Grades 3–5Probability & StatisticsPlanned
Data displays and the mean as a fair share
Bar graphs, line plots and tables with scales; reading and comparing displays; spotting misleading graphs; and the mean as a fair share.
math.prob.data-displays
The lesson for this topic has not been written yet. The outline below is part of the curriculum map and has not been reviewed.
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)