Question

the mean of 10 number is 47. if one number is excluded, mean of the remaining numbers become 46. find the excluded number

Answer 1

If the mean is 47, the total of all the no. will be 47 x 10 = 470
And if one no. Is excluded, it no. Remain
So the total of the no. left is 46 x 9 = 414
So the no. excluded is 470 - 414 = 56

Answer 2

The excluded number is "56".

Explanation:

Let the given numbers $x_{1} ,x_{2} ,x_{3} ,x_{4}$.... and $x_{10}$.

∴ $\dfrac{x_{1} +x_{2}+....+x_{10} }{10} =47$

⇒ $x_{1} +x_{2}+....+x_{10}$= 470     ....(1)

Also,

One number is excluded.

⇒ $x_{1} +x_{2}+....+x_{9}$= 46 × 9    

⇒ $x_{1} +x_{2}+....+x_{9}$= 414   ....(2)

∴ The excluded number =  470 - 414 = 56

Hence, the excluded number is "56".