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JEE Main 2026 · 4 Apr · Shift 2, Mathematics question 8

For 10 observations x1,x2,…,x10x_1,x_2,\dots,x_{10}, if ∑i=110(xi+2)2=180\displaystyle\sum_{i=1}^{10}(x_i+2)^2=180 and ∑i=110(xi−1)2=90\displaystyle\sum_{i=1}^{10}(x_i-1)^2=90, then their standard deviation is:

Choose one option
Answer and worked solution

Official answer: D

Mean. Subtracting the sums: ∑[(x+2)2−(x−1)2]=∑(6x+3)=90\sum\left[(x+2)^2-(x-1)^2\right]=\sum(6x+3)=90, so ∑x=10\sum x=10 and the mean is 1.

Variance. ∑(xi−1)2=90\sum(x_i-1)^2=90 is about the mean, so σ2=9\sigma^2=9 and σ=3\sigma=3.

(D)

Topics:Variance and standard deviation
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