3.1 Frequency Tables

A free GCSE Maths Foundation lesson for Edexcel (9–1) from OBA School: types of data, tally charts, frequency tables and grouped frequency tables. Watch the video, read the explanation and worked examples, then try the revision questions. You can work through the full lesson, with interactive activities, practice quizzes and printable worksheets, in our free online course.

What you will learn

• Say whether data is qualitative, discrete or continuous
• Record data in a tally chart and frequency table
• Sort data into a grouped frequency table using class intervals
• Read and use information from a frequency table

Key words

• Qualitative data: Data described in words, e.g. colour, favourite sport, type of pet.
• Discrete data: Numbers that can only take certain values, usually counted, e.g. number of goals.
• Continuous data: Numbers that are measured and can take any value in a range, e.g. time, mass, height.
• Frequency: How many times a value (or a group of values) occurs.
• Class interval: A group of values in a grouped frequency table, e.g. 10 < t ≤ 20.
• Mode / modal class: The value (or class) with the highest frequency.

Types of data

Before you organise data, decide what type it is. Qualitative data is words. Quantitative data is numbers, and it can be discrete (counted) or continuous (measured).

• Eye colour; Type Qualitative; Reason Described in words
• Number of people in a car; Type Discrete; Reason Counted: you cannot have 2.5 people
• Time to run 100 m; Type Continuous; Reason Measured: 13.27 s is possible
• Shoe size; Type Discrete; Reason Only certain values (5, 5½, 6 …) exist

Worked example: deciding the type

Is the mass of a bag of apples discrete or continuous?
Mass is measured, and a bag could weigh 1.2 kg, 1.25 kg, 1.253 kg … so it can take any value.

Answer: continuous

Tally charts and frequency tables

A tally chart helps you count data. Draw one stroke for each item, and cross every fifth stroke through the first four so you can count in fives. The frequency is the total of each tally.

Worked example: making a frequency table

20 people were asked how many pets they own:
0 2 1 0 3 1 1 2 0 1 4 2 1 0 1 3 2 1 0 2
Go through the list in order and make a tally mark for each answer. Then count the tallies.

Answer: see the table (drawn in the printable lesson notes). Check: 5 + 7 + 5 + 2 + 1 = 20 ✓

Key fact: Always add up the frequencies. The total must equal the number of data values.

Grouped frequency tables

When there are lots of different values, put them into class intervals. Classes must not overlap. For continuous data we use inequalities: 10 < t ≤ 15 means "more than 10, up to and including 15".

Worked example: grouping continuous data

The times (minutes) 16 people took to finish a puzzle are:
12.5 8.2 15.0 21.4 18.9 9.7 14.3 25.0 11.1 19.6 16.8 22.7 7.4 13.9 20.0 17.2
Use the classes 5 < t ≤ 10, 10 < t ≤ 15, 15 < t ≤ 20 and 20 < t ≤ 25.
15.0 goes in 10 < t ≤ 15 (it is "up to and including 15"). 20.0 goes in 15 < t ≤ 20.

Answer: frequencies 3, 5, 5, 3 (total 16)

• Frequency; 5 < t ≤ 10 3; 10 < t ≤ 15 5; 15 < t ≤ 20 5; 20 < t ≤ 25 3

For discrete data you can write classes like 0–4, 5–9, 10–14. Once data is grouped you lose the exact values, so you can only say which class a value is in.

Using a frequency table

A frequency table can answer many questions. The mode is the value with the highest frequency, not the frequency itself. To find a total (e.g. total goals), multiply each value by its frequency and add.

• Frequency; 0 4; 1 7; 2 6; 3 2; 4 1

Worked example: reading the table

(a) How many matches were played? 4 + 7 + 6 + 2 + 1 = 20
(b) What is the modal number of goals? The highest frequency is 7, for 1 goal.
(c) How many goals were scored altogether?
0 × 4 + 1 × 7 + 2 × 6 + 3 × 2 + 4 × 1 = 0 + 7 + 12 + 6 + 4 = 29
(d) In how many matches were 2 or more goals scored? 6 + 2 + 1 = 9

Answer: (a) 20 (b) 1 goal (c) 29 goals (d) 9 matches

Common mistakes

• Giving the highest frequency as the mode. In the goals table the mode is 1 goal, not 7.
• Adding the frequencies to find the total number of goals. You must multiply each value by its frequency first.
• Using overlapping classes such as 10–20 and 20–30: a value of 20 would fit in both.
• Putting a boundary value in the wrong class: 15 belongs in 10 < t ≤ 15, not 15 < t ≤ 20.

Revision questions

Try these, then check your answers below each one.

Question 1. The number of goals scored in a football match is which type of data? (Choose from: Qualitative, Discrete, Continuous.)

Answer: Discrete

Working: Goals are counted and can only be whole numbers, so the data is discrete.

Question 2. The time taken to run 200 m is which type of data? (Choose from: Qualitative, Discrete, Continuous.)

Answer: Continuous

Working: Time is measured and can take any value (e.g. 31.47 s), so it is continuous.

Question 3. The frequency table shows the number of brothers and sisters of some students. Number of siblings: 0, 1, 2, 3, 4. Frequency: 6, 9, 7, 3, 1. How many students were asked?

Answer: 26

Working: 6 + 9 + 7 + 3 + 1 = 26 students.

Related lessons

• Previous lesson: 2.7 Using Expressions and Formulae
• Next lesson: 3.2 Two-way Tables
• In this chapter: 3.3 Representing Data
• In this chapter: 3.4 Time Series
• In this chapter: 3.5 Stem and Leaf Diagrams

Continue in the full course

This lesson is section 3.1 (EGCMF0301) of our free GCSE Maths Foundation course. In the full course you get every video for this section, an animated interactive lesson, a self-marking practice quiz, a printable worksheet with a mark scheme, and your progress saved. Go to the full GCSE Maths Foundation course.