For a set, mean is 20 and standard deviation is 5. Which of these numb

Two approaches - Mathematical one is longer but gives precise answer. Theoretical one (scroll below) can confuse you if you anchor around mean in your thinking rather than the "distance between the point and mean".

Mathematical approach
Mathematically you can solve it like this. Lets say n numbers,

\(\sqrt{ [(x1-20)^2 + (x2-20)^2 ... (xn-20)^2]/n } = 5\)

Lets re-express the numerator as T as

\(\sqrt{ T/n } = 5\)
=> T = 25n .... (a)

When added another number P, the formula becomes

\(\sqrt{ [T + (P-20)^2]/(n+1) } = 5\)
T + (P-20)^2 = 25(n+1) .... (b)



(b) - (a)
(P-20)^2 = 25
=> P-20 = +/-5
P = 15 or P=25

Hence C

Intuitive/Logical Approach
Intuitively/Logically - the more values you bring around the same distance from the mean as the standard deviation, the less the impact on standard deviation. The real confusion happens between choice C and D. If you add a value = mean, you are actually reducing the standard deviation because the distance between mean and the new value is 0. So you add 0 to numerator and 1 to denominator creating a value that is further away from initial numerator.

Another way to think about it is that Standard deviation is kind of averages of distance between the "points and median". You need to keep this average distance same. The only way you keep the average same is by adding a value equal or close to average. If you add a value equal to mean, you are adding 0 to the series and that will reduce the average distance not keep it same.