Mode and range
Two quick measures: the mode is the most frequent value, the range the gap between the largest and the smallest value.
Worked example
Students said how many hours they study at weekends. Find the mode and the range.
8; 3; 3; 3; 6; 4; 2; 4; 8; 1
Worked solution
- 1.Mode = most frequent value = 3 (appears 3 times)
- 2.Range = maximum − minimum = 8 − 1 = 7
Typical mistake: Giving how often the mode occurs instead of the value itself.
Your turn
Three problems of exactly this type, each time with new numbers. 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 = 8)
Mode
Range
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: Giving how often the mode occurs instead of the value itself.
Frequently asked questions
What is the typical mistake in "Mode and range"?
Giving how often the mode occurs instead of the value itself.
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.