why we need to take mid point in continous series ?-statistics

see an example...


suppose there are  5 children with weights 20kg
4 children with weights 10 kg

how do you calculate average weight(mean) for all 9 children?

you go like this..
{total weight}/{total number of children}
=[(5*20) + (4*10)]/(5+4)

to get average value of weight.

In this example, the data is grouped. You couldn't find the mean the "normal way" (by adding up the numbers and dividing by the number of numbers) because you don't know what the values are. You know that five people have scored  between 0 and 10, for example, but you don't know what the scores are exactly. So we estimate the mean, using "?fx / ?f".

Thanks ...!