# Data Analysis: Average

*What is meant by average and how do we calculate it?*

*What is meant by average and how do we calculate it?*

Let's understand this concept using an example.

Joe uses building blocks to make 3 towers of different heights.

- Tower A has
8blocks- Tower B has
1block- Tower C has
3blocks

8 + 1 + 3 = 12Joe has 12 blocks in all.

He distributes themunequallyto get 3 towers of different heights (as in the figure above).

However, if he redistributes the 12 blocksequallyso that each tower has the same height, then he would have found theaverageheight of the towers (as in the figure below).

Redistributing the blocks does not change the total number of blocks.Now,

4 + 4 + 4 = 12So, the

- Tower A has
4blocks- Tower B has
4blocks- Tower C has
4blocksaverage of 8, 1 and 3 is 4.

We say,

On the average, each tower has 4 blocks.

Or,

The average number of blocks per tower is 4.

Formula to calculate average

Find the sum or total of all items.Step 1:

Divide the total by the number of items.Step 2:

Average =total of all items

number of items

*Example 1*

*Example 1*

The table below shows the books that Louis borrowed from the library.

TitleNumber of pagesExotic Cars 256 Dinosaurs for Kids 64 365 Bedtime Stories 448 A Desert Habitat 32 Art 50 What is the average number of pages that each book has?

SolutionTotal number of pages = 256 + 64 + 448 + 32 + 50 = 850

Number of books = 5

Average number of pages per book = 850 ÷ 5 = 170

Each book has an average of 170 pages.

*Example 2*

*Example 2*

The average age of 3 girls is 11 years. The average age of 2 of the girls is 12 years. What is the age of the third girl?

Solution

3 × 11 years = 33 years

The total age of the 3 girls is 33 years.

2 × 12 years = 24 years

The total age of 2 of the girls is 24 years.

33 years − 24 years = 9 years

The age of the third girl is 9 years.

*Example 3*

*Example 3*

A team of 5 friends gets an average pocket money of $15 per week. A sixth friend who gets $21 as pocket money per week joins their team. What is the average pocket money of the team now?

Solution

5 × $15 = $75

The total pocket money of 5 friends is $75.

$75 + $21 = $96

The total pocket money of 6 friends is $96.

$96 ÷ 6 = $16

The average pocket money of the team now is $16.

*Example 4*

*Example 4*

Amy, Dennis and Ruby have an average salary of $2650 per month. Amy earns twice as much as Dennis and Ruby earns $260 more than Amy each month. What is Ruby's monthly salary?

3 × $2650 = $7950

The total monthly salary of Amy, Dennis and ruby is $7950.

5 units = $7950 - $260 = $7690

1 unit = $7690 ÷ 5 = $1538

2 × $1538 + $260 = $3336

Ruby's monthly salary is $3336.

*Example 5*

*Example 5*

The following graph shows the number of children in 205 families in a township in the year 2009.

- What was the total number of children in the township in 2009?
- What was the average number of children per family in 2009? Round off your answer to 1 decimal place.
- In the year 2010, the number of children in the township increased by 56 while the total number of families remained unchanged. What was the average number of children per family in the township in 2010? Round off your answer to 1 decimal place.
Solution(39 × 0) + (29 × 1) + (73 × 2) + (46 × 3) + (18 × 4) = 385

The total number of children in the township in 2009 was 385.(Answer a)

385 ÷ 205 = 1.87 ≈ 1.9

The average number of children per family in the township in 2009 was 1.9.(Answer b)

385 + 50 = 435

Total number of children in the township in the year 2010 was 435.

435 ÷ 205 = 2.12 ≈ 2.1

The average number of children per family in the township in 2010 was 2.1.(Answer c)