Averages

In short: The average (mean) is the total divided by how many there are. Turning it around, total = average × how many, and most hard average problems are solved by finding totals first.

Before you start

• Adding a list of numbers and dividing.
• Simple equations, such as $39+n=48$ (see Solving Equations).

The mean

The total is the key

Turn the formula around:

$$\text{total}=\text{average}\times \text{how many}$$

Adding or removing a number

Averages with letters

The average of Lisa's 38 kg and Gina's $K$ kg is $\frac{38+K}{2}$ kg.

The total of 5 numbers is half of 10 dozen, which is 60. Their average is $60÷5=12$.

Quick summary

• Average (mean) $=$ total $÷$ how many.
• Total $=$ average $\times$ how many. Most hard average questions are solved with totals.
• To find a missing number, find the new total and the old total, then subtract.
• Do not average two averages unless the groups are the same size.
• The middle of an odd list of consecutive numbers is the average.

Quiz