To find the relative frequency by column, first calculate the sum the values in each column.
C
Practice makes perfect
We are given a two-way table that shows the amount of time students studied for a math test and the score they received.
Less Than 30 Minutes
More Than 30 Minutes
Score of 75 % or More
20
45
Score Below 75 %
33
27
We are asked to find the relative frequency by column of the students that studied more than 30 minutes and received a score of 75 % or more. Let's first find the sum of the values in each column.
Less Than 30 Minutes
More Than 30 Minutes
Score of 75 % or More
20
45
Score Below 75 %
33
27
Total
20+ 33=53
45+ 27=72
Now we will divide the numbers in each column by that column's total to find the relative frequencies by column.
Less Than 30 Minutes
More Than 30 Minutes
Score of 75 % or More
20;20/53≈ 0.38
45;45/72≈ 0.63
Score Below 75 %
33;33/53≈ 0.62
27;27/72≈ 0.38
Total
53
72
We found all relative frequencies by column! Finally, we want to identify the relative frequency of the students that studied more than 30 minutes and received a score of 75 % or more. Let's find it on our table.
Less Than 30 Minutes
More Than 30 Minutes
Score of 75 % or More
20;20/53≈ 0.38
45;45/72≈ 0.63
Score Below 75 %
33;33/3≈ 0.62
27;27/72≈ 0.38
Total
53
72
We can see that this relative frequency is equal to about 0.63. This result corresponds to the option C.
