Mean and Variance of Transformed Set (Jee Mains)

Dispersion and Variance

Medium

Mean and Variance of Transformed Set

Let X = $\left\{ {x \in {\Bbb N}:1 \leqslant x \leqslant 19} \right\}$ and for some a, b ∈ ${\Bbb R}$ , Y = $\left\{ {ax + b:x \in X} \right\}$ . If the mean and variance of the elements of Y are 30 and 750, respectively, then the sum of all possible values of b is

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