Data Presentation and Interpretation

This lesson covers methods of presenting and interpreting data as required by the Edexcel A-Level Mathematics specification (9MA0), Paper 3 Section A -- Statistics. You must be able to construct and interpret box plots, cumulative frequency diagrams, histograms (including those with unequal class widths), stem-and-leaf diagrams, and compare distributions.

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Box Plots (Box-and-Whisker Diagrams)

A box plot displays the five-number summary of a data set:

1. Minimum value (or lowest value that is not an outlier)
2. Lower quartile (Q1) -- the value below which 25% of the data falls
3. Median (Q2) -- the middle value (50th percentile)
4. Upper quartile (Q3) -- the value below which 75% of the data falls
5. Maximum value (or highest value that is not an outlier)

Structure of a box plot

• A box is drawn from Q1 to Q3. The length of the box is the interquartile range (IQR) = Q3 - Q1.
• A line inside the box marks the median.
• Whiskers extend from the box to the smallest and largest values within the non-outlier range.
• Outliers are plotted as individual points (crosses or dots) beyond the whiskers.

Identifying outliers