and considered the data speed when L is a whole number.

• The value of L is rounded to the next whole number if it is not a whole number. Then, the $L^{th}$value is considered the data speed.

 Step 3: Compute the observation for the 40th percentile

For k equal to 40 and n equal to 50 in the formula, the L value is calculated as follows:

$$\begin{gathered} L=\frac{k}{100}\times n \\ =\frac{40}{100}\times 50 \\ =20 \end{gathered}$$

As L =20 is a whole number, select the 20^th and the 21^st values after arranging the values from lowest to greatest. The corresponding values are 1 and 1.1, respectively.

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

$$\begin{gathered} x=\frac{{20}^{th}obs+{21}^{th}obs}{2} \\ =\frac{1.0+1.1}{2} \\ =1.05 \end{gathered}$$

Therefore, the data speed equal to 1.05 Mbpscorresponds to the 40^th percentile.