Average

An average or mean is a number that is typical of a group of numbers. The average of a group of numbers is often located in between, in the middle of that group of numbers. An average is found from the group of numbers by arithmetic.

To find an average

To find the average of $N$ numbers, the $N$ numbers are added and the total is divided by $N$.

In symbols, if the numbers are $X_1$, $X_2$, $X_3$, ... $X_N$, the total is:

$X_1 + X_2 + X_3 + ... + X_N$

The total is divided by $N$ to make the average:

${X_1 + X_2 + X_3 + ... + X_N} \over N$

Examples

• Lucy is 5 years old. Tom is 6 years old. Emily is 7 years old. To find the average age:
  • Add the three numbers :

$5+6+7=18$

• The total is 18. Divide the total 18 by three:

$18/3=6$

• The average of the three numbers is 6.

$\frac{5+6+7}{3}$

Therefore, the average age of Lucy, Tom and Emily is 6 years.

Sport

In some sports, such as cricket and baseball, averages are used to tell how good a player is (such as batting average or bowling average). Sporting averages have special rules for how to calculate them.