JEE Main 2025 · Mathematics · Statistics · medium

If three of them are 3,5,7 and the other two are x and y, then |x-y| equals

Single correct option

Five observations have mean

7

and variance

8

. If three of them are

3,5,7

and the other two are

x

and

y

, then

|x-y|

equals

Show answer and solution

Answer: (B) $2$

Sum

=35

, so

x+y=35-15=20

. From

\sigma^2=\frac{\sum x_i^2}{5}-\bar{x}^2

we get

\sum x_i^2=5(8+49)=285

. The known squares total

9+25+49=83

, so

x^2+y^2=202

. Then

2xy=400-202=198

xy=99

, and

(x-y)^2=(x+y)^2-4xy=400-396=4

. So

|x-y|=2

(indeed

x,y=9,11

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