 # Find the Mean

In this worksheet, students practise finding the mean from a small data set (Discrete values only). 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

When you have a whole load of information, it can be quite difficult to deal with.

For example, If I asked whether Boys were taller than Girls, you would have to do something to the data to be able to answer the question.

To do this we take averages.

What is an average?

An average is just one piece of information that represents all the other information in a data set.

What are the averages?

There are three averages. Mean, Median and Mode.

Each one has advantages and disadvantages, in this worksheet we are going to look at finding the mean.

How do we find the mean?

To find the mean, we add up all the values in a list and then divide by the total amount of numbers in the list.

Example 1: Find the mean of 4, 8, 7, 5, 9, 4, 8, 3

Step 1: Add up all the numbers

4 + 8 + 7 + 5 + 9 + 4 + 8 + 3 = 48

Step 2: Count the numbers in the list.

We have 8 numbers in this list

Step 3: Divide one by the other.

48 ÷ 8 = 6

Example 2: Find the mean of 21, 23, 20, 27, 25, 24, 25, 30, 21, 22, 28

Step 1: Add up all the numbers

21+23+20+27+25+24+25+30+21+22+28 = 266

Step 2: Count the numbers in the list.

We have 11 numbers in this list

Step 3: Divide one by the other.

266 ÷ 11 = 24.2

If the answer isn't an integer, give your answer to 1 decimal places unless the questions tells you otherwise.

To find the mean...

Find the mean for 7,8,3,6,7,3,8,5,4,9

If you were finding the mean for the numbers 1,2,0,2,5,3,1,0,1,2,3,4

There are two numbers you must show in your working to get the methd mark.

Select the numbers you must show.

1

2

0

12

24

Is the mean for 1,2,0,2,5,3,1,0,1,2,3,4

2

0.5

The mean for 3,7,5,8,4,6,7,8,9,3 is 6

Without working it out, what is the mean for 13,17,15,18,14,16,17,18,19,13

Three friends do some homework.

James spend 1 hr 30 mins

Johnny spends 51 minutes

Joe spends 1 and a quarter hours.

What is the average time (in minutes) the pupils spent on their homework.

The mean of 4 cards is 6.

If 3 of them have the values of 10, 5 and 4, what is the value of the 4th card?

Match the data sets with their means.

## Column B

4,5,6,5,6,4,5,2,1,5
4.3
7,10,6,4,8,6,5,1,2,5
5.4
11,5,9,4,2,2,6,6,2,4
5.1

5 walkers in a group are 38,28,30,42 and 37.

If a 41 year old joins their group, will th mean...

Increase

Decrease

Stay the same

The average pay of a group of workers is £350 per week.

If they all get a £50 raise. What will be the new mean wage.

• Question 1

To find the mean...

EDDIE SAYS
It's absolutely vital you know this definition. Add up all the numbers (even if they're zero) Divide this by how many numbers are in the list (irrelevant of what they are)
• Question 2

Find the mean for 7,8,3,6,7,3,8,5,4,9

6
EDDIE SAYS
Our first step is to add these up (we'll get 60) Counting up the numbers shows we have 10 numbers. 60 ÷ 10 =
• Question 3

If you were finding the mean for the numbers 1,2,0,2,5,3,1,0,1,2,3,4

There are two numbers you must show in your working to get the methd mark.

Select the numbers you must show.

12
24
EDDIE SAYS
The only numbers you have to show to get the method mark are the total you get when you add the numbers up (24) and the amount of numbers in the list (12)
• Question 4

Is the mean for 1,2,0,2,5,3,1,0,1,2,3,4

2
EDDIE SAYS
We know the numbers add up to 24 and there are 12 of them. The mistake people make here is that they divide them the wrong way round. There is a quick way to check if your answer is the right one. The average should be somewhere about the middle of the data. Which of my two options is about the middle of the data? That's the mean.
• Question 5

The mean for 3,7,5,8,4,6,7,8,9,3 is 6

Without working it out, what is the mean for 13,17,15,18,14,16,17,18,19,13

16
EDDIE SAYS
Did you notice that the numbers were all just 10 higher? This means the mean will be too!
• Question 6

Three friends do some homework.

James spend 1 hr 30 mins

Johnny spends 51 minutes

Joe spends 1 and a quarter hours.

What is the average time (in minutes) the pupils spent on their homework.

72
EDDIE SAYS
This question is just the same. The only issue is then getting them in the same form. 1 and a half hours is 90 mins 1 and a quarter hours is 75 minutes Just do it the same way as before.
• Question 7

The mean of 4 cards is 6.

If 3 of them have the values of 10, 5 and 4, what is the value of the 4th card?

7
EDDIE SAYS
This is just doing the question backwards. We know the average is 6 and there are 4 cards, the total on the cards must be 6 x 4 = 24 The first three that we know add up to 19, this means the number on the card we don\'t know must be...
• Question 8

Match the data sets with their means.

## Column B

4,5,6,5,6,4,5,2,1,5
4.3
7,10,6,4,8,6,5,1,2,5
5.4
11,5,9,4,2,2,6,6,2,4
5.1
EDDIE SAYS
There isn\'t unfortunately a short cut for this one. The only way to do it is, as before, to add them all up and then divide them by 10
• Question 9

5 walkers in a group are 38,28,30,42 and 37.

If a 41 year old joins their group, will th mean...

Increase
EDDIE SAYS
We could do this by finding the mean of the group before and after, but we don't need to. If we work out the average without the new person, it's 35. With the new person being older than the average. He's going to increase the average age so the mean will go up.
• Question 10

The average pay of a group of workers is £350 per week.

If they all get a £50 raise. What will be the new mean wage.

400
£400
£ 400
EDDIE SAYS
This one always catches people out. They look at it and see they don\'t know the individual numbers and say they can\'t do it. Just think, if everyone gets the same amount more, what will the average go up by?
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