Interpret, analyse and compare the distributions of data sets from…

The idea

This topic involves analysing and comparing univariate data distributions. You must use appropriate graphical representations: for discrete data, use bar charts or pictograms; for continuous or grouped data, use histograms or frequency polygons. Box plots are used to visualise the five-figure summary: minimum, lower quartile (Q₁), median (Q₂), upper quartile (Q₃), and maximum. Key calculations include measures of central tendency (mean, median, mode/modal class) and spread (range, inter-quartile range/IQR = Q₃ - Q₁). Outliers, extreme values that lie outside the main data distribution, can be identified using rules like being more than 1.5 × IQR below Q₁ or above Q₃. A core skill is comparing two distributions by commenting on both a measure of location (e.g., median) and a measure of spread (e.g., IQR), always interpreting your findings in the context of the data.

What earns the marks

• Calculate measures of central tendency (mean, median, mode, modal class) and spread (range, quartiles, IQR) from lists and frequency tables.
• Draw and interpret appropriate diagrams, including bar charts for discrete data, histograms and frequency polygons for grouped/continuous data, and box plots.
• Compare two distributions by commenting on a measure of central tendency (e.g., median) and a measure of spread (e.g., IQR), ensuring comments are contextualised.
• Identify outliers using a given rule (e.g., values more than 1.5 × IQR below Q₁ or above Q₃) and explain their effect on statistical measures like the mean and range.

Common mistakes and how to put them right

• Forgetting to use midpoints when estimating the mean from a grouped frequency table.

  Put it right: The estimated mean is calculated as Σfx / Σf, where 'x' is the midpoint of each class interval.

• Confusing the mode with the highest frequency.

  Put it right: The mode is the data value or class interval with the highest frequency, not the frequency value itself.

• When comparing distributions, just stating calculated values (e.g., 'The median for A is 25 and for B is 30').

  Put it right: You must interpret this in context (e.g., 'On average, group B's scores were higher than group A's because their median was higher').

Exam tips

• When comparing distributions (e.g., from box plots), always compare a measure of average (like the median) and a measure of spread (like the IQR). Then, explain what each comparison means in the context of the problem. For example, a smaller IQR means the data is more consistent.
• The mean is affected by outliers, whereas the median and IQR are resistant to them. Choose the median as the most appropriate average if the data contains extreme values.