Year 7 · Mathematics · Statistics
Mean, median, mode and range
Calculate and interpret the mean, median, mode and range of a data set, and decide which measure best describes the data.
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Learning goals
Learners will
- Calculate the mean, median and mode of a data set.
- Calculate the range to describe how spread out data is.
- Decide which measure of centre best represents a data set.
Success looks like
- I can find the mean by adding the values and dividing by how many there are.
- I can find the median, including when there is an even number of values.
- I can find the mode and the range.
- I can explain how an unusual value (outlier) affects the mean.
The big idea
When we collect data, it helps to describe it with a single “typical” value. There are three common ways to do this: the mean, the median and the mode.
The mean is found by adding all the values and dividing by the number of values. For 4, 7, 9, 10 and 5, the total is 35 and there are 5 values, so the mean is 35 ÷ 5 = 7.
The median is the middle value once the data is in order. With an odd number of values there is one middle value. With an even number of values there are two middle values, and the median is halfway between them (add them and divide by 2).
The mode is the value that appears most often. A data set can have one mode, more than one mode, or no mode at all if every value appears the same number of times.
The range tells us how spread out the data is: highest value − lowest value. It is not a measure of the centre.
An outlier can change the mean a lot but barely changes the median. If four friends earn $10, $12, $14 and $16 pocket money and a fifth earns $100, the mean jumps to $30.40 while the median is only $14. In cases like this the median gives a fairer picture.
Worked examples
Finding the mean
Find the mean of 4, 7, 9, 10 and 5.
- Add the values: 4 + 7 + 9 + 10 + 5 = 35.
- Count the values: there are 5.
- Divide: 35 ÷ 5 = 7.
Answer: The mean is 7.
Median with an even number of values
Find the median of 12, 3, 8, 15, 6 and 10.
- Put the values in order: 3, 6, 8, 10, 12, 15.
- There are 6 values, so there are two middle values: 8 and 10.
- Find halfway between them: (8 + 10) ÷ 2 = 18 ÷ 2 = 9.
Answer: The median is 9.
Mode and range
The number of goals scored by a netball team in seven games was 2, 5, 5, 7, 9, 5 and 3. Find the mode and the range.
- Put the values in order: 2, 3, 5, 5, 5, 7, 9.
- 5 appears three times, more than any other value, so the mode is 5.
- Range = highest − lowest = 9 − 2 = 7.
Answer: The mode is 5 and the range is 7.
Practice check
Have a go, then check your answers. Each answer comes with an explanation.
Answer guide for parents
What is the mean of 6, 8 and 10?
8 — 6 + 8 + 10 = 24, and 24 ÷ 3 = 8.
What is the median of 3, 9, 4, 7 and 2?
4 — In order the values are 2, 3, 4, 7, 9. The middle value is 4.
What is the mode of 1, 4, 4, 6, 7, 7, 7, 9?
7 — 7 appears three times, which is more than any other value.
What is the range of 15, 22, 9, 30 and 18?
21 — Highest − lowest = 30 − 9 = 21.
The maximum temperatures in Darwin over five days were 31 °C, 33 °C, 32 °C, 34 °C and 30 °C. What was the mean maximum temperature in degrees Celsius?
32 °C — 31 + 33 + 32 + 34 + 30 = 160, and 160 ÷ 5 = 32.
What is the median of 5, 1, 8 and 3?
4 — In order: 1, 3, 5, 8. The two middle values are 3 and 5, and (3 + 5) ÷ 2 = 4.
The mean of four test scores is 15. What is the total of the four scores?
60 — Mean = total ÷ number of values, so total = mean × number of values = 15 × 4 = 60.
The ages of five cousins are 9, 11, 12, 12 and 16. What is the range of their ages in years?
7 — Range = oldest − youngest = 16 − 9 = 7 years.
Watch out for
- Finding the median without ordering the data first. Always rewrite the values from smallest to largest before looking for the middle.
- Thinking the mode is the highest number, or the number with the biggest frequency count rather than the value itself. The mode is the value that occurs most often.
- Treating the range as a typical value. The range only measures spread.
- Assuming the mean must be one of the data values. The mean can be a value that does not appear in the data, and can even be a decimal.
Tips for parents
- Use family data: heights, shoe sizes, minutes of reading each day or weekly grocery costs make good data sets.
- After calculating, ask “Does this answer make sense? Is it somewhere in the middle of the data?”
- Discuss which measure is fairest when there is an outlier, such as one very expensive item in a list of prices.
Go further
- Record the daily maximum temperature for two cities for a week. Compare their means and ranges and write a short report.
- Find five numbers that have a mean of 10, a median of 9 and a mode of 8.
- Collect the scores from a sports team's season and investigate how removing the highest and lowest scores changes the mean.