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.

Q1

Short answer

The data speed corresponding to the first quartile is equal to 0.5 Mbps.

Step-by-step solution

Given information 

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

 Step 2: Steps for conversion of quartile to value 

The first quartileis the same as the 25^th percentile, that is,

$Q_1=P_{25}$

Therefore, the 25^th percentile value is required to becomputedto obtain the first quartile.

A percentile can be converted to a value in the following steps:

• Obtain $L=\frac{k}{100}\times n$.

Here, L is the locator of the value;

k is the percentile of the value;

n is the total number of values.

• If L is a whole number, the sum of the$L^{th}$ observation and the ${\left(L+1\right)}^{th}$observation from the sorted data is divided by 2, and the resulting value is the corresponding data value.

• If L is a decimal value, it is rounded to the next whole number. Hence, the rounded observation from the sorted data is treated as the data value.

Step 3: Compute the 25th percentile 

• Arrange the data values in ascending order.
• Find the total number of values.
• Apply the formula mentioned above to calculate the locator for k=25.

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

The data value corresponding to the 13^th observation from the arranged values is obtained as 0.5 Mbps.

Therefore,the data speed corresponding to the first quartile is equal to 0.5 Mbps.