Question

Mrs. Lemos' Block 4 Math 2 class had an average of 60% on a practice final exam with a standard deviation of 7.6. Mrs. Lemos gave each student an additional 10 points on their exam as a curve. Which of the following is always true?

The mean will increase by 10 points and the standard deviation will decrease.

The mean will remain the same and the standard deviation will increase.

The mean will remain the same and the standard deviation will remain the same.

The mean will increase by 10 points and the standard deviation will remain the same.

Answer 1

The mean will increase by 10 points and the standard deviation will remain the same.

When a constant value is added to every value in a data set, the mean of the data set will increase by the same amount as the value added. For example, if Mrs. Lemos' class had an average of 60% on the practice final exam, and she added 10 points to each student's exam score, the class's new average will be 60% + 10 points = 70%.

The standard deviation, on the other hand, measures the spread of the data around the mean. Adding a constant value to every value in a data set will not affect the spread of the data, so the standard deviation will remain the same.

Therefore, in this situation, the mean will increase by 10 points and the standard deviation will remain the same.