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Mean, median and mode

Summarise a set of numbers with the mean, median and mode, and learn when each one gives the best picture of the data.

Get the whole book: Maths for classes 9 and 10 (7 lessons, free to print)

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The big idea

A cricketer scores different runs in different matches. How do we describe all of them with one number? Mean, median and mode are three ways to do this.

The mean is the average. Add up all the values and divide by how many there are. Mean = sum of values ÷ number of values.

The median is the middle value when the numbers are arranged in order. If there is an odd number of values, take the middle one. If there is an even number, take the mean of the two middle values.

The mode is the value that appears most often. A set can have more than one mode, or none if every value appears once.

The range is the biggest value minus the smallest value. It tells how spread out the data is.

The mean uses every number, so one very big or very small value can pull it. The median is not affected as much. The mode is useful for the most common size or choice, such as a shoe size.

Runs scored in 5 matchesA bar chart of the runs scored in 5 matches: 10, 40, 10, 30 and 35. The two bars of 10 are shaded gold to show the mode. A dashed line across the chart at 25 shows the mean.Runs scored in 5 matches 10 40 10 30 35 Match 1 Match 2 Match 3 Match 4 Match 5 mean = 25 Gold bars: the mode (10 runs twice)
Mean = 25 (dashed line), median = 30 (middle value when ordered), mode = 10 (the gold bars).

Worked examples

See how it works

  1. Mean

    Find the mean of 5, 8, 6, 9, 7. Sum = 5 + 8 + 6 + 9 + 7 = 35. There are 5 values. Mean = 35 ÷ 5 = 7.

  2. Median with an odd number of values

    Find the median of 12, 5, 9, 3, 7. In order: 3, 5, 7, 9, 12. The middle value is 7. So the median is 7.

  3. Median with an even number of values

    Find the median of 4, 8, 6, 10, 2, 12. In order: 2, 4, 6, 8, 10, 12. The middle two values are 6 and 8. Median = (6 + 8) ÷ 2 = 7.

  4. Mode, and all three together

    Shoe sizes of 7 children are 6, 7, 7, 8, 6, 7, 9. The size 7 appears 3 times, more than any other, so the mode is 7. For the runs 10, 40, 10, 30, 35: mean = 125 ÷ 5 = 25, in order 10, 10, 30, 35, 40 the median is 30, and the mode is 10.

Try it at home

Name-length survey

You will need

  • Paper and a pencil
  • Family members or friends who agree to take part

What to do

  1. Ask 7 people for their first name and count the letters in each. Write the numbers down.
  2. Find the mean: add the numbers and divide by 7.
  3. Arrange the numbers in order and find the median (the 4th number).
  4. Find the mode, the number that appears most often.
  5. Find the range. Draw a bar chart of your numbers.

Ask a grown-up: An adult can help choose people to ask. Only first names are needed. Do not ask for private information.

Practice sheet

Check what you learned

Write your answers in a notebook, or print this sheet and write on it. When you finish, mark your work with the answer key.

Practice sheet: Mean, median and mode (Classes 9-10, Maths)

  1. Find the mean of 2, 4, 6, 8.
  2. Find the median of 3, 9, 5.
  3. Find the mode of 2, 3, 3, 5, 3, 7, 5.
  4. Find the mean of 10, 15, 20, 25, 30.
  5. Find the median of 8, 2, 10, 4, 6, 12.
  6. Find the range of 14, 9, 21, 5.
  7. The mean of 5 numbers is 12. What is their sum?
  8. Marks of 5 students are 40, 50, 35, 50, 45. Find the mean, median and mode.
  9. The mean of 4 numbers is 15. Three of them are 12, 18 and 10. Find the fourth number.
  10. The mean of 6 numbers is 8. A seventh number, 22, is added. What is the new mean?

Answer key

Answers: Mean, median and mode

Do the practice sheet first, then check here. If an answer is different from yours, read the lesson again and try once more.

  1. 5 (20 ÷ 4).
  2. 5 (in order 3, 5, 9).
  3. 3 (it appears three times).
  4. 20 (sum 100, divided by 5).
  5. 7 (in order 2, 4, 6, 8, 10, 12; the middle two are 6 and 8).
  6. 16 (21 − 5).
  7. 60 (12 × 5).
  8. Mean 44 (sum 220 ÷ 5), median 45 (in order 35, 40, 45, 50, 50), mode 50.
  9. 20 (the total must be 4 × 15 = 60, and 12 + 18 + 10 = 40, so the fourth is 20).
  10. 10 (old sum 6 × 8 = 48; new sum 48 + 22 = 70; 70 ÷ 7 = 10).

What next

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