The arithmetic mean of the observations 10 ,8 ,5 ,a ,b is 6 and their variance is 6.8, then ab is equal to

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Accepted Answer

Correct answer: D. (d) Given observations are 10 ,8 ,5 ,a ,b. Arithmetic Mean A .M .= 10+8+5+a+b5=623+a+b=30a+b=7 … (i ) Here, x_i (x_i-x) (x_i-x)^2 10 4 16 8 2 4 5 -1 1 a a-6 (a-6 )^2 b b-6 (b-6 )^2 ∴ (x_i-x)^2=a^2+b^2+93-12 (a+b ) Variance, 1n (x_i-x)^2=6.8 a^2+b^2+93-12 (a+b )5=6.8a^2+b^2+93-12 7=6.8 5a^2+b^2+93-84=34 [ ∵a+b=7 ]a^2+b^2=25 … … ( ii )( ∵ (a+b )^2=a^2+b^2+2 ab) (7 )^2=25+2 ab49=25+2 ab ab=12 [using Eqs. (i) and (ii)]

$The arithmetic mean of the observations 10, 8, 5, a, b is 6 and their variance is 6.8, then ab is equal to$

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