Statistics
The Mean (Average)
Year 6
- ✓By the end of this lesson students will be able to understand what the mean represents as an average.
- ✓By the end of this lesson students will be able to calculate the mean of a set of data.
- ✓By the end of this lesson students will be able to solve simple problems involving the mean.
- ✓By the end of this lesson students will be able to interpret the mean in the context of a given problem.
Key concepts
The mean is a type of average. To find the mean, you add up all the numbers in a set of data and then divide the total by how many numbers there are. It helps us find a 'fair share' or a typical value for the data. For example, if you share a packet of sweets equally among friends, the number each friend gets is the mean.
Key facts to remember
- 1The mean is a type of average that gives a 'typical' value for a set of data.
- 2To calculate the mean, you must first add up all the values in your data set.
- 3After finding the sum, you then divide this total by the number of values you added together.
- 4The mean does not have to be one of the original numbers in the data set.
- 5The mean is sometimes called the 'arithmetic mean'.
- 6It helps to share a total amount equally among a certain number of items.
Worked examples
Example 1
Find the mean of the following numbers: 4, 6, 7, 3, 5.
Answer
The mean is 5.
Example 2
Five children measured their heights in centimetres: 120 cm, 125 cm, 118 cm, 122 cm, 130 cm. What is their mean height?
Answer
The mean height of the children is 123 cm.
Remember to include the units in your final answer when solving word problems.
Example 3
The mean number of goals scored by a football team in 4 matches was 3. If they scored 2, 4, and 5 goals in the first three matches, how many goals did they score in the fourth match?
Answer
The team scored 1 goal in the fourth match.
This type of problem requires you to work backwards from the mean.
Common mistakes
- ✗Forgetting to divide the sum of the numbers by the count of numbers.
- ✗Making errors when adding the numbers, especially with larger numbers or longer lists.
- ✗Incorrectly counting how many numbers are in the data set.
- ✗Confusing the mean with other types of averages (like the median or mode, which are introduced at later stages).
- ✗Not understanding what the calculated mean represents in the context of the problem, leading to incorrect interpretation.
Exam tips
- ★Always show your working out clearly, especially the sum and the division, as this can earn you marks even if your final answer is incorrect.
- ★Double-check your addition and division calculations to avoid simple arithmetic errors.
- ★Read the question carefully to ensure you are using all the correct data and answering what is asked.
- ★If it's a word problem, make sure your answer makes sense in the context of the problem and include any relevant units (e.g., cm, goals).
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