100 Points Sherelle and Venita find two bags of coins in their grandmother’s attic. Each girl selects a bag, takes a random sample of 20 coins from that bag, and lists the dates of those coins as the number of years since 1900. Here are the results.
Sherelle: 72, 56, 81, 84, 75, 26, 39, 62, 65, 66, 85, 71, 74, 68, 73, 66, 83, 60, 58, 72
Venita: 45, 65, 73, 57, 79, 66, 69, 75, 51, 44, 53, 69, 58, 77, 51, 55, 53, 78, 70, 62

1. Find the five-number summary of each data set. Then construct box-and-whisker plots of the data sets. Draw both plots above the same number line. Label the plots with the girls’ names.

2. Solve.
(a) Contrast the shapes of the data sets displayed in the box-and-whisker plots in Question 1. Explain what the difference in the shapes means in context of the situation.
(b) Compare the spread of the data sets. Discuss both the overall spread and the spread within the boxes.
(c) Use an appropriate measure of central tendency to compare the center of the data sets. Explain what the difference in those measures means in context of the situation.

3. Sherelle and Venita’s grandmother said that one of the bags has a coin from 1916.
(a) What reasons might Sherelle give for saying that the 1916 coin is most likely in her bag?
(b) What reasons might Venita give for saying that the 1916 coin is most likely in her bag?
(c) Whose bag do you think is more likely to contain the 1916 coin? Explain your reasoning.