Let the mean and variance of four numbers 3, 7, x and y(x > y) be 5 and 10 respectively. Then the mean of four numbers 3 + 2x, 7 + 2y, x + y and x $-$ y is ______________.
Answer (integer)
12
Solution
$5 = {{3 + 7 + x + y} \over 4} \Rightarrow x + y = 10$<br><br>Var(x) = $10 = {{{3^2} + {7^2} + {x^2} + {y^2}} \over 4} - 25$<br><br>$140 = 49 + 9 + {x^2} + {y^2}$<br><br>${x^2} + {y^2} = 82$<br><br>x + y = 10<br><br>$\Rightarrow$ (x, y) = (9, 1)<br><br>Four numbers are 21, 9, 10, 8<br><br>Mean = ${{48} \over 4}$ = 12
About this question
Subject: Mathematics · Chapter: Statistics · Topic: Measures of Central Tendency
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