JEE Main2008MathematicsStatisticsActual

The mean of the numbers a, b, 8,5,10 is 6 and the variance is 6.80 . Then which one of the following gives possible values of a and b ?

Options

Aa=0, b=7
Ba=5, b=2
Ca=1, b=6
Da=3, b=4

Correct answer

D. a=3, b=4

Step-by-step solution

Mean of a, b, 8,5,10 is 6 aligned & a+b+8+5+10 5 =6 & a+b=7 aligned Given that Variance is 6.8 aligned & Variance = ( X _ i - A )^2 n & = ( a -6)^2+( b -6)^2+4+1+16 5 =6.8 aligned aligned & a^2+b^2=25 & a^2+(7-a)^2=25 & a^2-7 a+12=0 & a=4,3 and b=3,4 aligned

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