Data Sufficiency

If two numbers are selected from 1, 3, 5, 7, 9, 11, 13, 15, 17, and 19 randomly, what is the standard deviation of the new list?

1). The mean remains unchanged.
2). The median of the new list is 10.

Please explain. Thanks.

IMO - D. OA - E

1). The mean remains unchanged.

1, 3, 5, 7, 9, 11, 13, 15, 17, and 19

now here mean is 10 & sum is 100

so if we remove any two nos whose sum is 20 then mean will remain same

fo e.g. 9,11 17,3 , 1,19 etc

depending upon what is removed the std deviation i.e average distance of values from the mean will change

INSUFF

2). The median of the new list is 10.

now if median is 10 same logic as above applies i.e center values may be 9,11 , 17,3 etc which will have diff std dev

combine: again we can say both the stmts give similar data

hence INSUFF

E

Thanks a lot!