Statistics
Choose your practice ↓Statistics is the other half of the 15% that probability and statistics share on both tiers, and it is where the reasoning objective AO2 shows up most openly — many of the marks are for interpreting and comparing, not for calculating. It covers sampling and what can fairly be inferred from a sample, constructing and interpreting frequency tables, bar charts, pie charts, pictograms, vertical line charts and time series graphs, and choosing the representation that suits the data. The averages follow: mean, median, mode and modal class, together with the range and the treatment of outliers. Scatter graphs close the Foundation content — correlation, the line of best fit, prediction, and the important warning that correlation does not establish causation and that extrapolating beyond the data is unsafe. Higher adds histograms with equal and unequal class intervals, where frequency density rather than frequency is plotted, cumulative frequency graphs, box plots, quartiles and the interquartile range.
📚 What you learn here
- Sampling, inference about a population, and the limitations of a sample
- Frequency tables, bar charts, pie charts, pictograms, vertical line charts and time series graphs, and when each is appropriate
- Mean, median, mode and modal class; the mean from a frequency table and from grouped data
- Range, outliers, and (Higher) quartiles, the interquartile range and box plots
- Comparing two distributions using one measure of average and one of spread
- Scatter graphs, positive and negative correlation, lines of best fit and prediction
- Why correlation does not establish causation, and the danger of extrapolating past the data
- Histograms with equal and unequal class intervals, using frequency density (Higher)
- Cumulative frequency graphs and reading the median and quartiles from them (Higher)
Frequently asked questions
How do I find the mean from a grouped frequency table?
Use the midpoint of each class, multiply each midpoint by its frequency, total those products, and divide by the total frequency. The answer is an estimate, because the original values are lost once the data is grouped — say so if the question asks why.
What goes on the vertical axis of a histogram?
Frequency density, which is frequency ÷ class width. Plotting frequency itself is what turns a histogram into a bar chart and loses the marks when the class intervals are unequal. Histograms are Higher only.
How do I compare two sets of data properly?
Quote one average and one measure of spread, and say what each means in the context of the question. 'The median is higher and the interquartile range is smaller, so this group scored higher and more consistently' earns the reasoning marks that a bare pair of numbers does not.
Does correlation mean one thing causes the other?
No, and the specification says so explicitly. Two quantities can rise together because a third affects both. Saying that ice cream sales cause sunburn is the standard illustration of why the distinction matters.
✍️ Written by the MathsUK teamChecked against the National Curriculum and GCSE specifications