# If the arithmetic mean, 7, 8, x, 11, 14 is x, then x =

Question:

If the arithmetic mean, 7, 8, x, 11, 14 is x, then x =

(a) 9
(b) 9.5
(c) 10
(d) 10.5

Solution:

The given observations are 7, 8, x, 11, 14.

Mean = x       (Given)

Now,

Mean $=\frac{7+8+x+11+14}{5}$

$\Rightarrow x=\frac{40+x}{5}$

$\Rightarrow 5 x=40+x$

$\Rightarrow 4 x=40$

$\Rightarrow x=10$

Hence, the correct option is (c).

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