A table shows: Value 2 occurs 3 times. What is the frequency of 2?
Frequency = number of times it appears.
The value 2 appears 3 times.
Frequency Tables
Frequency tables organise data into groups to make it easier to analyse. They are often used before constructing graphs or calculating averages.
Overview
A frequency table is used to organise data by showing each value or category and how many times it appears.
Frequency = how many times something happens
Frequency tables make raw data easier to read, compare and use. They are often the first step before drawing charts or calculating averages.
What you should understand after this topic
- Understand what a frequency table shows
- Count frequencies accurately
- Complete a table from a list of data
- Find the total frequency
- Use a frequency table to answer questions
Key Definitions
Data
Information collected from a survey, test, experiment or list.
Frequency
The number of times a value or category appears.
Frequency Table
A table showing values or groups and their frequencies.
Tally
A counting method often used before writing the final frequency.
Total Frequency
The sum of all the frequencies in the table.
Category
A label or value used to organise the data in the table.
Key Rules
Read the data carefully
Make sure every value is counted once only.
Use tally marks if needed
Tallies help avoid losing track while counting.
Add all frequencies
This gives the total number of data values.
Check nothing is missed
The total frequency should match the original data list.
Quick Pattern Check
Single values
Example: test scores of 1, 2, 3, 4, 5.
Categories
Example: favourite fruit or eye colour.
Tallies first
Useful when data lists are long.
Total check
Add the frequencies at the end.
How to Solve
What is a frequency table?
A frequency table organises data by showing how often each value occurs. It makes patterns easier to see compared to a long list of numbers.
Raw data → count values → organise into a table
Example data
Here are the numbers of books read by 10 students:
1, 2, 3, 2, 1, 4, 2, 3, 1, 2
Step 1: List the possible values
The values are 1, 2, 3 and 4.
Exam tip: List values in order to avoid missing any.
Step 2: Count each value
1 appears 3 times.
2 appears 4 times.
3 appears 2 times.
4 appears 1 time.
Step 3: Complete the frequency table
Write each value with its frequency.
Check that every data value has been counted.
Step 4: Check the total frequency
\( 3 + 4 + 2 + 1 = 10 \)
The total frequency should match the number of original data values.
Exam habit: Always check this to avoid missing values.
Using tally marks
Tally marks help you count efficiently when dealing with longer data sets.
Tallies are grouped in fives for quick counting.
Each group of five is written as four vertical lines with a diagonal line across.
How to interpret a frequency table
Frequency tables are often used before drawing bar charts.
Most common
Find the largest frequency.
Least common
Find the smallest frequency.
Total
Add all frequencies together.
Specific value
Read the frequency beside that value.
Example Questions
Edexcel
Exam-style questions inspired by Edexcel GCSE Mathematics, focusing on reading frequency tables.
Edexcel
The table shows the number of pets owned by some students.
| Number of pets | Frequency |
|---|---|
| 0 | 3 |
| 1 | 5 |
| 2 | 4 |
| 3 | 2 |
How many students have 2 pets?
Using the table above, how many students are there in total?
AQA
Exam-style questions based on the AQA GCSE Mathematics specification, focusing on completing frequency tables.
AQA
The data below shows the number of goals scored in 10 matches.
\( 1,\ 3,\ 2,\ 1,\ 2,\ 2,\ 4,\ 3,\ 1,\ 2 \)
| Goals | Frequency |
|---|---|
| 1 | |
| 2 | |
| 3 | |
| 4 |
Complete the frequency table.
Which number of goals is most common?
OCR
Exam-style questions aligned with OCR GCSE Mathematics, emphasising interpretation and checking data.
OCR
A completed frequency table has a total frequency of 18.
The original data set contains 20 values.
Explain what this tells you.
OCR
The table shows the number of books read by students.
| Books | Frequency |
|---|---|
| 0 | 2 |
| 1 | 6 |
| 2 | 5 |
| 3 | 3 |
How many students read at least 2 books?
Exam Checklist
Step 1
Read the full data list carefully.
Step 2
List every value or category clearly.
