Mean and median (odd and even n)
The median is the middle value of the sorted list; for an even count, take the mean of the two middle values.
Worked example
A tutorial group scored these points. Work out the mean and the median.
10; 4; 12; 19; 16; 11; 20; 3; 8
Worked solution
- 1.x̄ = Σxᵢ / n = 103 / 9 = 11.44
- 2.Sorted: 3; 4; 8; 10; 11; 12; 16; 19; 20
- 3.n = 9 is odd: the median is the middle value = 11.0
Typical mistake: Reading the median from the unsorted list. Sort first!
Your turn
Three problems of exactly this type, each time with new numbers. Comma or point; fractions like 1/6 work too.
Task
A tutorial group scored these points. Work out the mean and the median.
Data (n = 10)
Mean x̄ (2 decimal places)
Median
Comma or point; fractions like 1/6 work too.
Formulas for this topic
- 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.
Typical mistake: Reading the median from the unsorted list. Sort first!
Frequently asked questions
What is the typical mistake in "Mean and median (odd and even n)"?
Reading the median from the unsorted list. Sort first!
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.