Working with Statistical Diagrams | Mathematics for GCSE/IGCSE - Year 11 PDF Download

Reading & Interpreting Statistical Diagrams

How do I read and interpret statistical diagrams?

• Questions might use statistical diagrams instead of raw data.
• These diagrams may be familiar or unfamiliar, but will be straightforward to read.
• No new skills are required to interpret unfamiliar diagrams.
• Reading and interpreting statistical diagrams involves extracting necessary information.
• This information allows calculation of meaningful statistics like mean, median, mode, range, and interquartile range.
• These statistics help draw conclusions about the data.
• Important aspects to look for in diagrams include:
  • A key or shading indicating what parts of the diagram represent (e.g., solid shading for boys' data, striped shading for girls' data in a bar chart).
  • Labels on the axes providing information.
  • Keywords such as frequency.
  • Any unusual or unexpected details mentioned around the diagram.
  • Anomalies or outliers.

Comparing Statistical Diagrams

What is meant by comparing statistical diagrams?

• Some questions present data as diagrams instead of lists.
• You may need to compare different diagrams representing different characteristics.
  • For example, one diagram might show data for dogs and another for cats, allowing comparison between them.
  • Another example could involve diagrams from different time points to reveal changes over time.
• Unfamiliar diagrams may be used, but they will be explained in the question or through a key.
• These unfamiliar diagrams are generally straightforward and easy to interpret.

How do I compare statistical diagrams?

• Compare data using differences or similarities in:
  • Averages: mean, median, mode.
  • Spread: range, interquartile range.
  • Unusual data values: anomalies or outliers.
• Aim to make at least two pairs of comments when comparing data.
• First pair of comments should use an average (mean or median, not mode):
  • Compare the averages with specific numbers.
    • Example: "Class A's median of 11 was higher than Class B's median of 6."
  • Explain the comparison in context.
    • Example: "On average, Class A scored higher on the test than Class B."
• Second pair of comments should use a measure of spread (range or interquartile range):
  • Compare the measures of spread with specific numbers.
    • Example: "Class A's interquartile range of 5 was higher than Class B's interquartile range of 3."
  • Explain the comparison in context.
    • Example: "The test scores in Class A showed more variation than in Class B."
• The mode can be mentioned if relevant, especially for non-numerical data, but it typically yields fewer marks.
• Before comparing data or diagrams, calculate the necessary averages and measures of spread.
• Consider and mention any assumptions or issues that could affect the reliability of the results and comparisons.
  • Examples:
    • "Do we assume that the test taken by Class A and Class B was the same?"
    • "Were Class A and Class B of similar ability or age?"
• These considerations may not be clear from the information provided but are important for validating comparisons.