Step 3
Count each one accurately, using tallies if needed.
Step 4
Add the frequencies to check the total.
Most common exam mistakes
Missed values
Forgetting to count one or more data values.
Wrong total
Not checking that the frequencies add up properly.
Messy counting
Losing track because no tally marks were used.
Reading error
Confusing the value with its frequency.
Common Mistakes
These are common mistakes students make when creating and interpreting frequency tables in GCSE Maths.
Counting values more than once
Incorrect
A student accidentally counts the same data value twice.
Correct
Each data value should be counted once only. Use a clear method such as tally marks to avoid double counting.
Missing categories
Incorrect
A student forgets to include one of the values or groups.
Correct
Make sure every category or value in the data is represented in the table. Check the original data carefully.
Adding frequencies incorrectly
Incorrect
A student makes an error when calculating the total frequency.
Correct
Add all frequencies carefully and double-check your total to avoid simple calculation mistakes.
Mixing up values and frequencies
Incorrect
A student confuses the data values with how often they occur.
Correct
The value column shows the data itself, while the frequency column shows how many times each value appears. Keep them clearly separated.
Not checking against the original data
Incorrect
A student does not verify that the table matches the data.
Correct
The total frequency should match the number of data values given. Always check this to confirm your table is correct.
Try It Yourself
Practise organising and interpreting data using frequency tables.
Foundation
Foundation Practice
Read and interpret frequency tables.
A table shows frequencies: 4, 6, 10. What is the total frequency?
Add all frequencies.
4 + 6 + 10 = 20.
A frequency table shows values: 1 occurs 2 times, 2 occurs 3 times. How many values in total?
Add frequencies.
2 + 3 = 5 values.
A table shows 5 values with frequency 4 and 6 values with frequency 2. Find total frequency.
Add frequencies only.
4 + 2 = 6.
What does frequency represent?
Think count.
Frequency = number of occurrences.
A table shows frequencies: 3, 7, 5. Find total frequency.
Add.
3 + 7 + 5 = 15.
A student adds values instead of frequencies. What is wrong?
Focus on counts.
Total frequency = sum of frequencies.
A value occurs 8 times. What is its frequency?
Frequency = occurrences.
Frequency is 8.
Which value has highest frequency if counts are 2, 5, 9?
Largest count.
9 is highest frequency.
A table shows 4 values with frequencies 2, 3, 4, 1. Find total frequency.
Add all frequencies.
2 + 3 + 4 + 1 = 10.
Higher
Higher Practice
Use frequency tables to calculate totals and averages.
Values: 2 (freq 3), 4 (freq 2). What is total frequency?
Add frequencies.
3 + 2 = 5.
Values: 1 (freq 4), 3 (freq 6). Find total frequency.
Add.
4 + 6 = 10.
Values: 2 (freq 3), 5 (freq 2). What is total sum of data?
Multiply value × frequency.
2×3 = 6, 5×2 = 10 → total = 16.
Values: 3 (freq 2), 6 (freq 4). Find total sum of data.
Multiply and add.
3×2 = 6, 6×4 = 24 → total = 30.
How do you find the mean from a frequency table?
Think mean formula.
Mean = total ÷ frequency.
Values: 2 (freq 3), 4 (freq 1). Find the mean.
Find total then divide.
Total = 6 + 4 = 10 → total freq = 4 → mean = 2.5.
A student forgets to multiply value by frequency. What is wrong?
Think weighted values.
Must multiply value × frequency.
Values: 5 (freq 2), 10 (freq 3). Find total sum.
Multiply and add.
5×2 = 10, 10×3 = 30 → total = 40.
What is the main purpose of a frequency table?
Think structure.
Frequency tables organise data.
Values: 1 (freq 5), 2 (freq 5). Find the mean.
Find total then divide.
Total = 5 + 10 = 15 → total freq = 10 → mean = 1.5.
Games
Practise this topic with interactive games.
Games coming soon.
Frequently Asked Questions
What is a frequency table?
A table showing how often values occur.
Why group data?
To simplify large datasets.
What comes next?
Graphs like histograms.