In Set A above, if positive integer x is subtracted from the 3 largest

Set A: {7, 4, 1, 0, 5, 8, 10, 10, 13, 21}

In Set A above, if positive integer x is subtracted from the 3 largest numbers in the list and x is added to the 3 smallest even numbers in the list, which of the following will be true?

A. The average of the set will stay the same.
Arithmetic mean is \(\frac{(sum of all number)}{(# of numbers)}\). The sum doesn't change, just the distribution. A is correct

B. There will be no mode in the new set.
This may or may not be true. x could be some absurd number like 100 whereby there is no mode, or it could be 1 where '1' would be the mode.

C. The standard deviation of the set will stay the same.
Standard deviation is the spread from the mean. As with mode, could perhaps coax the numbers for it to be the same, but it is likely to not be the same.

D. The median of the set will stay the same.
Currently the median is 7.5
If x=1
1, 1, 5, 7, 9, 9, 10, 12, 20
Median is now 9.

E. The median of the set will increase by x.
As just shown above.

A