If the mean and variance of eight numbers 3, 7, 9, 12, 13, 20, x and y be 10 and 25 respectively, then x.y is equal to _______.
Answer (integer)
54
Solution
Mean = ${{3 + 7 + 9 + 12 + 13 + 20 + x + y} \over 8}$ = 10
<br><br>16 = x + y ....(1)
<br><br>Variance (${\sigma ^2}$) = 25
<br><br>$\Rightarrow$ $${{{3^2} + {7^2} + {9^2} + {{12}^2} + {{13}^2} + {{20}^2} + {x^2} + {y^2}} \over 8}$$ - 100 = 25
<br><br>$\Rightarrow$ 125 × 8 = 9 + 49 + 81 + 144 + 169 + 400 + x<sup>2</sup>
+ y<sup>2</sup> - 800
<br><br>$\Rightarrow$ x<sup>2</sup>
+ y<sup>2</sup> = 148
<br><br>We know, (x + y)<sup>2</sup>
= x<sup>2</sup>
+ y<sup>2</sup>
+ 2xy
<br><br>$\Rightarrow$ 256 = 148 + 2xy
<br><br>$\Rightarrow$ x.y = 54
About this question
Subject: Mathematics · Chapter: Statistics · Topic: Measures of Dispersion
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