To find the relative frequencies by column, we calculate the ratios of each value and the total in that column.
Relative Frequencies:
Allowance
No Allowance
Total
Chores
13; 0.72
3; 0.43
16
No Chores
5; 0.28
4; 0.57
9
Total
18; 1.00
7; 1.00
25
Example Solution: Most of the students who receive an allowance do chores. The students who do not receive an allowance are split more evenly.
Practice makes perfect
We want to find relative frequencies by column. To do so, we will start by completing the given table.
Allowance
No Allowance
Total
Chores
13;
3;
No Chores
5;
4;
Total
Let's find the sums of each row and column.
Chores:& 13 + 3 = 16
No Chores:& 5 + 4 = 9
Allowance:& 13 + 5 = 18
No Allowance:& 3 + 4 = 7
Let's write the newly obtained information in our table.
Allowance
No Allowance
Total
Chores
13;
3;
16
No Chores
5;
4;
9
Total
18
7
We have two ways of calculating the grand total. We can add the number of students who do chores to the number of students who do not do chores, or we can add the students who receive an allowance to the students who do not receive an allowance. These two numbers must be the same!
Grand total
l 16+ 9 = 25 18+ 7= 25 ✓
Now, we can complete our table!
Allowance
No Allowance
Total
Chores
13;
3;
16
No Chores
5;
4;
9
Total
18
7
25
To find the relative frequencies by column, we calculate the ratios of each value and the total in that column. We will round the results to the nearest hundredth.
Allowance
No Allowance
Total
Chores
13; 13/18≈ 0.72
3; 3/7≈ 0.43
16
No Chores
5; 5/18 ≈ 0.28
4; 4/7≈ 0.57
9
Total
18; 18/18 = 1.00
7; 7/7 = 1.00
25
Looking at the relative frequencies, we can say that most of the students who receive an allowance do chores. The students who do not receive an allowance are split more evenly.
