GCSE Maths: Statistics — Topic Revision Workbook

Inside GCSE Maths: Statistics — Topic Revision Workbook

sort qualitative, quantitative, discrete and continuous data, find the mean, median, mode and range from lists and frequency tables, estimate the mean from grouped data and name the modal and median class, understand random, representative and biased samples, and read pie charts, scatter graphs and correlation — then compare two data sets like an examiner. About 30 minutes.

Learning objectives

• classifying data as qualitative or quantitative and discrete or continuous;
• finding the mean, median, mode and range from a list and from a frequency table;
• estimating the mean from grouped data using midpoints, and naming the modal and median class;
• understanding sampling — random, representative and biased samples;
• reading and drawing charts — pie chart angles, scatter graphs, correlation and pictograms — and comparing two distributions.

Activities in this book

1. Task 1 — Types of Data & Averages

   qualitative data describes words or categories (colour, name); quantitative data is numbers. Discrete data can only take set values you count (goals, shoe size); continuous data is measured and can take any value in a range (height, weight). To find the mean, add the values and divide by how many there are; the median is the middle value when they are in order; the range is largest minus smallest.

2. Task 2 — Averages from Lists & Frequency Tables

   from a list, order the numbers to read off the median and spot the mode (the most common value). From a frequency table, the mean is the total of (value × frequency) divided by the total frequency, and the mode is the value with the highest frequency.

3. Task 3 — Grouped Data & Sampling

   with grouped data you cannot find the exact mean, so use the midpoint of each class as a stand-in value: estimated mean = total of (midpoint × frequency) ÷ total frequency. The modal class is the group with the highest frequency. A good sample is random (everyone has an equal chance) and representative (it reflects the whole population); a biased sample leaves groups out.

4. Task 4 — Charts & Correlation

   on a pie chart the whole circle (360°) shares out the total, so each item is worth 360° ÷ total, and each slice angle = frequency × that value. On a scatter graph, positive correlation means both quantities rise together, negative means one rises as the other falls, and a line of best fit follows the trend. On a pictogram, multiply the number of symbols by what one symbol represents.

5. Task 5 — Comparing Two Data Sets at Home

   a good comparison in a GCSE answer always says TWO things: compare an average (which set is typically higher) AND compare the range (which set is more consistent or spread out). Write it in a full sentence, in context.

Suggestions for teaching

• Average + spread. Insist every comparison names an average and the range, written in context.
• Pie chart method. Model “360° ÷ total = degrees per item”, then angle = frequency × that value, and check the slices add to 360°.
• Midpoints for grouped data. Show why the mean from a grouped table is only an estimate, using the midpoint of each class.
• Frequency-table mean. Add a “value × frequency” column rather than treating the frequencies as data values.