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.
1.0 2.0 2.5 2.5 2.5 2.5 3.5 3.5 3.5 3.5 3.5 4.0 5.0 6.0 6.0 6.0 6.5 6.5 7.0 8.0
the 5 - number summary is (square,square,square,square,) and (square).
(use ascending order. type integers or decimals. do not round.)

Explanation:

Step1: Arrange data in ascending order

The data is already in ascending order: 1.0, 2.0, 2.5, 2.5, 2.5, 2.5, 3.5, 3.5, 3.5, 3.5, 3.5, 4.0, 5.0, 6.0, 6.0, 6.0, 6.5, 6.5, 7.0, 8.0

Step2: Find the minimum value

The minimum value is the first value in the ordered - set. So, the minimum is 1.0.

Step3: Find the first quartile ($Q_1$)

There are $n = 20$ data points. The position of $Q_1$ is $L_{Q_1}=\frac{n + 1}{4}=\frac{20+1}{4}=5.25$.
The first quartile is $Q_1=2.5+(0.25)\times(3.5 - 2.5)=2.5 + 0.25=2.75$.

Step4: Find the median ($Q_2$)

The position of the median for $n = 20$ (an even - numbered data set) is between the $\frac{n}{2}=10$th and $\frac{n}{2}+1 = 11$th ordered values.
$Q_2=\frac{3.5+3.5}{2}=3.5$

Step5: Find the third quartile ($Q_3$)

The position of $Q_3$ is $L_{Q_3}=\frac{3(n + 1)}{4}=\frac{3\times(20 + 1)}{4}=15.75$.
$Q_3=6.0+(0.75)\times(6.5 - 6.0)=6.0+0.375 = 6.375$

Step6: Find the maximum value

The maximum value is the last value in the ordered - set. So, the maximum is 8.0.

Answer:

1.0, 2.75, 3.5, 6.375, 8.0