Question

Sleep Q₃ For a sample of 80 sleep times, approximately how many of those times are less than Q₃?

Short answer

The observations of 60 sleep times in 80 would be less than the third quartile.

Step-by-step solution

Given information

The number of sampled sleep times is 80 (n,say).

Meaning of the third quartile

The third quartile is a variation measure expressing the observation in the data set that contains 75% values below it when arranged in ascending order.

The value is represented by $Q_3$.

Identify the third quartile

Here, 75% observations must fall under the third quartile of sleep time.

The count of observations of the sleep time less than $Q_3$ is computed below.

$$\begin{gathered} 75\%\text{of}80=\frac{75}{100}\times 80 \\ =60 \end{gathered}$$

Thus, approximately 60 observations are less than the third quartile.