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.
(1) Find the average number of wrong answers.
(2) Find the SD of the number of wrong answers.
1. 10 - 6.2 = ?
2. 1.4
1.3.8
2.1.4
"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.
To solve this problem, we need to understand that the total number of questions on the quiz is fixed at 10. Therefore, the number of wrong answers for each student can be calculated by subtracting the number of right answers from 10.
Let's solve each part of the problem step by step:
(1) Finding the average number of wrong answers:
To find the average number of wrong answers, we need to subtract the average number of right answers from the total number of questions.
Average number of wrong answers = Total number of questions - Average number of right answers
Average number of wrong answers = 10 - 6.2
Average number of wrong answers = 3.8
Therefore, the average number of wrong answers is 3.8.
(2) Finding the standard deviation (SD) of the number of wrong answers:
To find the SD of the number of wrong answers, we need to use the SD of the number of right answers.
SD of the number of wrong answers = SD of the number of right answers
SD of the number of wrong answers = 1.4
Therefore, the SD of the number of wrong answers is 1.4.