QJEEM20Ma171c: JEE Main 2020 Mathematics - Class 11 JEEM20Ma171c Solution: If the mean and variance of eight numbers 3, 7, 9, 12, 13, 20,…

Mean = $$\frac{3+7+9+12+13+20+x+y}{8}$$ = 10

16 = x + y ....(1)

Variance ($${\sigma }^2$$) = 25

$$\Rightarrow$$ $$\frac{3^2+7^2+9^2+{12}^2+{13}^2+{20}^2+x^2+y^2}{8}$$ - 100 = 25

$$\Rightarrow$$ 125 × 8 = 9 + 49 + 81 + 144 + 169 + 400 + x² + y² - 800

$$\Rightarrow$$ x² + y² = 148

We know, (x + y)² = x² + y² + 2xy

$$\Rightarrow$$ 256 = 148 + 2xy

$$\Rightarrow$$ x.y = 54