Question

For a midterm exam, student scores from section 1 have a standard deviation of 15.5%, while student scores from section 2 have a standard deviation of 38.9%. This tells us that, as compared to section 1, in section 2:

a) There is less variability in scores.

b) There is more variability in scores.

c) The average score is higher.

d) The average score is lower.

Answer 1

The information on standard deviations indicates that section 2 has more variability in scores than section 1, as section 2's standard deviation is higher. Standard deviation does not provide information about the average score itself.

Step-by-step explanation:

When comparing student scores from two different sections with standard deviations of 15.5% and 38.9%, it's important to recall that the standard deviation is a measure of the variability, or dispersion, of a set of values. A low standard deviation indicates that the values tend to be close to the mean (average) of the set, while a high standard deviation indicates that the values are spread out over a wider range. Therefore, as compared to section 1, in section 2 there is more variability in scores because the standard deviation is higher (38.9% vs 15.5%).

It's also important to note that the standard deviation does not directly tell us anything about the average score of the students. Option c) 'The average score is higher' and option d) 'The average score is lower' cannot be determined from the information about the standard deviation alone. The correct answer to the original question is b) There is more variability in scores.