Order the data before finding the median
For 7, 3, 5, 5, 9, first order it as 3, 5, 5, 7, 9.
The middle value only makes sense after the data has been put in order.
Year 7
Calculate mode, median, mean and range from small data sets
Calculate mode, median, mean and range accurately, then choose which measure best describes a small data set.
Lesson overview
Statistics and data - averages and spread
Averages summarise data in different ways. The mode is the most common value, the median is the middle value when the data is ordered, and the mean is the total divided by how many values there are. The range measures spread by subtracting the smallest value from the largest value.
Mean uses the total
For 4, 6, 8, 10, the total is 28 and 28 divided by 4 is 7.
Count how many values there are before dividing.
Range measures spread
If the smallest value is 3 and the largest is 11, the range is 8.
Range tells you how far apart the extreme values are.
Worked example
Find the mode, median, mean and range of 2, 4, 4, 7, 9.
| Statistic | Answer |
|---|---|
| Mode | 4 |
| Median | 4 |
| Mean | 5.2 |
| Range | 7 |
- The data is already ordered: 2, 4, 4, 7, 9.
- The mode is 4 because it appears most often.
- The median is the middle value, which is also 4.
- The total is 26, so the mean is 26 divided by 5 = 5.2, and the range is 9 - 2 = 7.
Try it
Order the data when needed, then calculate each statistic carefully.
Question 1
What is the mode of 3, 5, 5, 7, 9?
Question 2
What is the median of 2, 4, 6, 8, 10?
Question 3
What is the mean of 4, 6, 8, 10?
Question 4
What is the range of 3, 5, 8, 11?
| Smallest | Largest |
|---|---|
| 3 | 11 |
Question 5
Which average is the middle value in an ordered list?
most common
middle value
total divided by number of values
Common mistakes
Watch for these when working through the lesson.
- Finding the median without ordering the values first.
- Dividing by the wrong number when calculating the mean.
- Adding the largest and smallest values instead of subtracting for the range.
Related topics
These ideas fit closely with this lesson.
- Construct bar charts, pictograms and frequency tables.
- Plan, present and interpret a simple survey.
- Mental and written arithmetic with integers, decimals and fractions.