📏 Range and standard deviation
Measures of dispersion show how spread out the data is. Are values clustered together or widely spread?
Range
- Range = highest value − lowest value
- Simple and quick to calculate
- But only uses two values — ignores everything in between
- Can be distorted by a single outlier
Standard deviation
- Measures how far each value is from the mean on average
- Low SD = data clustered close to the mean (consistent)
- High SD = data spread out widely (variable, unpredictable)
- More reliable than range because it uses ALL data points
You won't need to calculate standard deviation in the exam — just understand what a high or low SD means for the business.
💼 What does dispersion tell a business?
- Low dispersion in sales → consistent, predictable revenue (easier to plan)
- High dispersion in sales → volatile revenue (harder to forecast and budget)
- Low dispersion in quality → consistent products (good for reputation)
- High dispersion in quality → products vary a lot (bad for customer trust)
Example: Two shops both average $10 000 in weekly sales. Shop A ranges from $9 000–$11 000 (low spread, predictable). Shop B ranges from $3 000–$17 000 (high spread, unpredictable). Shop A is much easier to manage.