Year 6: The mean as an average
Part of the Year 6 pie charts, line graphs and the mean chapter. Chapter overview · whole chapter on one page
The mean as an average
The mean is an average. It tells you the value that each one would have if the values were shared out equally. For example, if four children score 6, 8, 7 and 9 in a test, the mean is the score each child would get if all the points were shared equally.
To find the mean, follow three steps. First, add all the values to find the total. Second, count how many values there are. Third, divide the total by the number of values. Every value counts, even a zero.
The mean is always between the smallest value and the biggest value. It does not have to be one of the values in the list.
Key ideas
- Mean = total ÷ the number of values.
- Count every value, including a zero.
- The mean is between the smallest and the biggest value.
- The mean is also called the average.
Key words. The mean is the same as the average. Add all the values to get the total, then share the total equally between the number of values.
Method. Add all the values, then share the total equally between the number of values.
- Write the values. These are all the values. Count every one, even a zero.6, 8, 7, 9
- Add the values to find the total. The total is what all the values make together.6 + 8 + 7 + 9 = 30
- Count the values. Count how many numbers there are. Do not count the total.There are 4 values
- Divide the total by the number of values. Sharing the total equally between the values gives the mean.30 ÷ 4 = 7.5
Check. 7.5 × 4 = 30, so the mean is right. ✓
Watch out. Divide by how many values there are, not by the biggest value. Do not forget to count a zero.
Key words. The mean is the same as the average. Add all the values to get the total, then share the total equally between the number of values.
Method. Add all the values, then share the total equally between the number of values.
- Write the values. These are all the values. Count every one, even a zero.3, 5, 4, 2, 6
- Add the values to find the total. The total is what all the values make together.3 + 5 + 4 + 2 + 6 = 20
- Count the values. Count how many numbers there are. Do not count the total.There are 5 values
- Divide the total by the number of values. Sharing the total equally between the values gives the mean.20 ÷ 5 = 4
Check. 4 × 5 = 20, so the mean is right. ✓
Watch out. Divide by how many values there are, not by the biggest value. Do not forget to count a zero.
Key words. The mean is the same as the average. Add all the values to get the total, then share the total equally between the number of values.
Method. Add all the values, then share the total equally between the number of values.
- Write the values. These are all the values. Count every one, even a zero.0, 2, 3, 1
- Add the values to find the total. The total is what all the values make together.0 + 2 + 3 + 1 = 6
- Count the values. Count how many numbers there are. Do not count the total.There are 4 values
- Divide the total by the number of values. Sharing the total equally between the values gives the mean.6 ÷ 4 = 1.5
Check. 1.5 × 4 = 6, so the mean is right. ✓
Watch out. Divide by how many values there are, not by the biggest value. Do not forget to count a zero.
Watch out
Common mistake: dividing by the wrong number. Divide by how many values there are, not by the biggest value, and do not forget a zero. Also, the mean is not the middle number when the values are put in order. That middle number is a different average.
Exercise 12F Practice: finding the mean
Non-calculatorKey words. The mean is the same as the average. Add all the values to get the total, then share the total equally between the number of values.
Method. Add all the values, then share the total equally between the number of values.
- Write the values. These are all the values. Count every one, even a zero.4, 7, 9, 6
- Add the values to find the total. The total is what all the values make together.4 + 7 + 9 + 6 = 26
- Count the values. Count how many numbers there are. Do not count the total.There are 4 values
- Divide the total by the number of values. Sharing the total equally between the values gives the mean.26 ÷ 4 = 6.5
Check. 6.5 × 4 = 26, so the mean is right. ✓
Watch out. Divide by how many values there are, not by the biggest value. Do not forget to count a zero.
Key words. The mean is the same as the average. Add all the values to get the total, then share the total equally between the number of values.
Method. Add all the values, then share the total equally between the number of values.
- Write the values. These are all the values. Count every one, even a zero.12, 15, 9
- Add the values to find the total. The total is what all the values make together.12 + 15 + 9 = 36
- Count the values. Count how many numbers there are. Do not count the total.There are 3 values
- Divide the total by the number of values. Sharing the total equally between the values gives the mean.36 ÷ 3 = 12
Check. 12 × 3 = 36, so the mean is right. ✓
Watch out. Divide by how many values there are, not by the biggest value. Do not forget to count a zero.
Key words. The mean is the same as the average. Add all the values to get the total, then share the total equally between the number of values.
Method. Add all the values, then share the total equally between the number of values.
- Write the values. These are all the values. Count every one, even a zero.3, 0, 5, 4, 8
- Add the values to find the total. The total is what all the values make together.3 + 0 + 5 + 4 + 8 = 20
- Count the values. Count how many numbers there are. Do not count the total.There are 5 values
- Divide the total by the number of values. Sharing the total equally between the values gives the mean.20 ÷ 5 = 4
Check. 4 × 5 = 20, so the mean is right. ✓
Watch out. Divide by how many values there are, not by the biggest value. Do not forget to count a zero.
Key words. The mean is the same as the average. Add all the values to get the total, then share the total equally between the number of values.
Method. Add all the values, then share the total equally between the number of values.
