Step by step method for calculation of variance are included in the answer.

A calculus instructor uses computer aided instruction and allows students to take the midterm exam as many times as needed until a passing grade is obtained.  Following is a record of the number of students in a class of 20 who took the test each number of times.
                          

Students        Number of tests
10                        1
7                         2
2                         3
1                         4

Compute the variance.