Question

To increase the mean of 4 numbers by 2, by how much would the sum of the 4 numbers have to increase?

Answer 1

`8`

Explanation:

The mean of `4` numbers can be denoted as:

`barx=(sum_(n=1)^4a_n)/4`

When the mean increases by `2`,

`barx+2=(sum_(n=1)^4a_n)/4+2`

Common denominator,

`barx+2=(sum_(n=1)^4a_n+8)/4`

From the above, it is seen that,

`sum_(n=1)^4a_n+8=4(barx+2)`

Hence, to get an increment of `2` in the mean, the sum of the four numbers would have to increase by `8`.