GCSE Maths: Statistics — Deep Revision Workbook

Inside GCSE Maths: Statistics — Deep Revision Workbook

classify data, find averages and range from lists and frequency tables (including the median from a table), estimate the mean from grouped data and name the modal and median class, judge samples for bias, work out pie-chart angles, pictograms, correlation, a line of best fit and frequency polygons, then write a full exam-style comparison of two distributions using an average and a measure of spread. About 45 minutes.

Learning objectives

• classifying data as qualitative or quantitative and discrete or continuous;
• finding the mean, median, mode and range from a list (including an even-length list) and from a frequency table, including the median from a table;
• estimating the mean from grouped data using midpoints, and naming the modal and median class;
• judging samples for bias — random, representative, biased — and using the term population;
• reading and drawing charts — pie-chart angles, pictograms, scatter graphs, correlation, a line of best fit and frequency polygons — then writing a full comparison of two distributions with an idea of box plots and the interquartile range.

Activities in this book

1. Section 1 — Types of Data & Averages from a List

   qualitative data describes words or categories (team, colour); quantitative data is numbers. Discrete data can only take set values you count (siblings, goals); continuous data is measured and can take any value in a range (mass, time). For a list: the mean is the total divided by how many values there are; the median is the middle value once they are in order; the mode is the most common value; the range is largest minus smallest.

2. Section 2 — Averages from Lists & Frequency Tables

   with an even-length list the median is the mean of the two middle values. 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. To find the median from a table, count along the frequencies (a cumulative count) until you reach the middle position.

3. Section 3 — Grouped Data, Estimated Mean & 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; the median class is the group containing the middle value (count the cumulative frequency to the middle position). A good sample is random (equal chance) and representative; a biased sample systematically leaves groups out.

4. Section 4 — Charts, Correlation & Lines of Best Fit

   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; the angles must add to 360°. On a pictogram, multiply the number of symbols by what one symbol represents. 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 lets you estimate a value in between. A frequency polygon plots frequency against the midpoint of each class.

5. Section 5 — Exam-Style: Compare Two Distributions

   a full-mark comparison always says TWO things in context: compare an average (which set is typically higher) AND compare a measure of spread — the range, or for higher tier the interquartile range from a box plot (smaller spread = more consistent). Write it in full sentences, in the context of the data.

Suggestions for teaching

• Average + spread. Insist every comparison names an average and a measure of spread (range or IQR), 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, and count cumulative frequency to locate the median class.
• Frequency-table mean. Add a “value × frequency” column rather than treating the frequencies as data values, and count along to find the median.