Skip to content
Auralith Learning

Year 8 · Maths · Averages · Lesson 2

Averages from frequency tables

Find the mode, mean, median and range from frequency tables, using an f × x column and running totals.

Whiteboard video lesson: Averages from frequency tables

29-minute video lesson

Teaching, worked examples and 20 practice questions solved step by step.

Watch free for a month

What your child will learn

  • Read a frequency table
  • Find the mode from a table
  • Calculate the mean using f × x
  • Find the median using running totals
  • Find the range from a table

The method

  1. Mode: the value with the highest frequency.
  2. Mean: total of (f × x) ÷ total frequency.
  3. Median: position (n + 1) ÷ 2, using running totals.
  4. Range: biggest value − smallest value.

Key words: frequency, frequency table, mean, median, mode, range.

Worked examples

The first three practice questions from the lesson, with every step.

Question 1

The table shows some data. Find the mode.

  1. Step 1: Look at the table
  2. Step 2: Highest frequency: 9
  3. Step 3: Mode = 1

Answer: 1

Question 2

The table shows some data. Find the mode.

  1. Step 1: Look at the table
  2. Step 2: Highest frequency: 11
  3. Step 3: Mode = 7

Answer: 7

Question 3

The table shows some data. Find the range.

  1. Step 1: Look at the table
  2. Step 2: Biggest value: 5. Smallest: 1
  3. Step 3: Range = 5 − 1 = 4

Answer: 4