JEE Main 2026 · 6 Apr · Shift 1 · Mathematics Q9

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MathematicsSingle correct+4 / -1Question 9 of 75

A data consists of 20 observations $x_1,x_2,\dots,x_{20}$ . If $\displaystyle\sum_{i=1}^{20}(x_i+5)^2=2500$ and $\displaystyle\sum_{i=1}^{20}(x_i-5)^2=100$ , then the ratio of mean to standard deviation of this data is:

2:1

3:1

3:2

4:1

Answer and worked solution

Official answer: B

Subtract the sums. $20\sum x_i=2400$ , so $\sum x_i=120$ and the mean is 6.

Add the sums. $2\sum x_i^2+20\cdot50=2600$ , so $\sum x_i^2=800$ .

Spread. $\sigma^2=40-36=4$ , so $\sigma=2$ .

Ratio: $6:2=3:1$ .

(B)

Topics:Variance and standard deviation

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JEE Main 2026 · 6 Apr · Shift 1, Mathematics question 9