Sets x₁, x₂, ..., x₁₀₀ and y₁, y₂, ..., y₁₅₀ have means zero and the same standard deviations. Which of the following is the ratio of $$\sum_{1}^{100} x_i^2 \text{ to } \sum_{1}^{150} y_i^2$$​​

Correct option is C

Concept:
(1) Standard deviation = √ variance 
(2) variance = ∑ 1/N (x_i- mean)² (N = total number of terms)
Solution:
Let take x_i = 1 when i is even 
 x_i = -1 when i is odd
Similarly,
y_i = 1 when i is even 
y_i = -1 when i is odd
Clearly, both have means zero and the same standard deviations.
Now,

and 

Now, 100:150 = 2:3
Final Answer:
(c) 2 : 3.