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

Question

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

fitzpratik · Answer

Hi  arjittak

The question states that  ONE  element a, not all elements,is replaced by b, where b<a. \
So the new set is {b, 2a, 3a, 4a, 5a}

So Mean and SD will change, Median would not!

So the answer is  B

shivam2506 · Answer

We can answer by looking the options. 
If suppose mean changes, then definitely standard deviation would change and vice versa. But in options I & III together are not given. So definitely D & E are not the answer. Similar to that A & C can't be the answer also. So only option remaining is B

generis · Answer

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   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

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

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