Which data set is the most spread from its mean? 26,6, 20,36 or 28,15,30,15 or 49,17,4,18 or 14,20,24,30?

The third set 49,17,4,18.

Step-by-step explanation:

Mean for the first set is (26+6+20+36) / 4 = 88/4 = 22.

Mean for the 2nd set = 28+15+30+15 / 4 = 22 also.

Mean for the 3rd set = 49+17+4+18 / 4 = 22

Mean for the 4th set = 14+20+24+30/4 = =22.

The mean is the same for all 4 data sets.

On inspection, the set which has the biggest values furthest from 22 is the 3rd set (values 4 and 49.) so this looks like the one.

The other with more spread than the rest is the first set. We can confirm by working out the Mean Absolute deviation for both sets:

MAD for set 1 = [ (26-22) + (22-6) + (22-20) + (36-22) ] / 4 = 9.

MAD for set 3 = [ (49-22) + (22-17) + (22-4) + (22-18) ] / 4 = 13.5.

So it is the 3rd set.