The way the data sets are given makes the problem more confusing. Let's write them in a more conventional way:
Set A:
61, 61, 62, 65, 70, 71, 75, 81, 82, 90
Set B:
59, 63, 69, 70, 73, 73, 76, 77, 78, 83
The beauty of doing this is you can more easily read off the numbers when doing the computations. It's also easier for computer packages and Excel too. Now let's get to work.
1) A data set's mean is to add all the things in the set and divide by the number of items in the set. Each set has 10 items.
Thus, mean of set A = (61 + 61 + 62 + 65 + 70 + 71 + 75 + 81 + 82 + 90) / 10
= 718 / 10 = 71.8
Mean of set B = (59 + 63 + 69 + 70 + 73 + 73 + 76 + 77 + 78 + 83)/10
=721/10 = 72.1
2) Mean Absolute Deviation is found in this way:
A) Find out how far each point is from the mean, point minus mean
B) Take the absolute value to make things positive
C) Add up the positive values and find its mean.
For set A, the mean is 71.8. The first point in the MAD is found by subtracting that point, 61, from the mean, 71.8. It gives you -10.8, but we take the absolute value of it and have 10.8. Repeat this for each point. Change the mean and the points and repeat the process for set B.
Set A: 61, 61, 62, 65, 70, 71, 75, 81, 82, 90
Set A Absolute deviations: 10.8, 10.8, 9.8, 6.8, 1.8, 0.8, 3.2, 9.2, 10.2, 18.2
We add the absolute deviations, divide by 10, and find the mean.
(10.8 + 10.8 + ... + 18.2) / 10 = 81.6 / 10 = 8.16 is the MAD of set A.
Set B: 59, 63, 69, 70, 73, 73, 76, 77, 78, 83
Set B Absolute Deviations (mean is 72.1): 13.1, 9.1, 3.1, 2.1, 0.9, 0.9, 3.9, 4.9, 5.9, 10.9
Set B MAD = (13.1 + 9.1 + + 10.9)/10 = 54.8 / 10 = 5.48
3) We compare both MADs to answer.
A = 8.16
B = 5.48
This can be said in one of two ways but the idea is the same. The more variability something has, the higher amount of deviations it will have. (Or the less variable, the less amount of deviations.)
Set A has a higher MAD than set B, so set A is more variable than set B. So A is more variable. (Flip the logic around and the conclusion is the same).
