Question

Forty students have completed a math test. The mean score was 60 and a mean absolute deviation was 12. The teacher has decided to adjust the scores by adding 5 points to each test score. Calculate the new mean and mean absolute deviation.

Answer 1

new mean = 65

new MAD= 12

Explanation:

The teacher adds 5 points to each data. This action will simply increase the mean by 5 because each data have 5 more value. Let the number of data is x, then the new mean will be:

old mean = total score/x

new mean = (total score + 5*x) / x

new mean = (total score/x) + 5

new mean = old mean + 5 = 60 +5 = 65

Mean absolute deviation (MAD) is the average difference of each data with the mean. Each data increased by 5 and the mean is increased by 5 too. The difference will not be changed since both increased by 5. So, new MAD equal to old MAD.