GCSE Maths: Statistics and Data Handling

Statistics questions at GCSE test whether you can move between raw data, summary measures and graphical representations — and whether you know which tool suits which situation. This quiz covers the Statistics strand across both tiers, finishing with the Higher-only techniques.

The averages questions probe understanding rather than rote calculation: which properties genuinely distinguish the mean from the median (sensitivity to outliers versus positional robustness), where the median of twenty ordered values actually sits (between the 10th and 11th), and the grouped-data convention of using each class midpoint when estimating a mean — the fact examiners test almost every year.

Sampling gets two questions: recognising systematic sampling from its every-nth-person description, and identifying the genuine sources of bias in survey design — unrepresentative samples and leading questions — against plausible-sounding decoys. Scatter graphs and correlation appear through interpreting a downward trend as negative correlation and stating what that means for the two variables.

The Higher tier cluster covers the techniques that anchor the top of the statistics mark range: frequency density for histograms with unequal class widths (frequency divided by class width, tested on a 20-wide class), the interquartile range as the spread of the middle half of the data, reading the IQR from box plot quartiles, and interpreting the 50th percentile of a cumulative frequency graph as the median.

Every question carries its data in the question text, and each explanation states the defining rule being applied. Together with the Probability quiz in this collection, it completes the data side of the specification — and the concepts here are precisely the assumed knowledge that A-Level maths statistics builds on.

• Compare the mean and median, including outlier sensitivity and locating the median in ordered data
• Estimate a mean from grouped data using class midpoints
• Recognise sampling methods and identify sources of bias
• Interpret scatter graphs and correlation
• Use Higher tier techniques: frequency density, quartiles, IQR, box plots and cumulative frequency graphs

Topic scope follows the Statistics strand of the Department for Education's GCSE mathematics subject content: sampling and its limitations, charts and grouped data, measures of central tendency and spread, scatter graphs and correlation, and (Higher) histograms with unequal class intervals, quartiles and cumulative frequency.