Question

the following are the tolls of men by women in an experiment including speed - dating. use the given data to construct a boxplot and identify the 5 - number summary.
30 35 45 45 55 55 65 65 65 65 65 75 85 90 90 90 100 100 100 100

the 5 - number summary is , , , and
(use ascending order. type integers or decimals. do not round.)

Explanation:

Step1: Sort the data

30, 35, 45, 45, 55, 55, 65, 65, 65, 65, 65, 75, 85, 90, 90, 90, 100, 100, 100, 100

Step2: Find the minimum

The minimum value is 30.

Step3: Find the first - quartile (Q1)

There are 20 data points. The position of Q1 is $\frac{n + 1}{4}=\frac{20+1}{4}=5.25$. So, Q1 is $0.75\times55 + 0.25\times65=57.5$.

Step4: Find the median (Q2)

The position of the median is $\frac{n + 1}{2}=\frac{20 + 1}{2}=10.5$. So, Q2 is $\frac{65+65}{2}=65$.

Step5: Find the third - quartile (Q3)

The position of Q3 is $\frac{3(n + 1)}{4}=\frac{3\times(20 + 1)}{4}=15.75$. So, Q3 is $0.25\times90+0.75\times90 = 90$.

Step6: Find the maximum

The maximum value is 100.

Answer:

30, 57.5, 65, 90, 100