# Question: The following bivariate data on age in years and gender

The following bivariate data on age (in years) and gender were obtained from the students in a freshman calculus course. The data show, for example, that the first student on the list is 21 years old and is a male.

a. Group these data in the following contingency table. For the first student, place a tally mark in the box labeled by the "21-25" column and the "Male" row, as indicated. Tally the data for the other 49 students.

b. Construct a table like the one in part (a) but with frequencies replacing the tally marks. Add the frequencies in each row and column of your table and record the sums in the proper "Total" boxes.

c. What do the row and column totals in your table in part (b) represent?

d. Add the row totals and add the column totals. Why are those two sums equal, and what does their common value represent?

e. Construct a table that shows the relative frequencies for the data. (Hint: Divide each frequency obtained in part (b) by the total of 50 students.)

f. Interpret the entries in your table in part (e) as percentages.

Relative-Frequency Polygons. Another graphical display commonly used is the relative-frequency polygon. In a relativefrequency polygon, a point is plotted above each class mark in limit grouping and above each class midpoint in cutpoint grouping at a height equal to the relative frequency of the class. Then the points are connected with lines. For instance, the grouped days-to-maturity data given in Table 2.10(b) on page 55 yields the following relative-frequency polygon.

a. Group these data in the following contingency table. For the first student, place a tally mark in the box labeled by the "21-25" column and the "Male" row, as indicated. Tally the data for the other 49 students.

b. Construct a table like the one in part (a) but with frequencies replacing the tally marks. Add the frequencies in each row and column of your table and record the sums in the proper "Total" boxes.

c. What do the row and column totals in your table in part (b) represent?

d. Add the row totals and add the column totals. Why are those two sums equal, and what does their common value represent?

e. Construct a table that shows the relative frequencies for the data. (Hint: Divide each frequency obtained in part (b) by the total of 50 students.)

f. Interpret the entries in your table in part (e) as percentages.

Relative-Frequency Polygons. Another graphical display commonly used is the relative-frequency polygon. In a relativefrequency polygon, a point is plotted above each class mark in limit grouping and above each class midpoint in cutpoint grouping at a height equal to the relative frequency of the class. Then the points are connected with lines. For instance, the grouped days-to-maturity data given in Table 2.10(b) on page 55 yields the following relative-frequency polygon.

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