Question

The scores on a statistics test had a mean of 81 and a standard deviation of 9. One student was absent on the test day and his score wasn't included in the calculation. If his score of 78 was added to the distribution of scores, what would happen to the mean and standard deviation?
A) Mean will increase, standard deviation will decrease.

B) Mean will increase, standard deviation will increase.

C) Mean will decrease, standard deviation will stay the same.

D) Mean will decrease, standard deviation will increase.

E) Mean will decrease, standard deviation will decrease.

Answer 1

Answer: E) Mean will decrease, standard deviation will decrease

Step-by-step explanation:

Initial mean = 81

Initial standard deviation = 9

New score = 78

Taking a look at the initial mean(averahe) score, which is 81 and the new score to be added to the initial scores, the initial average is greater than the new score. Hence, this will result in a decrease in the new mean score after adding the new score of 78.

Also, taking a look at the standard deviation which is 9, we can conclude that the variability in initial scores from the mean scores is high. However, the new score of 78 and the initial mean are very close, and tend to low variation. Hence, adding the new score will lead to a decrease in variability and hence a decrease in the value of standard deviation.