GCSE Maths Statistics

Frequency Tables

Frequency Table

Here we will learn about frequency tables, including what a frequency table is and how to make a frequency table.  We will also look at how they can be used to help analyse a set of data.

There are also frequency table worksheets based on Edexcel, AQA and OCR exam questions, along with further guidance on where to go next if you’re still stuck.

What is a frequency table?

A frequency table is a way of organising collected data.

To do this we draw a table with three columns:

  • The first column is for the different items in the data set. 
  • The second column is for the tally marks. 
  • The last column is the frequency column where we can add up the tally marks and write in the corresponding frequencies.

We can add up all of the frequencies to find the total frequency of the set of data.

For example,

Organise the colours of the 12 shirts in a wardrobe into a frequency table.

blue       pink      blue    white    white    blue

black     white     blue     pink     blue     white

Frequency Table Image 1

The total number of shirts is 12.

What is a frequency table?

What is a frequency table?

Averages from frequency tables

We use frequency tables to find descriptive statistics.  These are values which help describe the set of data such as the mean, median and mode of a set of data. 

For example,

A frequency table showing the ages of 25 students on a college course.

Frequency Table Image 2

The mode is 18

The median is the 13^{th} value which is 18

The mean can be calculated using the total of all the values, divided by the total of the frequencies, n.

\text{mean}=\frac{\text{total}}{n}=\frac{(18\times 15)+(19\times 6)+(20\times 4)}{25}=\frac{464}{25}=18.56

Step-by-step guide: Averages from a frequency table

See also: Mean from a frequency table and Mode from a frequency table

Grouped frequency table

Numerical data can also be organised into grouped data.  Here the data is put into different classes with class intervals.

For example,

A grouped frequency table showing the heights of 15 students.

Frequency Table Image 3

The mode class is 140<h\leq150

The median is the 8^{th} value which is in the 140<h\leq150 class interval

We can only calculate an estimate for the mean using the midpoints of the class intervals.  The total of the frequencies is n.

\text{mean}=\frac{\text{total}}{n}=\frac{(135\times 3)+(145\times 7)+(155\times 5)}{15}=\frac{2195}{15}=146.3 (1 d.p.)

Step-by-step guide: Grouped frequency table

See also: Median from a frequency table and Modal class

Frequency tables can be used to draw bar charts, pie charts or histograms.  They can also be used to find cumulative frequency which in turn can be used to estimate median values and upper and lower quartiles for grouped data.

How to make and use frequency tables

In order to make and use frequency tables, here are some tips to consider:

  • Read the frequency table carefully and check the headings.
  • If there are groups, check the beginning and end of the intervals.
  • If you are finding an average, check which one you are asked to find.

Explain how to make and use frequency tables

Explain how to make and use frequency tables

Frequency table worksheet

Frequency table worksheet

Frequency table worksheet

Get your free frequency table worksheet of 20+ questions and answers. Includes reasoning and applied questions.

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Frequency table worksheet

Frequency table worksheet

Frequency table worksheet

Get your free frequency table worksheet of 20+ questions and answers. Includes reasoning and applied questions.

DOWNLOAD FREE

Frequency table examples

Example 1: categorical data

Here are the makes of 20 cars.

Ford      BMW      Honda      Honda      VW     Toyota

Ford      Toyota     Honda     Toyota      Ford      Honda

Honda     VW       Toyota      Honda      Ford      Ford

  • Complete the frequency table.

Frequency Table Example 1 Image 1

  • Go along the data set and for each item put a tally mark in the table.  When you have finished, add up the tally marks to find the frequencies.

Frequency Table Example 1 Image 2

  • Add up the frequencies in the final column to get the total number of items in the data set.

Example 2: numerical data

Here are the temperatures at midday for 7 days (in ०C)

23 \quad \quad \quad 24 \quad \quad \quad 24 \quad \quad \quad 23 \quad \quad \quad 24 \quad \quad \quad 25 \quad \quad \quad 21

  • Complete the frequency table.

Frequency Table Example 2 Image 1

  • Go along the data set and for each item put a tally mark in the table.  When you have finished, add up the tally marks to find the frequencies.

Frequency Table Example 2 Image 2

  • Add up the frequencies in the final column to get the total number of items in the data set.

