Averages and range
Objective. Calculate and compare mean, median, mode and range.
- 1. Learn
- 2. Worked example
- 3. Practice
- 4. Feedback
- 5. Continue
Learn: the key idea
An average is a single value that represents a typical figure within a data set, with the three common types being the mean, median and mode. The mean is found by adding all the values and dividing by how many there are; the median is the middle value once the data is ordered; and the mode is the value that appears most often. The range measures spread rather than average, found by subtracting the smallest value from the largest. For example, for the data set 3, 5, 5, 8, 9, the mean is (3+5+5+8+9)÷5=6, the median is 5, the mode is 5, and the range is 9−3=6.
Worked example
Find the mean, median and range of the data set: 4, 7, 7, 10, 12.
- 1Find the mean: add the values 4+7+7+10+12=40, then divide by 5, giving 8.
- 2Order the data (already ordered) and find the middle value: 7, which is the median.
- 3Find the range: subtract the smallest from the largest, 12−4=8.
- 4State all three statistics together.
Answer: Mean = 8, median = 7, range = 8
Concept mastery
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Practice
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Start practisingCommon mistake. Pupils sometimes forget to order the data before finding the median, picking the middle value of the unsorted list instead. Always arrange the data in ascending order first.
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