Key Idea: Statistics turn a page of figures into a few numbers and a picture. This topic is the averages, the spread, the charts, and how to use them without being misled.
Averages
- Mean: add them up, divide by how many.
- Median: the middle figure once they are in order.
- Mode: the figure that comes up most often.
Spread
- Interquartile range: Q3 − Q1, the spread of the middle half.
- Standard deviation: how far figures sit from the mean on average.
- Same mean, bigger spread: harder to plan.
Charts and decisions
- Bar charts compare; pie charts show shares of one whole.
- Choose the average that one extreme figure cannot pull.
- Small samples and old figures can mislead.
The words to know
| Word | Means | Do not confuse with |
|---|---|---|
| Mean | the total divided by the number of figures | the median |
| Median | the middle figure when the figures are in order | the mean |
| Mode | the figure that occurs most often | the highest figure |
| Interquartile range | Q3 − Q1: the spread of the middle half of the data | the range, highest − lowest |
| Standard deviation | a measure of how spread out figures are around the mean | the mean itself |
Write the working, then the answer with its unit. For a Comment, say what the figure shows about the business and what it means for a decision.
Exam-style question
In one week the Market Square shop sold 380, 360, 400, 410, 450, 630 and 380 loaves. Calculate the mean number of loaves sold a day (show all your working).
Model answer plan
See the mark-by-mark plan — for / against / judgement, with marking guidance — in study mode.
Important: Saturday's 630 pulls Kofi's mean up to 430, while the median is 400. Baking the mean every day would leave bread over on most days. Check the median and the spread before deciding.
Tap each card to check yourself.
Median and mode of Kofi's week? In order: 360, 380, 380, 400, 410, 450, 630. Median 400, mode 380.
High Street and Park Road have similar means. Which is harder to bake for? Park Road: standard deviation 76.5 against High Street's 12.2.
When is a pie chart the right choice? When the parts make up one whole, such as why 200 customers chose the bakery.
Why use the median for pay? One very high salary pulls the mean up; the median shows what a typical worker earns.
One limitation of statistics in a decision? A small or old sample may not show what customers will do next.
What does a large standard deviation tell a manager? Sales swing a lot from day to day, so plans built on the mean will often be wrong.
Exam tips
- Show the working for every average.
- Put the unit on every answer.
- Choose the average that fits the data: the median when one figure is extreme.
- Read the spread as well as the average.
- A Comment says what the figure means for the decision.