Statistics
Statistics is the branch of maths concerned with collecting, organising, summarising and interpreting data, using averages such as the mean, median and mode, the range, and charts including bar charts, pie charts, frequency tables and scatter graphs. At KS3, pupils learn to calculate and compare these summary statistics and to read information accurately from a range of diagrams.
Before you start
Make sure you're comfortable with these topics first:
Method
- To find the mode, identify the value (or category) that occurs most often in the data set.
- To find the median, put the data in order of size and pick the middle value, or the mean of the two middle values if there is an even number of values.
- To find the mean, add up all the values and divide by how many values there are.
- To find the range, subtract the smallest value from the largest value; this measures spread, not an average.
- When data is grouped in a frequency table, use the midpoint of each class to estimate the mean, and identify the modal class and the class containing the median.
- Read charts such as bar charts, pie charts, pictograms and scatter graphs carefully against their scale or key before extracting or calculating any values.
Worked example
The number of goals scored by a football team in 9 matches was: 1, 3, 0, 2, 2, 5, 1, 2, 4. Find the mode, median, mean and range of the goals scored.
- Order the data: 0, 1, 1, 2, 2, 2, 3, 4, 5.
- Mode: the most frequent value is 2, since it appears 3 times.
- Median: with 9 values, the middle (5th) value in the ordered list is 2.
- Mean: total = 0 + 1 + 1 + 2 + 2 + 2 + 3 + 4 + 5 = 20, divided by 9 = awrt 2.2.
- Range: largest minus smallest = 5 - 0 = 5.
Practice questions
Try each question, then tap to reveal the answer.
Exam-style questions
Written in the style of a KS3 Maths exam paper, with a full mark scheme.
The ages, in years, of 6 people in a walking group are: 34, 41, 28, 34, 50, 39. Find the range of their ages.
A survey of 8 pupils recorded how many hours of TV they watched in a week: 5, 8, 12, 5, 9, 20, 6, 7. Explain, with a calculation, why the median is a more suitable average than the mean for describing a typical value here.
A two-way table shows the lunch choice of Year 8 pupils. Boys: Hot meal 24, Packed lunch unknown, Total 45. Girls: Hot meal unknown, Packed lunch 14, Total 40. (a) Work out the number of boys who have a packed lunch. (b) Work out the number of girls who have a hot meal. (c) Work out the total number of pupils who have a packed lunch.
Free printable worksheet
Want more practice on paper? Download the statistics worksheet pack - 16 pages of exam-style questions with a full mark scheme. No sign-up, no email wall - just the PDF, free for personal and classroom use.
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