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 4 5 5 9 3 3 7 7
8 7 2 9 0 9 3 4 8
6 5 9 0 2 5 7 9 9
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 hours per day.
(type an integer or decimal rounded to one decimal place as needed)

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: Locate $Q_3$ on the box - and - whisker plot

Since the box - and - whisker plot is not provided here, assume we have ordered the data set of 28 values. First, order the data from smallest to largest. For a data set of size $n = 28$, the position of $Q_3$ is calculated as $i=\frac{3(n + 1)}{4}=\frac{3\times(28+1)}{4}=\frac{3\times29}{4}=21.75$. The value of $Q_3$ is the 22nd value when the data is ordered.

Step3: Find the 22nd value in the ordered data set

Order the data: 0, 0, 1, 2, 2, 3, 3, 3, 4, 4, 5, 5, 5, 5, 6, 7, 7, 7, 7, 8, 8, 9, 9, 9, 9, 9, 11. The 22nd value in the ordered data set is 8.

Answer:

8