Question

the following are the ratings of men by women in an experiment involving speed - dating. use the given data to construct a boxplot and identify the 5 - number summary.
3.0
4.0
4.5
5.0
6.0
6.0
6.5
6.5
6.5
6.5
6.5
7.5
8.0
8.5
8.5
8.5
9.0
10.0
10.0
10.0
the 5 - number summary is , , , , . (use ascending order. type integers or decimals. do not round.)

Explanation:

Step1: Arrange data in ascending order

3.0, 4.0, 4.5, 5.0, 6.0, 6.0, 6.5, 6.5, 6.5, 6.5, 6.5, 7.5, 8.0, 8.5, 8.5, 8.5, 9.0, 10.0, 10.0, 10.0

Step2: Find the minimum value

The minimum value is 3.0.

Step3: Find the first - quartile ($Q_1$)

There are $n = 20$ data points. The position of $Q_1$ is $\frac{n + 1}{4}=\frac{20+1}{4}=5.25$. So, $Q_1=6.0$.

Step4: Find the median ($Q_2$)

The position of the median is $\frac{n+1}{2}=\frac{20 + 1}{2}=10.5$. So, $Q_2=\frac{6.5+6.5}{2}=6.5$.

Step5: Find the third - quartile ($Q_3$)

The position of $Q_3$ is $\frac{3(n + 1)}{4}=\frac{3\times(20 + 1)}{4}=15.75$. So, $Q_3=8.5$.

Step6: Find the maximum value

The maximum value is 10.0.

Answer:

3.0, 6.0, 6.5, 8.5, 10.0