Charts and graphs

Bar charts, pie charts, frequency diagrams and pictograms, drawn and read accurately.

  • Define and explain Charts and graphs in your own words
  • Use key terms such as Range accurately
  • Apply what you have learned to new examples and questions
  • Avoid the common mistakes learners make with this topic

This lesson focuses on Charts and graphs: bar charts, pie charts, frequency diagrams and pictograms, drawn and read accurately.

Definition: Charts and graphs

Bar charts, pie charts, frequency diagrams and pictograms, drawn and read accurately.

Key ideas

Reading charts carefully

Check the axes first: a bar chart that starts above zero can exaggerate small differences, and a pie chart must show sectors proportional to the data. Frequency diagrams need equal class widths, or frequencies must be scaled by width.

Choosing an average

Use the mean for symmetric data with no extremes, the median when a few extreme values would distort the mean (such as salaries), and the mode for categories (such as favourite colours). Always consider the range too, since identical averages can hide very different spreads.

Key term — Range: The difference between the largest and smallest values, giving a simple measure of how spread out the data is.

Worked example: Charts and graphs

A scatter diagram shows points rising left to right. What type of correlation is this?

Positive correlation.

Answer: Positive correlation.

Common mistakes
  • Reading a truncated bar chart at face value If the y-axis does not start at zero, bars exaggerate differences — check the scale before comparing.
  • Finding the median without ordering the data Always sort the values first; the median is the middle of the ordered list, not the middle of the original list.

Practice

Why might a bar chart with a y-axis starting at 50 be misleading?
Think about how bar lengths compare.

Bars look far more different than the values are, because the truncated axis exaggerates small differences.

Find the mean of 4, 7, 9, 12, 18.
Add, then divide by 5.

Sum = 50; mean = 50 ÷ 5 = 10.

Find the median of 11, 4, 9, 2, 7.
Order the data first.

Ordered: 2, 4, 7, 9, 11; median = 7.

Find the mode and range of 2, 6, 4, 6, 6, 3.
Mode is most frequent; range is max minus min.

Mode = 6; range = 6 − 2 = 4.

Quick check

Charts and graphs — quick check

Which of these best defines "Range"?

The difference between the largest and smallest values, giving a simple measure of how spread out the data is.

Six test scores are 5, 6, 7, 8, 9 and 40. Which average best represents a typical score?

The median (7.5); the mean (12.5) is distorted by the outlier 40.
Key takeaways
  • Charts and graphs: bar charts, pie charts, frequency diagrams and pictograms, drawn and read accurately.
  • Reading charts carefully: Check the axes first: a bar chart that starts above zero can exaggerate small differences, and a pie chart must show sectors proportional to the data.
  • Correlation: A pattern in a scatter diagram where two variables move together — positive, negative or none — which does not by itself prove causation.
  • Watch out for: reading a truncated bar chart at face value