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 :
Solution
Mean = ${{3 + 5 + 7 + a + b} \over 5}$ = 5
<br><br>$\Rightarrow$ $a$ + b = 10
<br><br>Variance = ${{{3^2} + {5^2} + {7^2} + {a^2} + {b^2}} \over 5}$ - (5)<sup>2</sup> = 4
<br><br>$\Rightarrow$ ${{a^2} + {b^2}}$ = 62
<br><br>$\Rightarrow$ ${\left( {a + b} \right)^2} - 2ab$ = 62
<br><br>$\Rightarrow$ $ab$ = 19
<br><br>So $a$ and b are the roots of the equation
<br><br>x<sup>2</sup> – 10x + 19 = 0
About this question
Subject: Mathematics · Chapter: Statistics · Topic: Measures of Central Tendency
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