Question

16. The mean of four observations is 10 and
when a constant 'a' is added to each
observation, the mean becomes 13. The
value of a is
(MQB)
a) 2 b)-3 D3 d) None​

Answer 1

Answer:

(c) 3

Step-by-step explanation:

Let , the four observations are

x₁ , x₂ , x₃ , x₄

then, mean will be

$\frac{x_1+x_2+x_3+x_4}{4} = 10 -------equation (1)$

when each observation is increased by 'a' then the four observations will be,

x₁ + a , x₂ + a , x₃ + a , x₄ + a

and, new mean will be

$\frac{x_1+a +x_2+a+x_3+a+x_4+a}{4} = 13\\\\\frac{a+a+a+a + x_1+x_2+x_3+x_4}{4} = 13\\\\\frac{4a + x_1+x_2+x_3+x_4}{4} = 13$

$a+\frac{x_1+x_2+x_3+x_4}{4} = 13\\\\( using \ equation\ (1)\ we\ will \ get )\\\\ a + 10 = 13\\\\a = 13 - 10\\\\a = 3$

HENCE, THE VALUE OF 'a' IS  '3' .