Charts, graphs and probability

Learn

Tables and bar charts

Before reading any table or chart, check the title, the labels and the units, and look at the scale on the axis — each square might be worth 1, 2, 5 or 10. Many lost marks come from assuming each line is worth 1. When you draw a bar chart, give it a title, label both axes, use an even scale starting at zero, and make the bars the same width with equal gaps.

Pie charts and line graphs

A pie chart shows how a whole is split into parts. The full circle is 360°, so each item's angle is its fraction of the total × 360. If 15 out of 60 people walk to work, 15 ÷ 60 = 1/4, and 1/4 of 360° is 90°. Working backwards, an angle of 72° out of 360° is 1/5 of the total. Pie charts show proportions, not actual numbers, so two pie charts can only be compared in numbers if you know both totals.

Line graphs show how something changes over time, such as temperature through a day or monthly sales. Read values by going up from the horizontal axis to the line and across to the vertical axis. The steeper the line, the faster the change.

Probability

Probability measures how likely something is, on a scale from 0 (impossible) to 1 (certain), with 0.5 meaning an even chance. It can be written as a fraction, a decimal or a percentage. When all outcomes are equally likely, probability = number of favourable outcomes ÷ total number of outcomes. A bag holding 3 red, 5 blue and 2 green counters gives P(blue) = 5/10 = 0.5.

The probabilities of all possible outcomes add up to 1, so P(not happening) = 1 − P(happening). If the chance of rain is 0.35, the chance of no rain is 0.65. Expected frequency is probability × number of trials: if 15% of trains run late, you would expect about 9 of 60 trains to be late.

Combined events, two-way tables and scatter diagrams (Level 2)

For two independent events — where one does not affect the other — multiply the probabilities to find the chance of both happening. The chance of a 4 on a four-sided spinner and heads on a coin is 1/4 × 1/2 = 1/8. Listing every outcome in a sample space table is a good check.

A two-way table splits data by two features at once, such as full-time or part-time and whether staff drive. Fill in missing cells using the row and column totals, then read probabilities directly from it.

A scatter diagram plots pairs of values to see whether they are related. If points rise from left to right there is positive correlation; if they fall, negative correlation; no clear pattern means no correlation. A line of best fit lets you estimate values. Correlation does not prove that one thing causes the other.

Watch out

Common mistakes

• Assuming each square on a chart's axis is worth 1 without checking the scale.
• Giving a probability greater than 1 or writing it as a ratio such as “3:10”.
• Adding probabilities for two events that must both happen; multiply instead.
• Saying a scatter diagram proves that one thing causes another.

Real life

Where you'll use this at work or home

• Reading sales, attendance or performance charts in workplace reports.
• Understanding weather forecasts and risk information.
• Presenting survey results clearly at work or in a community group.
• Spotting trends, such as whether higher temperatures link to higher ice-cream sales.