The selling amount of money of a shopkeeper in 7 days of any week are given below (in rupees). 115,98, 102,126,85,91,107
Find the average of the amount of rupees sold per day.

Explanation

Here, the values of the variable x , is near the values 100 of x
If we transfer the origin A to 100 , then the values of u are 15-2,2,26,-15,-8,7.
`therefore baru=1/7(15-2+2+26-15-9+7)=(50-26)/(7)=(24)/(7)=3.43` (approx.)
`therefore baru=100+3.43 =103.43` (approx)
`therefore ` the required daily seling amount =Rs. 103.43
Now , let x is a descrete variable. The possible values of `x_(1), x_(2),.............., x_(n)` . Frequency distribution of x are made from n values of x. Let the frequencies of `x_(1), x_(2), .........x_(n)` be `f_(1),f_(2), ..............f_(n)` i.e. `x_(1)` occurs `f_(1)` times , `x_(2)` occurs `f_(2)` times, .......`f_(n)` occurs n-times and `f_(1)+f_(2) +........+f_(n)=n`
Now , `underset(i=1)overset(n)sum f_(i)x_(i)=x_(i)xxf_(i)+x_(2)xxf_(2) + ........+x_(n)xxf_(n)`
and `=f_(1)+f_(2)+............+f_(n)=n`
Arithmetic mean of `x=barx=(x_(1)f_(1)+x_(2)f_(2)+.....+x_(n)f_(n))/(f_(1)+f_(2)+.......+f_(n))`
`=(underset(i=1)overset(n)sumx_(i)f_(i))/(underset(i=1)overset(n)sum f_(i)=(1)/(n)underset(i=1)overset(n)sum x_(i)f_(i)................(""^(**)4)`
This `barx` is the weighted mean of the variable x.