the following are the ratings of men by women in an experiment involving speed dating. use the given data to…

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.)

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.)

Answer

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