Example 3: grouped data

Here are the speeds of 20 vehicles, to the nearest mph.

\begin{aligned} &45 \quad \quad 65 \quad \quad 72 \quad \quad 48 \quad \quad 74 \quad \quad 67 \quad \quad 68 \quad \quad 46 \quad \quad 56 \quad \quad 53 \\\\ &58 \quad \quad 68 \quad \quad 72 \quad \quad 64 \quad \quad 62 \quad \quad 49 \quad \quad 72 \quad \quad 55 \quad \quad 67 \quad \quad 51 \end{aligned}

  • Complete the grouped frequency table:

Frequency Table Example 3 Image 1

  • Go along the data set and for each item put a tally mark in the table.  When you have finished, add up the tally marks to find the frequencies.  Take care with the inequalities and the minimum value and the maximum value in each class interval.

Frequency Table Example 3 Image 2

  • Add up the frequencies in the final column to get the total number of items in the data set.

Example 4: average from a frequency table

Write down the mode.

Frequency Table Example 4

  • The mode is ‘Car’ as it has the highest frequency.  The modal vehicle is ‘Car’.

Example 5: averages from a frequency table

Find the mode, median and mean from this frequency table

Frequency Table Example 5

  • The mode is 20^{\circ}

  • The median is the 11^{th} value which is 19^{\circ}

  • The mean is

    \frac{(17\times 1)+(18\times 4)+(19\times 6)+ (20\times 8)+(21\times 2)}{21}=\frac{405}{21}=19.3^{\circ} [\katex] (1 d.p.)</li></ul> </div> </div> <p id="example-6"></p> <div class="wp-container-24 wp-block-columns"> <div class="wp-container-23 wp-block-column"> <h3 id="h-example-6-averages-from-a-grouped-frequency-table">Example 6: averages from a grouped frequency table</h3> <p></p> <p>Find the modal class, the class interval in which the median lies and the estimated mean from this grouped frequency table</p> <p></p> <figure class="wp-block-image size-large"><img width="345" height="212" src="https://thirdspacelearning.com/wp-content/uploads/2021/11/Frequency-Table-Example-6.svg" alt="Frequency Table Example 6" class="wp-image-107041"/></figure> <p></p> <ul><li>The <strong>modal class</strong> is the one with the highest frequency which is [katex] 60 \leq x <70 degrees

  • The median will be the 13^{th} value which is in the interval 60 \leq x <70

  • An estimate for the mean can be found from using the midpoints. Where n is the total frequency.

    \text{Mean}=\frac{\text{total}}{n}=\frac{(45times 4)+(55\times 8)+(65\times 10)+ (75\times 3)}{25}=\frac{1495}{25}=59.8 \ \text{mph}

Common misconceptions

  • Counting the items

When attempting to count the items in each group and fill in the frequencies it is easy to make a mistake. Using tally marks can help with accuracy.

  • Check which average you are being asked for

Check if you have been asked for the median, mode or mean average.

  • Classes for grouped frequency tables can be written in different ways

The class intervals used in grouped frequency tables can be written in different ways. Take care with inequalities that the item goes in the correct group, especially the minimum value and the maximum value.

E.g.

0 to 5

0-5

0\le x<5

0<x \le5

Practice frequency table questions

1. Which is the correct frequency table for the following set of data? 

 

golf             football        hockey        athletics       football

 

athletics      rugby          hockey        football         rugby

 

hockey        football        golf              hockey         rugby

 

football        hockey        rugby          football        athletics

Frequency Table Practice Question 1 Answer 1

GCSE Quiz False

Frequency Table Practice Question 1 Answer 2

GCSE Quiz True

Frequency Table Practice Question 1 Answer 3

GCSE Quiz False

Frequency Table Practice Question 1 Answer 4

GCSE Quiz False

Athletics occurs 3 times in the data set, football 6 times, golf 2 times, hockey 5 times and rugby 4 times.

2. Which is the correct frequency table for the following set of data?

 

\begin{aligned} &11 \quad \quad 12 \quad \quad 14 \quad \quad 13 \quad \quad 12 \\\\ &14 \quad \quad 15 \quad \quad 12 \quad \quad 11 \quad \quad 11 \\\\ &12 \quad \quad 11 \quad \quad 15 \quad \quad 14 \quad \quad 15 \\\\ &12 \quad \quad 11 \quad \quad 13 \quad \quad 14 \quad \quad 11 \end{aligned}

Frequency Table Practice Question 2 Answer 1

GCSE Quiz True

Frequency Table Practice Question 2 Answer 2

GCSE Quiz False

Frequency Table Practice Question 2 Answer 3

GCSE Quiz False

Frequency Table Practice Question 2 Answer 4

GCSE Quiz False

The number 11 occurs six times in the data set, the number 12 five times, the number 13 two times, the number 14 five times and the number 15 three times.

