Question

the data show the number of hours spent studying per day by a sample of 28 students. use the box - and - whisker plot below to answer parts (a) through (c) below.
1 11 5 4 4 5 3 7 5 6
9 5 1 9 7 3 6 9 4
6 5 2 8 0 8 9 6 4
click the icon to view the box - and - whisker plot
(a) about 75% of the students studied no more than how many hours per day?
about 75% of the students studied no more than 7.5 hours per day. (type an integer or decimal rounded to one decimal place as needed.)
(b) what percent of the students studied more than 5 hours per day?
about 75% of the students studied more than 5 hours per day.

Explanation:

Step1: Recall box - and - whisker plot properties

In a box - and - whisker plot, the third quartile ($Q_3$) represents the value below which 75% of the data lies.

Step2: Analyze part (a)

For part (a), we are looking for the value such that about 75% of the students studied no more than that number of hours. This is the third - quartile value. Given the answer for part (a) is 7.5 hours.

Step3: Analyze part (b)

In a box - and - whisker plot, the median ($Q_2$) divides the data into two halves. If the median is 5 hours, then the percentage of data above the median is 50% of the data above the first half. Since the box - and - whisker plot divides the data into four equal - sized parts (quartiles), and the median is 5 hours, the percentage of students who studied more than 5 hours is 50% of the upper half of the data plus the lower half of the data. The lower half of the data is 50% and the upper half of the data above the median is 25%, so in total about 75% of the students studied more than 5 hours.

Answer:

(a) 7.5
(b) 75%