fitzpratik wrote:
Set X is given by {a, 2a, 3a, 4a, 5a} where ‘a’ is a positive integer. If element ‘a’ in Set X is replaced by ‘b’ and b < a, then which of the following must be true?
I. Mean would not change.
II. Median would not change.
III. Standard deviation would not change
A. I only
B. II only
C. III only
D. Both I and II
E. Both II and III
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
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