- Write the values. These are all the values. Count every one, even a zero.20, 25, 15, 30, 10, 20
- Add the values to find the total. The total is what all the values make together.20 + 25 + 15 + 30 + 10 + 20 = 120
- Count the values. Count how many numbers there are. Do not count the total.There are 6 values
- Divide the total by the number of values. Sharing the total equally between the values gives the mean.120 ÷ 6 = 20
Check. 20 × 6 = 120, so the mean is right. ✓
Watch out. Divide by how many values there are, not by the biggest value. Do not forget to count a zero.
Key words. The mean is the same as the average. Add all the values to get the total, then share the total equally between the number of values.
Method. Add all the values, then share the total equally between the number of values.
- Write the values. These are all the values. Count every one, even a zero.18, 22, 20, 24
- Add the values to find the total. The total is what all the values make together.18 + 22 + 20 + 24 = 84
- Count the values. Count how many numbers there are. Do not count the total.There are 4 values
- Divide the total by the number of values. Sharing the total equally between the values gives the mean.84 ÷ 4 = 21
Check. 21 × 4 = 84, so the mean is right. ✓
Watch out. Divide by how many values there are, not by the biggest value. Do not forget to count a zero.
Key words. The mean is the same as the average. Add all the values to get the total, then share the total equally between the number of values.
Method. Add all the values, then share the total equally between the number of values.
- Write the values. These are all the values. Count every one, even a zero.5, 6, 4, 7, 8
- Add the values to find the total. The total is what all the values make together.5 + 6 + 4 + 7 + 8 = 30
- Count the values. Count how many numbers there are. Do not count the total.There are 5 values
- Divide the total by the number of values. Sharing the total equally between the values gives the mean.30 ÷ 5 = 6
Check. 6 × 5 = 30, so the mean is right. ✓
Watch out. Divide by how many values there are, not by the biggest value. Do not forget to count a zero.
Key words. The mean is the same as the average. Add all the values to get the total, then share the total equally between the number of values.
Method. Add all the values, then share the total equally between the number of values.
- Write the values. These are all the values. Count every one, even a zero.2, 4, 6, 8
- Add the values to find the total. The total is what all the values make together.2 + 4 + 6 + 8 = 20
- Count the values. Count how many numbers there are. Do not count the total.There are 4 values
- Divide the total by the number of values. Sharing the total equally between the values gives the mean.20 ÷ 4 = 5
Check. 5 × 4 = 20, so the mean is right. ✓
Watch out. Divide by how many values there are, not by the biggest value. Do not forget to count a zero.
Key words. The mean is the same as the average. Add all the values to get the total, then share the total equally between the number of values.
Method. Add all the values, then share the total equally between the number of values.
- Write the values. These are all the values. Count every one, even a zero.1, 3, 5
- Add the values to find the total. The total is what all the values make together.1 + 3 + 5 = 9
- Count the values. Count how many numbers there are. Do not count the total.There are 3 values
- Divide the total by the number of values. Sharing the total equally between the values gives the mean.9 ÷ 3 = 3
Check. 3 × 3 = 9, so the mean is right. ✓
Watch out. Divide by how many values there are, not by the biggest value. Do not forget to count a zero.
Key words. The mean is the same as the average. Add all the values to get the total, then share the total equally between the number of values.
Method. Multiply the mean by the number of values to get the total.
- Write the mean and the number of values. The mean is the average of the values.mean 10, number of values 4
- Multiply the mean by the number of values. Sharing the total equally gave the mean, so multiplying gives the total back.10 × 4 = 40
- Write the answer. This is the total of all the values.40
Check. 40 ÷ 4 = 10, so the mean is right. ✓
Watch out. Multiply to find the total from a mean. Divide only when you need the mean from a total.
Key words. The mean is the same as the average. Add all the values to get the total, then share the total equally between the number of values.
Method. Add all the values, then share the total equally between the number of values.
- Write the values. These are all the values. Count every one, even a zero.2, 4, 9
- Add the values to find the total. The total is what all the values make together.2 + 4 + 9 = 15
- Count the values. Count how many numbers there are. Do not count the total.There are 3 values
- Divide the total by the number of values. Sharing the total equally between the values gives the mean.15 ÷ 3 = 5
Check. 5 × 3 = 15, so the mean is right. ✓
Watch out. Divide by how many values there are, not by the biggest value. Do not forget to count a zero.
Key words. The mean is the same as the average. Add all the values to get the total, then share the total equally between the number of values.
Method. Add all the values, then share the total equally between the number of values.
- Write the values. These are all the values. Count every one, even a zero.8, 6, 9, 7, 5
- Add the values to find the total. The total is what all the values make together.8 + 6 + 9 + 7 + 5 = 35
- Count the values. Count how many numbers there are. Do not count the total.There are 5 values
- Divide the total by the number of values. Sharing the total equally between the values gives the mean.35 ÷ 5 = 7
Check. 7 × 5 = 35, so the mean is right. ✓
Watch out. Divide by how many values there are, not by the biggest value. Do not forget to count a zero.
Watch out
Watch out: the mean can be a decimal, such as 7.5 or 1.5. Do not round it to a whole number unless the question asks you to.
Exam tip
Check your mean by multiplying it by the number of values. You should get the total back.