We are given an incomplete two-way frequency table. To complete it, we need to recognize that the last row and the last column show totals. Let a be the total number of students who got a pass grade and b be the total number of students who did not study
Preparation
Grade
Studied
Did Not Study
Total
Pass
6
a
Fail
10
Total
38
b
50
Note that the sum of the Total row and the Total column should add up to 50, the total number of students. With this information, we can find the values of a and b.
Pass Grade:&& a&= 50- 10= 40
Did Not Study:&& b&= 50- 38= 12
We can substitute those values in our table. Next, let c be the number of students who failed and did not study whereas d will be the number of students who passed and studied.
Preparation
Grade
Studied
Did Not Study
Total
Pass
d
6
40
Fail
c
10
Total
38
12
50
Once again, we will use the values from the Total row and the Total column to find the values of c and d.
Failed And Did Not Study:&& c&= 12-6= 6
Passed And Studied:&& d&= 40-6= 34
We can substitute those values in our table. Finally, let e be the number of students who failed but studied.
Preparation
Grade
Studied
Did Not Study
Total
Pass
34
6
40
Fail
e
6
10
Total
38
12
50
We can chose either 38 or 10 value in the Totals to calculate the value of e. Remember that they must be the same!
Using Row Total:&& e&= 10- 6= 4
Using Column Total:&& e&= 38- 34= 4
Since we got the same answer in both cases, we can be sure we made no mistakes. With this in mind, we can finish our table!
