Question

Suppose your score on an exam is 76 and the exam scores are normally distributed with a mean of 70. Which is better for you: A distribution with a small standard deviation or a large standard deviation? Explain.

Answer 1

Standard deviation is a measure to analyse the variation of a set of values.

A lower standard deviation indicate the values are closed to the mean value, and a higher standard deviation indicate the values are spread out from the mean value.

Here, a mean of 70 with a higher standard deviation means the score of others are spread out over a wider range from 70. This means that some others score can be higher than 76.

And , a mean of 70 with a lower standard deviation means the score of all others are close or equal to 70.This means that, a score of 76 will be among one of the top scores when standard deviation is smaller.

So , The distribution with small standard deviation will be better.