The marks obtained by 41 students in an examination in Math are given below:

Find the average of the marks obtained by them.

Explanation

Here , the total number of the marks obtained `underset(i=1)overset(41)sum x_(i) =15+25+32+………+42=1,015`
`therefore ` the arithmetic mean, `barx=(sumx_(i))/(n)=(1,015)/(41)=24.8` (approx)
Now, for the convenient of the computing of average of any variable we can transfer the origin or base of the variable x. Thus , if we transfer the origin of x at A , then the new variable u=x-A .
Here, `underset(i=1)overset(n)sum u_(i) =underset(i=1)overset(n)sum x_(i)-nA`, or `(1)/(n)sum u_(i)=(1)/(n)sum x_(i)-A`
or, `baru=barx-A` or `barx=baru+A.....................(""^(**)3)`
Here , firstly the values of `u_(i)` should be determined by subtracting A from the values of x, then the values of `baru` is to be detemined . When A is added to `baru` , we get the average `barx`.