Chapter 1.3, Problem 124E

To determine

Effect on mean and standard deviation, if the score of 84 was added to the distribution of scores.

Answer to Problem 124E

Mean will increase, and standard deviation will decrease.

Explanation of Solution

Given information:

Mean, $\mu =81$

Standard deviation, $\sigma =9$

Last student’s score, $x=84$

The last student’s score is 84.

Whereas,

The current mean is 81.

However,

The student’s score is above the average.

Thus,

When 84 is added, it will slightly increase the mean.

Also,

The last student’s score is not dramatically different from the mean.

Thus,

It will probably lessen the variance.

We know that

The standard deviation is the square root of the variance.

Thus,

Smaller the variance, smaller will be the standard deviation.

Conclusion:

Addition of 84 to the mean slightly increases the mean.

With less variance, the standard deviation will decrease.

Thus,

Mean will increase, and standard deviation will decrease.

Hence,

The correct answer is option (b).