Q. 2.114 - Elementary Statistics

Question

The following bivariate data on age (in years) and gender were obtained from 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 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 total 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.

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

Step-by-Step Solution

Answer

Part a. The group of the data is shown in figure \(1\).

Part b. The table is shown in figure \(1\).

Part c. The row total represents the number of males and number of females in the data set.

The column total represents the number of the people in the data set in each age category.

Part d. The sum for both is equal.

Part e. The table for relative frequency of data is shown in table \(1\)

Part f. Refer to the explanation.

Part a. Step 1. Given information

The given table:

Part a. Step 2. Explanation

The following figure gives the requires data:

Part b. Explanation

The following figures gives the required data:

Part c. Step 1. Explanation

The row total represents the number of males and number of females in the data set.

The column total represents the number of the people in the data set in each age category.

Part d. Step 1. Explanation

The sum of the total of rows and column will be equal because they represents the same thing.

Part e. Step 1. Explanation

Divide each value in the table in figure \(1\) by \(50\) then,

	Under \(21\)	\(21-25\)	Over \(25\)	Total
Male	\(0.16\)	\(0.20\)	\(0.08\)	\(0.44\)
Female	\(0.24\)	\(0.26\)	\(0.06\)	\(0.56\)
Total	\(0.40\)	\(0.46\)	\(0.14\)	\(1\)

Part f. Step 1. Explanation

Consider table \(1\),

\(16%\) of the individuals in the data set are males younger than \(21\) years old.

\(24%\) of the individuals in the data set are females younger than \(21\) years old.

\(20%\) of the individuals in the data set are males between \(21\) and \(25\) years old.

\(26%\) of the individuals in the data set are females between \(21\) and \(25\) years old.

\(8%\) of the individuals in the data set are males over \(25\) years old.

\(6%\) of the individuals in the data set are females over \(25\) years old.