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. 2.0 2.5 3.0 4.0 4.5 4.5 5.0 5.0 5.0 5.0 5.0 6.0 6.5 6.5 6.5 6.5 7.0 8.0 9.0 10.0 the 5 - number summary is □,□,□,□, and □. (use ascending order. type integers or decimals. do not round.)

Explanation:

Step1: Arrange data in ascending order

The data is already in ascending order: 2.0, 2.5, 3.0, 4.0, 4.5, 4.5, 5.0, 5.0, 5.0, 5.0, 5.0, 6.0, 6.5, 6.5, 6.5, 6.5, 7.0, 8.0, 9.0, 10.0

Step2: Find the minimum value

The minimum value is the first value in the ordered - data set. So, the minimum is 2.0.

Step3: Find the first quartile ($Q_1$)

There are $n = 20$ data points. The position of $Q_1$ is $L_{Q_1}=\frac{n + 1}{4}=\frac{20+1}{4}=5.25$.
$Q_1=4.5+(0.25)\times(5.0 - 4.5)=4.5 + 0.125=4.625$.

Step4: Find the median ($Q_2$)

The position of the median for $n = 20$ (an even - numbered data set) is $\frac{n}{2}=10$ and $\frac{n}{2}+1 = 11$.
The median $Q_2=\frac{5.0 + 5.0}{2}=5.0$.

Step5: Find the third quartile ($Q_3$)

The position of $Q_3$ is $L_{Q_3}=\frac{3(n + 1)}{4}=\frac{3\times(20 + 1)}{4}=15.75$.
$Q_3=6.5+(0.75)\times(6.5 - 6.5)=6.5$.

Step6: Find the maximum value

The maximum value is the last value in the ordered - data set. So, the maximum is 10.0.

Answer:

2.0, 4.625, 5.0, 6.5, 10.0