Question

Please solve it.
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Answer 1

Answer:

Let, required two observations be x and y.

Here, Mean = 8 and Variance = 16

now, mean = (2+4+10+12+14+x+y)/7

or, 56 = x+y+42

or, x+y = 14. ...(1)

and, variance can be calculated as

$\frac{4 + 16 + 100 + 144 + 196 + {x}^{2} + {y}^{2} }{7} - 64$

or, 560 = x^2+y^2+460

or,x^2+y^2 = 100

or, 2(x^2+y^2) = 200

or,

${(x + y)}^{2} + {(x - y)}^{2} = 200$

${(x - y)}^{2} = 200 - 196 = 4$

or, x-y = 2. ....(2)

adding equation (1) and (2):-

x = 8. and y = 6

Hence, the required two observations are 8 and 6.

Answer 2

Answer:

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