Mean, median, mode and range
Summing up data with one number
Five friends' scores in a game: 4, 7, 7, 9, 13.
| Measure | How to find it | Here |
|---|---|---|
| Mean (average) | add them all, divide by how many | (4 + 7 + 7 + 9 + 13) ÷ 5 = 40 ÷ 5 = 8 |
| Median | the middle value when in order | 4, 7, 7, 9, 13 → 7 |
| Mode | the most common value | 7 (twice) |
| Range | largest − smallest (how spread out) | 13 − 4 = 9 |
With an even number of values, the median is halfway between the middle two: for 2, 4, 9, 13 it's (4 + 9) ÷ 2 = 6.5.
Real data: travel time to school
A Year 7 class of 25 recorded how many minutes it takes them to get to school (in order):
5, 7, 10, 10, 10, 12, 12, 15, 15, 15, 15, 15, 18, 20, 20, 20, 20, 22, 25, 25, 25, 30, 30, 35, 55
- Mean = 486 ÷ 25 = 19.44 minutes
- Median = the 13th value = 18 minutes
- Mode = 15 minutes (5 students)
- Range = 55 − 5 = 50 minutes
One student takes 55 minutes — much more than everyone else. A value far from the rest is an outlier. Without it, the mean drops to 17.96 and the range to 30, but the median stays 16.5. That's why the median is often the best "typical value" when there are outliers — it's why house prices are reported as medians.
Two kinds of numerical data
- Discrete data is counted, in whole steps: number of pets, goals scored
- Continuous data is measured and can be any value in a range: height, time, temperature
Your turn
Use a pencil and paper. The answers are at the bottom of the page — try first!
- For 3, 8, 5, 8, 6 find the mean, median, mode and range.
- Find the median and mean of 2, 4, 9, 13.
- A street's house prices include one mansion worth $9 million. Should a real estate report use the mean or the median price? Why?
- Is "the number of siblings you have" discrete or continuous?
- Is "the time to run 100 m" discrete or continuous?
Answers
- Mean 30 ÷ 5 = 6; in order 3, 5, 6, 8, 8 so median 6; mode 8; range 5
- Median (4 + 9) ÷ 2 = 6.5; mean 28 ÷ 4 = 7
- The median — the mansion is an outlier that would pull the mean up a lot
- Discrete (counted)
- Continuous (measured)
For parents and teachers — this lesson covers the Victorian Curriculum Mathematics Version 2.0, Level 7:
- VC2M7ST01: acquire data sets for discrete and continuous numerical variables and calculate the range, median, mean and mode; make and justify decisions about which measures of central tendency provide useful insights into the nature of the distribution of data
Downloads
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