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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 radius of circle whose centre is $(\frac{a}{15}, \frac{b}{7})$ and passing through (1,2) is

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a

5

b

20

c

21

d

19

answer is A.

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Detailed Solution

$M e a n = \frac{a + b + 68 + 44 + 48 + 60}{6} = 55 \Rightarrow a + b = 110 V a r i a n c e = \sum \frac{{(x_{i} - \vec{x})}^{2}}{n} = \frac{{(55 - a)}^{2} + {(55 - b)}^{2} + {(13)}^{2} + {(11)}^{2} + 7^{2} + 5^{2}}{6} = 194 \Rightarrow a^{2} + b^{2} - 110 (a + b) = - 5250 \Rightarrow a^{2} + b^{2} = 6850$
After solving equation (1) and (2), we get $a = 75 & b = 35$

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