Question

joeys first 14 quiz grades in a marking period had a mean of 85 and a standard deviation of 8. (a) suppose joey makes an 85 on the next quiz. would the standard deviation of his 15 quiz scores be greater than, equal to, or less than 8? justify your answer. the standard deviation will be blank 8. the quiz score of 85 is blank the mean and would have a deviation from the mean of blank. this will blank the standard deviation, which represents the typical amount that the quiz scores vary from the mean. (b) suppose instead that joey has an unexcused absence and makes a 0 on the next quiz. would the standard deviation of his 15 quiz scores be greater than, equal to, or less than 8? justify your answer. the standard deviation will be blank 8. the quiz score of 0 is blank the mean and would have a deviation from the mean that is blank. this will blank the standard deviation, which represents the typical amount that the quiz scores vary from the mean.

Explanation:

Step1: Recall standard - deviation concept

Standard deviation measures the typical deviation from the mean.

Step2: Analyze case (a)

The original mean is 85. When Joey scores 85 on the next quiz, the deviation of this new score from the mean is $85 - 85=0$. Adding a data - point with a deviation of 0 from the mean will decrease the overall standard deviation. Since the previous standard deviation was 8, the new standard deviation will be less than 8.

Step3: Analyze case (b)

The original mean is 85. The new score of 0 has a deviation from the mean of $0 - 85=- 85$. Adding a data - point with a large deviation from the mean will increase the overall standard deviation. So the new standard deviation will be greater than 8.

Answer:

(a) The standard deviation will be less than 8. The quiz score of 85 is equal to the mean and would have a deviation from the mean of 0. This will decrease the standard deviation, which represents the typical amount that the quiz scores vary from the mean.
(b) The standard deviation will be greater than 8. The quiz score of 0 is less than the mean and would have a deviation from the mean that is large. This will increase the standard deviation, which represents the typical amount that the quiz scores vary from the mean.