Given the table showing the number of students who do or do not perform chores, and who do or do not receive an allowance, we can add the numbers along the rows and columns, as shown in the diagram below:
Now, that we have summed the numbers along the vertical and horizontal directions, we can now proceed to answer the questions asked.
a.) The total number of students who do chores is equal to the horizontal sum of the numbers in the 'DO CHORES' row. This value is 16
Thus, 16 students do chores
b) The relative frequency of the students that do chores and get an allowance to the number of students that do chores is simply the ratio of the value in the cell that represents an intersection of the first 'DO CHORES' row, and the first 'ALLOWANCE' column, to the value that represents the sum of all the students that do chores ( i.e, the value at the end of the first row).
Thus, this is equal to = 13/16
Therefore, 13/16 is the relative frequency of the students that do chores and get an allowance to the number of students that do chores
c) The relative frequency of the students that do not do chores nor get an allowance to the total number of students, is simply the ratio of the value in the cell that represents an intersection of the second 'DO NOT DO CHORES' row, and the second 'NO ALLOWANCE' column, to the sum of the values in the last row or the last column.
Thus, this is equal to = 4/( 18 + 7) OR 4/(16 + 9) both of which is still 4/25
Therefore, 4/25 is the relative frequency of the students that do not do chores nor get an allowance to the total number of students.
d) The students who do not do chores are a total of 9
Of this 9, the number of students that do receive their allowance fall under the 'ALLOWANCE' column, and is equal to 5.
Therefore, expressed as a percentage of those who do not do their chores, the students who do not get an allowance are = (5/9) * 100 = 55% ( to the nearest whole number)
Thus 55% of students who do not do chores do not get an allowance