IGCSE Maths / Working with data
Two-way tables and reading statistical diagrams revision notes
Edexcel International GCSE Maths (4MA1), chapter 19: Working with data, specification point 6.1b-f. Free lesson.
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Two-way tables organise two pieces of information and let you find missing values and probabilities. Complete each row and column from its totals, then use the correct total as the denominator.
What a two-way table shows
A two-way table puts two types of information about the same group into a grid. Here, the rows show whether students are boys or girls, and the columns show how they travel to school. Each cell belongs to both a row and a column. The row and column totals describe the groups, and the grand total is the total number of students.
How to fill in missing cells
A missing cell is the line total minus the values already in that row or column. Once you have filled the gaps, check the table in both directions because a value can make one row correct but leave a column wrong. The boys' row totals 30. With 12 boys coming by bus and 8 by car, 10 boys walk. The girls' row also totals 30. Since 14 girls walk and 22 students come by bus, the table gives 6 girls coming by car. Check every row and column. The row totals and column totals should both agree with the grand total, 60.
How to read probabilities from the table
A probability is the number of outcomes that match the question divided by the number of possible outcomes. For a student chosen at random from all 60 students, the denominator is 60, the grand total. 22 students come by bus, so the probability is 22/60. 14 students are girls who walk, so the probability is 14/60. 8 boys and 6 girls come by car. That is 14 students, so the probability of coming by car is 14/60.
When the denominator changes
Read the question carefully to see who is being chosen from. Chosen at random means the whole group, so use the grand total. If the question restricts the choice to one row, use that row's total instead. For a girl who walks chosen from all students, use 14/60, not 14/30. If the question says the student is a girl, the choice is restricted to the girls, so the denominator is the girls' row total, 30.
More lessons in Working with data
- Bar charts, pie charts and pictograms
- Mean from a frequency table
- Estimated mean and modal class for grouped data
- Frequency density
- Drawing a histogram
- Reading frequencies from a histogram
- Completing a histogram from a part drawn graph
- Estimating a frequency within a class
- Building a cumulative frequency table
- Plotting a cumulative frequency diagram
- Reading values from a cumulative frequency graph
- Estimating how many are above or below a value
- Estimating the median from a cumulative frequency diagram
- Estimating the interquartile range from a cumulative frequency diagram
- Comparing two cumulative frequency distributions
- Mean, median, mode and range
- Quartiles and the interquartile range for discrete data
- What a measure of spread tells you
- Using the interquartile range to compare distributions