9.2 Interpreting Statistical Data

2026 Syllabus Objectives

By the end of these notes, you will be able to:

  1. Read, interpret, and draw inferences from tables and statistical diagrams.
  2. Compare sets of data using tables, graphs, and statistical measures.
  3. Appreciate the restrictions on drawing conclusions from given data.
  4. Compare averages and ranges between two data sets.
  5. Compare averages and measures of spread between two data sets.

Main Content

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Part 1: Reading and Interpreting Tables and Statistical Diagrams

What Does "Interpret" Mean?

When you interpret data, you read it carefully and explain what it is telling you. You don't just copy the numbers — you say what those numbers mean in real life.

Types of Statistical Diagrams You Need to Know

1. Frequency Tables

A frequency table lists different values (or groups of values) and shows how many times each one occurs. The count is called the frequency.

ScoreFrequency
13
27
35
44
51

From this table you can read off: 7 students scored 2, only 1 student scored 5, and the most common score is 2.

2. Bar Charts

A bar chart uses rectangular bars to show frequencies. Each bar represents a category or value. The height of the bar shows the frequency.

  • Bars should be the same width and have equal gaps between them.
  • The taller the bar, the more frequent that value is.

How to interpret a bar chart:

  • Find the tallest bar → this is the mode (most common value).
  • Read the height of any bar to find its frequency.
  • Add all bar heights together to find the total number of data values.

3. Pie Charts

A pie chart is a circle divided into sectors (slices). Each sector represents a category. The bigger the slice, the larger the proportion of the total that category represents.

  • The whole circle = 360° = 100% of the data.
  • To find what fraction a sector represents: divide its angle by 360.

Example: If a sector has an angle of 90°, it represents 90/360 = 1/4 of the total.

How to interpret a pie chart:

  • Compare the sizes of slices to see which category is most or least common.
  • Use the angles to calculate exact proportions or actual frequencies (if you know the total).

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