L: Data presentation and interpretation: Recognise and interpret possible outliers in data sets and statistical diagrams. Select or critique data presentation techniques in the context of a statistical problem. Be able to clean data, including dealing with missing data, errors and outliers.

The idea

Outliers are values that lie an unusual distance from the bulk of the data. A common rule is that a value is an outlier if it is more than 1.5 times the interquartile range below the lower quartile or above the upper quartile. You must recognise such values in lists, box plots, histograms or scatter diagrams, and interpret their possible causes. When choosing or criticising a presentation, consider whether it shows the distribution clearly, whether the scale is misleading, and whether the diagram suits the data type. Cleaning data means checking for missing entries, impossible values such as negative heights, and outliers, then deciding whether to remove, correct or keep them, and recording your decision.

What earns the marks

• Correctly calculate the interquartile range and use the 1.5 × IQR rule to identify possible outliers.
• Interpret an outlier in context, suggesting a plausible reason such as a recording error, a genuine extreme value, or a different population.
• Evaluate a statistical diagram by commenting on its suitability, for example a histogram for continuous data or a box plot for comparing distributions.
• Critique a presentation by identifying misleading features such as a truncated axis, unequal class widths without frequency density, or a 3D effect that distorts areas.
• Describe a data-cleaning process that checks for missing values, impossible values and outliers, and states what action is taken for each.
• Justify whether to remove or retain an outlier, referring to the context and the effect on summary statistics.

Common mistakes and how to put them right

• Using the range instead of the interquartile range when applying the 1.5 × IQR rule.

  Put it right: Find Q1, Q3 and IQR first, then test values below Q1 − 1.5 × IQR or above Q3 + 1.5 × IQR.

• Assuming every outlier is an error and deleting it automatically.

  Put it right: Investigate the context; an outlier may be a genuine extreme value that should be kept and discussed.

• Choosing a pie chart for continuous data or a histogram for categorical data.

  Put it right: Match the diagram to the data type—pie charts for proportions of a whole, histograms for continuous grouped data, bar charts for categories.

• Ignoring missing data or treating blanks as zero.

  Put it right: Identify missing entries, decide whether to exclude them or estimate them, and state the effect on the analysis.

Exam tips

• When asked to identify outliers, show the quartiles, the IQR and the boundary calculations clearly so the method is visible.
• In critique questions, make at least two distinct points about the diagram, such as axis scale, choice of average, or clarity of labels.
• For data cleaning, structure your answer as a checklist: missing data, errors, outliers, and the action taken for each.
• Use the context in your interpretation; a numerical answer without a contextual comment may not gain full credit.