Primary 6 Average Study Guide

Primary 6 average in five short steps, all built on one link between the average, the total and the number of data. Each step has bars to level, and worked examples follow.

Start here

What is an average, and how do you find it?

An average is the level the bars come to when the total is shared out equally.

Picture each value as a bar. Move the extra from the tall bars into the short ones until every bar is the same height. Nothing is added and nothing is lost, so the total stays the same. That shared height is the average: total value ÷ number of data.

In this chapter, your child learns to:

  • find an average by adding the values and dividing by how many there are, counting a 0 too;
  • find a missing value by going through the total;
  • find a new average when a value joins, using two totals;
  • work out how many values there were at first;
  • read the values off a graph or table, then find their average.

Total: 12 + 5 + 9 + 6 = 32

1

Step 1

How to find the average of a set of data

Add every value, then share the total out equally. An average is what each value would be if they were all the same. Add the values to get the total, count how many values there are, then divide. A 0 is still a value: it is a bar with no height, and it counts.

Books collected on 4 days: 11, 5, 0 and 8. Find the average.

Tap Next step

Mon11Tue5Wed0Thu8
Each day is one bar. Wednesday's bar has no height, because 0 books came in. Tap Next step to level the bars.
Try it

Find the average of 9, 0, 14, 6 and 11.

Level the bars10 questions
2

Step 2

Finding a missing value from the average

Go through the total, and the missing one is what's left. When the average is given, every value levels at that height, so the total is the average times the number of values. Write that total on its own line first. Add the values you know, then subtract them from the total.

Newspaper in 5 weeks. The average was 36 kg. How much was collected in Week 3?

Tap Next step

?Week 145Week 230Week 3?Week 435Week 528
Four weeks are given. Week 3 has no height yet, but it is still one of the 5 weeks.
Try it

The average of 4 numbers is 25. Three of them are 18, 30 and 22. What is the fourth number?

Go through the total10 questions
3

Step 3

Finding the new average when one value joins

When the count changes, there are two totals. Find the total before from the old average and the old count. Add the new value to get the total after, then divide by the new count. The new average comes from the new total, never from halfway between two numbers.

4 parcels average 15 kg. A 5 kg parcel joins. What is the average of the 5?

Tap Next step

151234average 15 kg
We do not know each parcel's mass, only their average. So all 4 are drawn at 15 kg.
Try it

3 boxes have an average mass of 8 kg. A fourth box of 12 kg is added. What is the average mass of the 4 boxes?

When one joins11 questions
4

Step 4

Finding how many values there were at first

The extra above the new average fills equal gaps. Every old value is short of the new average by the same gap. The new value stands above the new average, and only that extra can fill the gaps. Divide the extra by one gap: the number of pieces is the number of values at first.

Candles average 12 cm. A 40 cm candle is added and the average becomes 16 cm. How many candles were there at first?

Tap Next step

12? candlesnewaverage 12 cm40 cm
The old candles level off at 12 cm. How many there are is what we need, so the row ends in a ?. The new candle is 40 cm.
Try it

Some bags have an average mass of 5 kg. A 23 kg bag is added, and the average becomes 8 kg. How many bags were there at first?

How many there were13 questions
5

Step 5

Finding the average from a graph or table

Count the data the question asks for, then divide. A graph gives one reading for each month or day, and each reading is one value. The number of data is how many readings the question asks about, not how many the graph shows. Read those values, add them in order, then divide.

Rain at a weather station. What was the average rain per month from March to July?

Tap Next step

Rain (mm)020406080100120JanFebMarAprMayJunJulMonth
Mar?
Apr?
May?
Jun?
Jul?
The graph shows 7 months. Read the question again: it asks only from March to July.
Try it

A shop sold 40 shirts on Monday, 24 on Tuesday, 33 on Wednesday, 36 on Thursday and 27 on Friday. What was the average number sold a day from Tuesday to Thursday?

Averages off a graph7 questionsMixed practice · 6 questions

Primary 6 average questions, worked step by stepFind the total and the count yourself first. Then open a hint, or the working line by line.

Level the barsBasic

Mrs Tan recorded the library books returned on 5 days: 14, 9, 0, 17 and 15. Find the average number of books returned in a day.

Add all 5 values. The day with 0 books still counts as a day.
  1. Total = 14 + 9 + 0 + 17 + 15 = 55.
  2. Number of data = 5, the 0 day included.
  3. Average = 55 ÷ 5 = 11.
Answer: 11 books
Go through the totalBasic

Ravi's average score for 5 spelling tests was 17. His scores in the first 4 tests were 15, 18, 20 and 14. What did he score in the fifth test?

Use the average to find the total of all 5 tests first.
  1. Total of 5 tests = 17 × 5 = 85.
  2. First 4 tests = 15 + 18 + 20 + 14 = 67.
  3. Fifth test = 85 − 67 = 18.
Answer: 18
When one joinsIntermediate

The average height of 6 boys is 142 cm. Two more boys join them, and the average height of the 8 boys becomes 144 cm. What is the total height of the two boys who joined?

The count changes from 6 to 8, so write two totals.
  1. Total of the 6 = 142 × 6 = 852 cm.
  2. Total of the 8 = 144 × 8 = 1152 cm.
  3. Two new boys = 1152 − 852 = 300 cm.
Answer: 300 cm
How many there wereIntermediate

Some children had an average of $24 in savings. Mei Ling joined them with $60, and the average became $28. How many children were there at first?

How far is each child at first below the new average? How much of Mei Ling's $60 is above it?
  1. Each gap = $28 − $24 = $4.
  2. Extra above the new average = $60 − $28 = $32.
  3. Number of children at first = 32 ÷ 4 = 8.
  4. Check: 8 × $24 + $60 = $252, and $252 ÷ 9 = $28.
Answer: 8 children
Mixed practiceChallenge

The average mark of Ali, Ben and Siti is 76. The average mark of Ben, Siti and Devi is 72. Devi scored 65. What was Ali's mark?

Turn each average into a total. Both totals contain Ben and Siti.
  1. Ali + Ben + Siti = 76 × 3 = 228.
  2. Ben + Siti + Devi = 72 × 3 = 216.
  3. Ali is 228 − 216 = 12 marks more than Devi.
  4. Ali = 65 + 12 = 77.
Answer: 77
6

Step 6

Check yourself

Five short average questions. Nothing is saved, and each reply names the set of questions that matches.

1. Find the average of 7, 0, 5 and 12.

2. The average of 3 numbers is 40. Two of them are 35 and 52. What is the third number?

3. 5 pupils have an average of 30 stickers. A sixth pupil with 42 stickers joins them. What is the new average?

4. Some jars hold an average of 10 sweets. A jar of 34 sweets is added, and the average becomes 14. How many jars were there at first?

5. A stall sold 12, 7, 0 and 9 cakes on 4 days. After the fifth day, the average was 8 cakes a day. How many cakes were sold on the fifth day?

0/5
Answer all five to see where to practise next.
For parents

How to use this guide. Before your child presses Next step, ask what the bars will level at and which numbers make the total. Let the bars confirm the guess. Each step takes a few minutes.

In any average question, ask your child to write each total on its own line before dividing or subtracting. When the number of values changes, there are two totals, one before and one after, and the answer comes from them.

More study guides

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Lessons and practice

P6 Average lessons and practice

6 lesson videos and 57 questions across five subtopics, from Basic to Challenge, each with a worked solution.

Watch and practise →