Data, averages and range Edexcel International GCSE Mathematics A revision
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In plain words
An average is one number that stands for a whole set of data. There are three kinds, and they can tell different stories about the same numbers, so it matters which one you choose.
Three things to know
- Mean: add them all up and divide by how many there are. Median: the middle value when they are in order. Mode: the one that occurs most often. Range: largest minus smallest, a measure of spread.
- From a frequency table, the mean is the total of (value × frequency) divided by the total frequency. For grouped data, use the midpoint of each group: the answer is then an estimate.
- Discrete data can only take certain values (a number of people). Continuous data can take any value in a range (a height).
Worked example
Find the mean, median, mode and range of 3, 7, 5, 9, 7, 5, 7.
- In order: 3, 5, 5, 7, 7, 7, 9. Mean = 43 ÷ 7 = 6.14.
- Median = the 4th value = 7. Mode = 7.
- Range = 9 − 3 = 6.
Tips and tricks
- Put the numbers in order before finding the median. With an even number of values, it's halfway between the middle two.
- With a frequency table, divide by the total frequency, not by the number of rows.
It lands in your notebook with its questions as flashcards.
Data, averages and range: 5 questions and answers
These are the quiz’s questions. Do the quiz first, then come back here for the ones that got you.
What is the mean of 2, 4, 6, 8?
20 ÷ 4.
What is the median of 1, 3, 3, 6, 7?
The middle value of five.
What is the mode of 2, 3, 3, 5, 7, 7, 7?
It occurs most often.
What is the range of 4, 9, 2, 11, 6?
11 − 2.
Which of these is continuous data?
It can take any value, not just whole numbers.
Quiz
5 questions
Tap an answer and you’ll see straight away whether it’s right, and why.
Worksheet
4 questions, 9 marks. Write your answers on paper, then check them.
Data, averages and range
Edexcel International GCSE Mathematics A 4MA1 · 9 marks · papermunch.org
Name ______________________________ Date ______________
Find the mean of 4, 8, 6, 5, 7.[2]
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6. 30 ÷ 5.
Find the median of 12, 3, 8, 15, 6, 10.[2]
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9. In order: 3, 6, 8, 10, 12, 15; halfway between 8 and 10.
In a test, 2 students scored 3, 5 scored 4 and 3 scored 5. Find the mean score.[3]
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4.1. (6 + 20 + 15) ÷ 10.
The mean of five numbers is 8. Four of them are 6, 7, 9 and 10. Find the fifth.[2]
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8. The total must be 40; 40 − 32.
Answers: Data, averages and range
- 1. 6. 30 ÷ 5.
- 2. 9. In order: 3, 6, 8, 10, 12, 15; halfway between 8 and 10.
- 3. 4.1. (6 + 20 + 15) ÷ 10.
- 4. 8. The total must be 40; 40 − 32.