# Find the Mean from a Frequency Table

In this worksheet, students find the mean from a frequency table.

Key stage:  KS 4

GCSE Subjects:   Maths

GCSE Boards:   AQA, Eduqas, Pearson Edexcel, OCR

Curriculum topic:   Statistics

Curriculum subtopic:   Statistics, Analysing Data

Difficulty level:

### QUESTION 1 of 10

Finding an average is incredibly useful when you want to find one piece of data that describe a whole set of data.

You will already know that if I wanted to find the average from a list of numbers, I would just add the numbers and then divide by how many there were.

What if the list is really, really long?

Imagine that you collected the shoe size of 500 people. Would you want to add them all together?

There has to be a quicker way.

Using a frequency table.

If we have loads of data, we would normally put it in a frequency table. Let's look at an example.

Example 1: I collect the shoe sizes of a group of people and put it into a frequency table. What is the mean of the shoe sizes?

 Shoe Size 3 4 5 6 7 8 9 10 11 12 Number of people 5 7 9 14 21 28 16 6 5 1

Let's look at the first column. This means 5 people have a shoe size of 3. If I wrote this as a list I would have 3,3,3,3,3   (Adds to 15)

The second column means that 7 people have a shoe size of 4. If I wrote this as a list I would have 4,4,4,4,4,4,4 (Adds to 28)

Can you spot the link?

To find the total, all I do to start with is multiply the two numbers together! If I did this for all of them, I would get...

 Shoe Size 3 4 5 6 7 8 9 10 11 12 Number of people 5 7 9 14 21 28 16 6 5 1 15 28 45 84 147 224 144 60 55 12

Once we have this, we can work out what all the shoe sizes added together would be by adding the numbers in red. (814 )

We now have one of the bits of information I need to find the mean (what they all add up to)

All I need now is to find out how many people I asked. I can get this by adding up all the numbers in the number of people row. (112)

To find the mean, all I now have to do is to divide one of these numbers by the other (814 &div; 112) to get an average of 7.3

A couple of points.

Does it matter that the answer is a decimal, you can't have a shoe size of 7.3.

No - It's not a real shoe, it just represents all the others, decimals are fine.

How do I know which way round to divide?

If you can't remember, try them both ways round. You'll get two answers (7.3 and 0.14).

Remember that the average must be in the middle(ish) of the data so it must be 7.3.

Can you summarise for me?

Step 1: Multiply the two columns together

Step 2: Add all these new numbers up

Step 3: Add up all the frequencies

Step 4: Divide to find the mean.

To find the the mean from a frequency table we ...

I survey a group of students about how many pets they have.

I display the data in a frequency table.

 Pets 0 1 2 3 4 5 Frequency 3 7 9 6 2 1 A B C D E F

I want to find the mean number of pets

What numbers need to go in A-F

 Number A B C D E F

I survey a group of students about how many pets they have.

I display the data in a frequency table.

 Pets 0 1 2 3 4 5 Frequency 3 7 9 6 2 1 0 7 18 18 8 5

How many pets are there in total?

I survey a group of students about how many pets they have.

I display the data in a frequency table.

 Pets 0 1 2 3 4 5 Frequency 3 7 9 6 2 1 0 7 18 18 8 5

What is the mean number of pets

2

0.5

I survey a group of adults about how many children they have.

I display the data in a frequency table.

 Kids 0 1 2 3 4 5 Frequency 6 21 72 84 3 1 A B C D E F

I want to find the mean number of children in a family

What numbers need to go in A-F

 Number A B C D E F

I survey a group of adults about how many children they have.

I display the data in a frequency table.

 Kids 0 1 2 3 4 5 Frequency 6 21 72 84 3 1 0 21 144 252 12 5

I want to find the mean number of children in a family

How many children did the parents have in total?

I survey a group of adults about how many children they have.

I display the data in a frequency table.

 Kids 0 1 2 3 4 5 Frequency 6 21 72 84 3 1 0 21 144 252 12 5

What is the average number of kids per family?

