Averages and spread

AQA GCSE Maths

8 ready-made resources for teaching Averages and spread, written for AQA GCSE Maths. Slides, worksheets, mark schemes, homework, an assessment and retrieval quizzes, all with SEN-friendly scaffolding built in as standard. Below is what the topic requires and where students usually go wrong, free to read whether or not you sign up.

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What is in this bundle

Assessment mark schemeWord, editable
End-of-topic assessmentWord, editable
HomeworkWord, editable
Retrieval-practice quizzesWord, editable
SlidesPowerPoint, editable
Starter & exit ticketWord, editable
Tiered worksheetWord, editable
Worksheet mark schemeWord, editable

Foundation tier

Calculate the mean, median, mode, and range from a list of data.
Calculate the mean, median, and range from a frequency table of discrete data.
Compare two distributions using averages and range, and write a simple comparative conclusion.
Identify the modal class and estimate the mean from grouped (continuous) frequency data.

Higher tier, in addition

Estimate the median and interquartile range from grouped data, including from a cumulative frequency graph.
Construct and interpret a cumulative frequency graph and a box plot.
Compare distributions using the interquartile range as a more robust measure of spread than range alone.
Explain how outliers affect the mean but not the median, in a given data context.

Where students go wrong

Calculating the mean from a frequency table by dividing by the number of rows/categories rather than the total frequency.
Confusing the modal class with the class that contains the median in grouped data.
Reading the wrong axis, or an incorrect cumulative frequency value, when constructing or interpreting a cumulative frequency graph.
Comparing distributions using only one measure (e.g. mean alone) without also considering spread, leading to an incomplete conclusion.
Believing "median" always means "the middle data value" rather than "the value at the middle position once the data is ordered."

How it gets asked in the exam

"Calculate the mean/median/range", "Compare the distributions", "Estimate the median from the graph", "Draw a box plot for this data".

Key vocabulary

Mean, median, mode, range, interquartile range, grouped data, modal class, cumulative frequency, box plot, outlier.

Assumed prior knowledge

Fraction and decimal arithmetic.
Basic graph-reading skills.
Sorting and ordering data.
Understanding of grouped frequency tables.

How Speca scaffolds this topic

Structure worked examples for median-finding as three explicit, chunked steps, "order the data," "find the position," "read the value", since skipping the ordering step is a frequent, avoidable error.
Provide comparative-conclusion sentence frames (e.g. "On average, ___ because the mean/median is ___. The data for ___ is more consistent/spread out because...") to scaffold the written-comparison skill separately from the calculation itself.
Use consistent colour-coding between a grouped frequency table and its corresponding bar chart or cumulative frequency graph to strengthen the link between tabular and graphical representations.

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