Let the mean and the variance of 6 observations a,b, 68, 44, 48, 60 be 55 and 194, respectively. If a > b, then a + 3b is

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Solution

Q.
Let the mean and the variance of 6 observations $a, b$ , 68, 44, 48, 60 be 55 and 194, respectively. If a > b, then a + 3b is: [2024]

1 210

2 190

3 200

4 180

Ans.
(4)

Given, mean $(\bar{x}) = 55$

$∴$ $\frac{a + b + 68 + 44 + 48 + 60}{6} = 55 \Rightarrow a + b = 110$ ...(i)

Given, variance $(σ^{2}) = 194$

$∴$ $\frac{a^{2} + b^{2} + {(68)}^{2} + {(44)}^{2} + {(48)}^{2} + {(60)}^{2}}{6} - {(55)}^{2} = 194$

$\Rightarrow a^{2} + b^{2} = 6850$ ...(ii)

From (i) and (ii), we get

$a = 75$ and $b = 35$

$∴$ $a + 3 b = 75 + 3 (35) = 180$

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