3. Which is the correct grouped frequency table for the following set of data?

 

\begin{aligned} &11 \quad \quad 23 \quad \quad 30 \quad \quad 17 \quad \quad 24 \\\\ &38 \quad \quad 37 \quad \quad 7 \quad \quad \;\; 12 \quad \quad 5 \\\\ &8 \quad \quad \;\; 15 \quad \quad 33 \quad \quad 19 \quad \quad 27 \end{aligned}

Frequency Table Practice Question 3 Answer 1

GCSE Quiz False

Frequency Table Practice Question 3 Answer 2

GCSE Quiz False

Frequency Table Practice Question 3 Answer 3

GCSE Quiz True

Frequency Table Practice Question 3 Answer 4

GCSE Quiz False

Checking the first group, there are 3 numbers in the 0 to 9 class. Checking the second group, there are 5 numbers in the 10 to 19 class. There are 3 numbers in the 20 to 29 class and 4 numbers in the 30 to 39 class.

4. The frequency table shows the number of passengers for 20 buses. Find the modal class interval of passengers:

 

Frequency Table Practice Question 4

12
GCSE Quiz False

15 to 19

GCSE Quiz False

17
GCSE Quiz False

30 to 44

GCSE Quiz True

‘30 to 44’ is the modal class interval as it has the highest frequency.

5. The frequency table shows the number of siblings for 45 children. Find the median number of siblings:

 

Frequency Table Practice Question 5

0
GCSE Quiz False

1
GCSE Quiz True

2
GCSE Quiz False

3
GCSE Quiz False

There are 45 items of data. The middle value will be the 23^{rd} value. This will be ‘1’. So 1 is the median

6. The frequency table shows the heights of 20 shrubs.  Find the estimate for mean height:

 

Frequency Table Practice Question 6

45 \; cm
GCSE Quiz False

46 \; cm
GCSE Quiz True

47 \; cm
GCSE Quiz False

48 \; cm
GCSE Quiz False

We need to multiply the heights by their frequencies to get the total.

 

\text{Mean}=\frac{\text{total}}{n}=\frac{(10\times 2)+(30\times 6)+(50\times 7)+(70\times 4)+(90\times 1)}{20}=\frac{920}{20}=46

 

The estimate of the mean is 46

Frequency table GCSE questions

1. Mrs Smith asked 20 children how they got to school.

Here are the results:

 

Frequency Table GCSE Question 1

 

(a) Complete the frequency table.

 

Frequency Table GCSE Question 1a Image 1

 

(b) Write the mode.

 

(3 marks)

Show answer

(a)

 

Frequency Table GCSE Question 1b Image 2

For at least one correct tally or frequency

(1)

For all frequencies correct

(1)

 

(b)   Mode is ‘walk’

(1)

2. The price of 1 pint of milk is recorded from 40 different shops.

Here are the results, in a grouped frequency table.

 

Frequency Table GCSE Question 2

 

(a) State the mode.

 

(b) Find the median.

 

(c) Calculate the mean price.

 

(4 marks)

Show answer

(a) 50

(1)

 

(b)  49

(1)

 

(c)

 

\frac{(48\times 8)+(49\times 13)+(50\times 14)+(51\times 2)+(52\times 2)+(53\times 1)}{40}=\frac{1908}{40}

(1)

 

=49.5

(1)

3. Jai times 23 people on how long it takes for them to complete a wordsearch.

Here are the results, in a grouped frequency table.

 

Frequency Table GCSE Question 3

 

(a) State the modal class interval.

 

(b) Find the class interval which contains the median.

 

(c) Calculate an estimate for the mean time.

Give your answer correct to 1 decimal place.

 

(5 marks)

Show answer

(a) 20<t\leq 30

(2)

 

(b)  10<t\leq 20

(1)

 

(c)

 

5, 15, 25 and 35

For the midpoints

(1)

 

\frac{(5\times 5)+(15\times 8)+(25\times 9)+(35\times 1)}{23}=\frac{405}{23}=17.6087...

For the dividing the sum of the products by 23

(1)

 

=17.6087...=17.6 \ \text{(3 s.f.)}

For the correct answer

(1)

Learning checklist

You have now learned how to:

  • Make frequency tables and grouped frequency tables
  • Find averages from frequency table and grouped frequency table

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GCSE Maths Papers - November 2022 Topics

Practice paper packs based on the November advanced information for Edexcel 2022 Foundation and Higher exams.



Designed to help your GCSE students revise some of the topics that are likely to come up in November exams.

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