Set X is given by {a, 2a, 3a, 4a, 5a} where a is a positive integer.

With values this small, try numbers if not sure. It's very quick.

Only first term, a, changes, not the multiples of a. Otherwise prompt would say "If [EACH] element ‘a’ in Set X is replaced by . . ."

a = 2
Set 1: (2, 4, 6, 8, 10)

b = 1
Set 2: (1, 4, 6, 8, 10)

MUST be true?

I. Mean would not change.
Set 1 mean = 6
Set 2 mean = 29/5 = 5.8
FALSE

II. Median would not change.
Set 1 median = 6
Set 2 median = 6
TRUE

III. Standard deviation would not change

Either remember: If you add or subtract the same number to every number in original set, SD does not change. If you change just one number, SD changes. OR

SD, roughly: how tightly are all the values clustered around the mean? Look at values on the right side of the mean that don't change (here, numbers 8 and 10).

In Set 1, mean is 6. Value 8 is exactly 2 away from mean, 10 is exactly 4 away from mean

In Set 2, mean is 5.8. Values 8 and 10 are farther from 5.8 than they are from 6. The numbers now are "clustered" differently around (in test cases farther from) the mean. FALSE

Answer B