Multiple Choice Select the best answer for Exercises 123–126.

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 84 was added to the distribution of scores, what would happen to the mean and standard deviation?

(a) Mean will increase, and standard deviation will increase.

(b) Mean will increase, and standard deviation will decrease.

(c) Mean will increase, and standard deviation will stay the same.

(d) Mean will decrease, and standard deviation will increase.

(e) Mean will decrease, and standard deviation will decrease.

The given information is:

The average result on a statistics test was 81, with a standard deviation of 9. On the day of the test, one student was missing, and his score was not factored into the equation.

We are provided with five options, we need to tell which statement is correct according to the given statement.

Since the previous student's score was 84 and the current mean was 81, he or she scored higher than the average. As a result, when it's added, it'll raise the average significantly.

Because the last student's score is not significantly different from the mean, the variance will most likely be reduced. The lesser the variance, the smaller the standard deviation, because standard deviation is the square root of variance.

Therefore, Option (b) "Mean will increase, and standard deviation will decrease" is correct.