Q. 2.114 - Elementary Statistics

Question

Age 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 labelled 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.

Step-by-Step Solution

Answer

(a)

 

(b)

(c) The total number of males and females in the data set is represented by the row total.

The total column reflects the total number of participants in each age group in the data set.

(d) The total of the rows and columns will be equal. 

(e)

(f) $16\%,24\%,20\%,26\%,8\%,6\%$.

Part (a) Step 1 : Given information

The given data is 

Part (a) Step 2: Explanation

The group of the data is 

Part (b) Step 1: Given information

The given data is 

Part (b) Step 2: Explanation

The frequencies in each row and column of your table is

Part (c) Step 1: Given information

The given data is 

Part (c) Step 2: Explanation

The total number of males and females in the data set is represented by the row total.

The total column reflects the total number of participants in each age group in the data set.

Part (d) Step 1: Given information

The given data is 

Part (d) Step 2: Explanation

Because they represent the same thing, the total of the rows and columns will be equal.

Part (e) Step 1: Given information

The given data is 

Part (e) Step 2: Explanation

The table that shows the relative frequencies for the data is 

Part (f) Step 1: Given information

The given data is 

Part (f) Step 2: Explanation

Males under the age of $21$ accounts for $16\%$ of the individuals in the data set.

Females under the age of $21$accounts for $24\%$ of the persons in the data set. Males between the ages of $21$and $25$ account for $20\%$ of the persons in the data set.

Females between the ages of $21$ and $25$ make up $26\%$ of the persons in the data set.

Males above the age of $25$ accounts for $8\%$ of the persons in the data set. Females over the age of $25$ account for $6\%$ of the participants in the data set.