Data displays and the mean as a fair share

Builds on

Required prerequisites, all the way down: 5

You will learn to

• Draw and read bar graphs with scales and line plots, including measurements in fractions of a unit.
• Answer comparison questions from displays and recognise misleading scales.
• Interpret the mean as the amount each person would get if the total were shared equally.

Definition

• A bar graph shows each category as a bar whose length represents its count or amount.
• A scale states how many items each unit of length on an axis represents.
• The mean of a list of numbers is their sum divided by how many numbers there are.

Theorem

• A bar graph whose axis does not start at zero can exaggerate differences.
• The mean multiplied by the number of values equals the total.

Common misconceptions

• Reading bar heights without checking the scale.
• Thinking the mean must be one of the data values.

Leads to

Optional discoveries

• Sampling and statistical reasoning A sample can look different from the whole population; statistics asks how different it is likely to be.

Further reading

• Darrell Huff, How to Lie with Statistics (1954)