Calculations with the Mean (Cambridge International IGCSE Maths)

Calculations with the mean

How do I solve harder problems involving the mean?

• Remember what the mean is

  • Mean = total of values ÷ number of values

    • It is a formula involving three quantities
    • if you know any two, you can find the other one

• A question may require you to work backwards from a known mean

  • It helps to rearrange the formula
  • Total of values = mean × number of values

• Find the total of the values before and after to help with question that involve:

  • missing values
  • adding in, or taking out, a value

Exam Hint It can help to think of the mean as a formula which you can rearrange.

Total of values = mean × number of values

Worked Example A class of 24 students has a mean height of 1.56 metres. A new student joins the class. The mean height of the class is now 1.57 metres.

Find the height of the new student.

Answer:

Rearrange the formula for mean to get 'total of heights = mean height × number of students' Find the total of heights before

Total of heights before = 1.56 × 24 = 37.44

Find the total of heights after Remember there are now 25 students

Total of heights after = 1.57 × 25 = 39.25

The height of the new student is the difference of the two totals above

39.25 - 37.44 = 1.81

Final answer: The height of the new student is 1.81 metres