Learning outcomes
- explain what dispersion means
- compute range
- understand the idea of variance and standard deviation
- compare datasets by spread
What is dispersion?
- Dispersion describes how spread out the data values are.
- Two datasets may have the same mean but different spread.
Range
- Range = largest value - smallest value
- Data:
3, 5, 8, 10 - Range =
10 - 3 = 7
Variance
- Variance measures average squared deviation from the mean.
- It shows how far values tend to spread from the center.
- find the mean
- subtract mean from each value
- square deviations
- average the squared deviations
- Population and sample variance use slightly different formulas in advanced treatment.
- At this level, understand the idea clearly even if detailed formula handling is limited.
Standard deviation
- Standard deviation is the square root of variance.
- It is in the same unit as the original data.
- easier to interpret than variance because unit matches the data
Comparing spread
- smaller standard deviation -> data closer to the mean
- larger standard deviation -> data more spread out
Exam hints and traps
- Range uses only two values, so it can miss the overall pattern.
- Variance is in squared units.
- Standard deviation is not found by adding deviations directly.
- A dataset with the same mean as another can still have larger spread.
Quick practice
- Find the range of
12, 15, 18, 20, 25. - Which has more spread?
5, 5, 5, 51, 5, 9, 13
- Why is standard deviation often easier to interpret than variance?
Answer key
25 - 12 = 131, 5, 9, 13- Because it is expressed in the original unit of the data.