Math miscellaneousHard
Question
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
A.a = 0, b = 7
B.a = 5, b = 2
C.a = 1, b = 6
D.a = 3, b = 4
Solution
Mean of a, b, 8, 5, 10 is 6
⇒
⇒ a + b = 7 .....(1)
Given that Variance is 6.8
∴ Variance =
⇒ a2 + b2 = 25
a2 + (7 - a)2 = 25 (Using (1))
⇒ a2 - 7a + 12 = 0
∴ a = 4, 3 and b = 3, 4.
⇒
⇒ a + b = 7 .....(1)
Given that Variance is 6.8
∴ Variance =
⇒ a2 + b2 = 25
a2 + (7 - a)2 = 25 (Using (1))
⇒ a2 - 7a + 12 = 0
∴ a = 4, 3 and b = 3, 4.
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