Question

The scores of a test had a mean of 78, median of 84, standard deviation of 7, and interquartile range of 19. To boost each student's grade, 3 points of extra credit are added to each test.

For the test scores with extra credit:

The mean is

standard deviation is

The median is

the interquartile range is

Answer 1

The new mean is 81, the standard deviation remains 7, the new median is 87, and the interquartile range remains 19 after adding 3 points of extra credit to each test score.

Step-by-step explanation:

When 3 points of extra credit are added to each test score, the mean increases by 3 points, so the new mean is 81 (78 + 3).

The standard deviation does not change when a constant is added to each score, so it remains 7.

The median, like the mean, also increases by 3 points to 87 (84 + 3), and the interquartile range remains the same at 19 because it is a measure of spread that is not affected by adding a constant to every score.