Question

the following are the ratings of men by women in an experiment involving speed dating. use the given data to construct a box - plot and identify the 5 - number summary. 1.0 1.5 2.5 3.5 3.5 3.5 4.5 4.5 4.5 4.5 4.5 5.5 6.0 6.5 6.5 6.5 7.0 7.0 7.0 7.0 the 5 - number summary is □,□,□,□, and □. (use ascending order. type integers or decimals. do not round.)

Explanation:

Step1: Sort the data

1.0, 1.5, 2.5, 3.5, 3.5, 3.5, 4.5, 4.5, 4.5, 4.5, 4.5, 5.5, 6.0, 6.5, 6.5, 6.5, 7.0, 7.0, 7.0, 7.0

Step2: Find the minimum

The minimum value is 1.0

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 $Q_1=3.5$ (the 5th value plus 0.25 of the difference between the 5th and 6th values, but since they are both 3.5, $Q_1 = 3.5$)

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 $Q_2=\frac{4.5 + 4.5}{2}=4.5$

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 $Q_3 = 6.5$ (the 15th value plus 0.75 of the difference between the 15th and 16th values, but since they are both 6.5, $Q_3=6.5$)

Step6: Find the maximum

The maximum value is 7.0

Answer:

1.0, 3.5, 4.5, 6.5, 7.0