If the mean and the standard deviation of the data 3, 5, 7, a, b are 5 and 2 respectively,…

Question

If the mean and the standard deviation of the data 3, 5, 7, a, b are 5 and 2 respectively, then a and b are the roots of the equation:

Accepted Answer

Mean = $${{3 + 5 + 7 + a + b} \over 5}$$ = 5

$$ \Rightarrow $$ $a$ + b = 10

Variance = $${{{3^2} + {5^2} + {7^2} + {a^2} + {b^2}} \over 5}$$ - (5)2 = 4

$$ \Rightarrow $$ ${{a^2} + {b^2}}$ = 62

$$ \Rightarrow $$ $${\left( {a + b} \right)^2} - 2ab$$ = 62

$$ \Rightarrow $$ $ab$ = 19

So $a$ and b are the roots of the equation

x2 -- 10x + 19 = 0

Solutions · 1