Mean, median and mode
Measures of location show where the data lie. The mean uses every value, the median resists outliers and the mode is the most frequent value.
Formulas
- Mean: x̄ = Σxᵢ / n
- Median: sort the values; for odd n the middle value, for even n the mean of the two middle values.
- Mode: the most frequent value.
- Range: maximum − minimum.
Your turn
Three problems on this topic. Comma or point, fractions like 1/6 work too.
Task
Students said how many hours they study at weekends. Find the mode and the range.
Data (n = 9)
Mode
Range
Comma or point; fractions like 1/6 work too.
Worked example
A tutorial group scored these points. Work out the mean and the median.
16; 9; 5; 6; 7; 6; 8
Worked solution
- 1.x̄ = Σxᵢ / n = 57 / 7 = 8.14
- 2.Sorted: 5; 6; 6; 7; 8; 9; 16
- 3.n = 7 is odd: the median is the middle value = 7.0
Typical mistake: Reading the median from the unsorted list. Sort first!
Students said how many hours they study at weekends. Find the mode and the range.
1; 8; 7; 7; 8; 8; 1; 2; 4
Worked solution
- 1.Mode = most frequent value = 8 (appears 3 times)
- 2.Range = maximum − minimum = 8 − 1 = 7
Typical mistake: Giving how often the mode occurs instead of the value itself.
Frequently asked questions
When is the median better than the mean?
With outliers or skewed data such as income: one very large value shifts the mean a lot but the median hardly at all.