A quiz consists of 10 questions. Each question is marked either “right” or “wrong.” For each student in the class, the instructor keeps a record of the number of right answers the student got. In the class, the average number of right answers is 6.2 and the SD of the number of right answers is 1.4.

Question

(1) Find the average number of wrong answers.

(2) Find the SD of the number of wrong answers.

Answer 1

1. 10 - 6.2 = ?

2. 1.4

Answer 2

1.3.8
2.1.4

Answer 3

"number wrong" = 10 - "number right" is a linear transformation that says, "Multiply the list by -1, then add 10." The addition does nothing to the SD, and the multiplication by -1 multiplies the SD by |-1|=1. So there's no change to the SD. In terms of the histogram, the histogram for "number wrong" is a flip of the histogram for "number right," so the SD stays the same.