Question

Suppose you have a distribution with 500 IQ scores, which are normally distributed with a mean of 100 and standard deviation of 15, and all scores are integers. Then one new data point is added which is far above any of the scores previously in your distribution by a considerable margin. For the following questions, report if there would be an increase, decrease, stay the same, or not enough information.

What happens to the value of the mean?

Answer 1

If one new data point is added to a distribution of 500 IQ scores, which are normally distributed with a mean of 100 and a standard deviation of 15, and the new data point is considerably higher than the previous scores, the value of the mean will generally increase.

The mean is a measure of central tendency, and adding a significantly higher score will pull the mean in the direction of that high score. Therefore, in most cases, the mean will increase as a result of adding this outlier.

Answer 2

The number of scores greater than 200 will increase. Option A is answer.