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Data, averages and range Cambridge IGCSE Mathematics 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

  1. 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.
  2. 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.
  3. 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.

  1. In order: 3, 5, 5, 7, 7, 7, 9. Mean = 43 ÷ 7 = 6.14.
  2. Median = the 4th value = 7. Mode = 7.
  3. 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.
5 questions, about 2 minutes.

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.

  1. What is the mean of 2, 4, 6, 8?
    • 4
    • 5 (the answer)
    • 6
    • 20

    20 ÷ 4.

  2. What is the median of 1, 3, 3, 6, 7?
    • 1
    • 3 (the answer)
    • 4
    • 6

    The middle value of five.

  3. What is the mode of 2, 3, 3, 5, 7, 7, 7?
    • 3
    • 5
    • 7 (the answer)
    • 4.9

    It occurs most often.

  4. What is the range of 4, 9, 2, 11, 6?
    • 2
    • 6
    • 9 (the answer)
    • 11

    11 − 2.

  5. Which of these is continuous data?
    • the number of pets
    • shoe size
    • height (the answer)
    • the number of goals

    It can take any value, not just whole numbers.

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