2.3

0.4

I survey a group of teachers about how long they spend marking in a week

 Hours marking 1 2 3 4 5 6 Frequency 5 7 14 21 3 1 A B C D E F

I want to find the mean number of hours a teacher spend marking.

What numbers need to go in A-F

 Number A B C D E F

I survey a group of teachers about how long they spend marking in a week

 Hours Marking 1 2 3 4 5 6 Frequency 5 7 14 21 3 1 5 14 42 84 15 6

What is the total time teachers spent marking

I survey a group of teachers about how long they spend marking in a week

 Hours Marking 1 2 3 4 5 6 Frequency 5 7 14 21 3 1 5 14 42 84 15 6

What is the average teachers spent marking

3.3

0.3

• Question 1

To find the the mean from a frequency table we ...

EDDIE SAYS
I sometimes remember the steps a bit easier than the words. Multiply, Add, Add, Divide
• Question 2

I survey a group of students about how many pets they have.

I display the data in a frequency table.

 Pets 0 1 2 3 4 5 Frequency 3 7 9 6 2 1 A B C D E F

I want to find the mean number of pets

What numbers need to go in A-F

 Number A B C D E F
EDDIE SAYS
Remember the first rule? Multiply...
• Question 3

I survey a group of students about how many pets they have.

I display the data in a frequency table.

 Pets 0 1 2 3 4 5 Frequency 3 7 9 6 2 1 0 7 18 18 8 5

How many pets are there in total?

56
EDDIE SAYS
Look at the columns here. The first one is 3 people have no pets etc All we needed to do was add the numbers in red together.
• Question 4

I survey a group of students about how many pets they have.

I display the data in a frequency table.

 Pets 0 1 2 3 4 5 Frequency 3 7 9 6 2 1 0 7 18 18 8 5

What is the mean number of pets

2
EDDIE SAYS
If we find the total number of people I asked, there's 28 of them. We need to divide so we either do 56 ÷ 28 or 28 ÷ 56. Which one gives the sensible answer?
• Question 5

I survey a group of adults about how many children they have.

I display the data in a frequency table.

 Kids 0 1 2 3 4 5 Frequency 6 21 72 84 3 1 A B C D E F

I want to find the mean number of children in a family

What numbers need to go in A-F

 Number A B C D E F
EDDIE SAYS
Remember the first rule? Multiply...
• Question 6

I survey a group of adults about how many children they have.

I display the data in a frequency table.

 Kids 0 1 2 3 4 5 Frequency 6 21 72 84 3 1 0 21 144 252 12 5

I want to find the mean number of children in a family

How many children did the parents have in total?

434
EDDIE SAYS
All we need to do is to add up these new numbers.
• Question 7

I survey a group of adults about how many children they have.

I display the data in a frequency table.

 Kids 0 1 2 3 4 5 Frequency 6 21 72 84 3 1 0 21 144 252 12 5

What is the average number of kids per family?

2.3
EDDIE SAYS
If we add up the number of families, we get 187 We now know we have 434 kids split between 187 families. Which way round do I need to divide them? If you can't remember, just try them both and decide which of your answers is more sensible.
• Question 8

I survey a group of teachers about how long they spend marking in a week

 Hours marking 1 2 3 4 5 6 Frequency 5 7 14 21 3 1 A B C D E F

I want to find the mean number of hours a teacher spend marking.

What numbers need to go in A-F

 Number A B C D E F
EDDIE SAYS
Remember the first rule? Multiply...
• Question 9

I survey a group of teachers about how long they spend marking in a week

 Hours Marking 1 2 3 4 5 6 Frequency 5 7 14 21 3 1 5 14 42 84 15 6

What is the total time teachers spent marking

166
EDDIE SAYS
All we need to do is to add up these new numbers.
• Question 10

I survey a group of teachers about how long they spend marking in a week

 Hours Marking 1 2 3 4 5 6 Frequency 5 7 14 21 3 1 5 14 42 84 15 6

What is the average teachers spent marking

3.3
EDDIE SAYS
If we add up the number of teachers, we get 51 We now know we have 166 hours split between 51 teachers Which way round do I need to divide them? If you can't remember, just try them both and decide which of your answers is more sensible.
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