IGCSE Maths / Working with data

Mean from a frequency table revision notes

Edexcel International GCSE Maths (4MA1), chapter 19: Working with data, specification point 6.2b-f. Free lesson.

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A frequency table groups repeated values, so you need to find the total value represented by each group before calculating the mean. Divide the total value by the total frequency to find the mean per item or person.

Why you need an extra column

A frequency table gives the number of times each value occurs. To find the mean, you need the total of all the values, not just how many times they occur. Multiply each value by its frequency to show the total contributed by that group. Five families have 0 pets: 5 × 0 = 0 pets. Eight families have 1 pet: 8 × 1 = 8 pets. Four families have 2 pets: 4 × 2 = 8 pets. Three families have 3 pets: 3 × 3 = 9 pets.

How to find the mean

Add the frequency times value column to find the total number of items. Then add the frequencies to find how many items or people there are altogether. Divide the first total by the second, because the mean is the total shared evenly across the whole group.

Worked example: mean number of pets

The table represents the pets owned by 20 families. The products count the pets, while the frequencies count the families.

Use the frequency total, not the number of rows

The number of rows tells you how many different values appear in the table. It does not tell you how many items or people are included. The bottom of the mean fraction must be the total frequency, because that is the number being shared between. There are 4 rows, but 20 families. 25 ÷ 4 = 6.25 is incorrect. 25 ÷ 20 = 1.25 is the mean per family.

A mean does not have to be a whole number

The mean is the total shared evenly, so it can fall between whole-number values. It describes the group, not a particular family. A mean of 1.25 pets per family is valid even though no family owns exactly 1.25 pets. Do not round unless the question asks you to. Quick check: 6 people have 0 brothers, 3 have 1 and 1 has 2. Total brothers: (6 × 0) + (3 × 1) + (1 × 2) = 5. Total people: 6 + 3 + 1 = 10. Mean: 5 ÷ 10 = 0.5 brothers per person.