# Use Statistics to Compare Distributions

In this worksheet, students practise using an average and a measure of spread to describe a distribution

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 we find averages is to find one number that describes a set of data (this is properly called a distribution).

The reason we do this is so we are able to compare two distributions.

How do we compare?

To compare distributions, we need to find an average (this normally the mean) and a measure of spread (for a small data set, this is normally the range)

When a question comes up in the exam, you need to make a comment on the average and a comment on the range.

Example 1: Dan can catch either the number 1 or number 2 bus to school. He records how many minutes late they are over the course of 10 days.

Number 1: 4, 2, 0, 6, 4, 8, 8, 6, 3, 9

Number 2: 3, 4, 0, 10, 3, 5, 13, 1, 0, 1

By comparing the mean and range for each. Which bus should Dan catch if he wants to be at school on time

Number 1:

Mean = 50 ÷ 10 = 5.

Range = 8 - 0 = 8

Number 2:

Mean = 40 ÷ 10 = 4

Range = 13 - 0 = 13

You could argue for either bus.

The number 2 bus is less late so he should catch that one (the mean is lower for number 2)

The number 1 bus is more consistent so he should catch that one (the range is lower for number 1)

To compare distributions, we need to find an average. The three averages are...

Jonny records the number of school papers he sells in two weeks. Find the mean number of papers for each week.

 Monday Tuesday Wednesday Thursday Friday Week 1 65 73 75 80 90 Week 2 112 92 87 77 68

 Week 1 Week 2 Mean

Two strikers are on trial at a football club. They both play six games before the manager makes a decision on who to sign.

 Game 1 Game 2 Game 3 Game 4 Game 5 Game 6 Week 1 2 3 6 1 2 1 Week 2 3 2 2 2 3 3

Find the mean goals scored per game.  Give your answers to 1 decimal place.

 Player A Player B Mean

Two strikers are on trial at a football club. They both play six games before the manager makes a decision on who to sign.

 Game 1 Game 2 Game 3 Game 4 Game 5 Game 6 Week 1 2 3 6 1 2 1 Week 2 3 2 2 2 3 3

Find the range of goals for each player.

 Player A Player B Range

Two strikers are on trial at a football club. They both play six games before the manager makes a decision on who to sign.

 Game 1 Game 2 Game 3 Game 4 Game 5 Game 6 Week 1 2 3 6 1 2 1 Week 2 3 2 2 2 3 3

Which player should the manager choose?

Player A

Player B

Chloe and Rob play five rounds of golf together and get the following scores.

 Monday Tuesday Wednesday Thursday Friday Chloe 72 80 56 86 86 Rob 74 78 80 72 76

Find the mean for each player.

 Chloe Rob Mean

Chloe and Rob play five rounds of golf together and get the following scores.

 Monday Tuesday Wednesday Thursday Friday Chloe 72 80 56 86 86 Rob 74 78 80 72 76

Find the range of scores for each player.

 Chloe Rob Range

Chloe and Rob play five rounds of golf together and get the following scores.

 Monday Tuesday Wednesday Thursday Friday Chloe 72 80 56 86 86 Rob 74 78 80 72 76

If there was one spot on the golf team, who should the manager give it to?

Chloe

Rob

Andy and Kate both take five maths tests. These are their scores.

 Test 1 Test 2 Test 3 Test 4 Test 5 Andy 45 56 47 77 82 Kate 39 78 32 92 62

Find the mean and range for both students.

 Andy Kate Mean Range

Andy and Kate both take five maths tests. These are their scores.

 Test 1 Test 2 Test 3 Test 4 Test 5 Andy 45 56 47 77 82 Kate 39 78 32 92 62

Who do you think is better at Maths?

• Question 1

To compare distributions, we need to find an average. The three averages are...

EDDIE SAYS
This can get confusing, why did they have them all start with M? Try to remember if this way. Mode sounds like Most Median sounds like Middle The mean is the other one
• Question 2

Jonny records the number of school papers he sells in two weeks. Find the mean number of papers for each week.

 Monday Tuesday Wednesday Thursday Friday Week 1 65 73 75 80 90 Week 2 112 92 87 77 68

 Week 1 Week 2 Mean
EDDIE SAYS
Did you remember how to find the mean? Add up all the numbers and divide by how many numbers there are.
• Question 3

Two strikers are on trial at a football club. They both play six games before the manager makes a decision on who to sign.

 Game 1 Game 2 Game 3 Game 4 Game 5 Game 6 Week 1 2 3 6 1 2 1 Week 2 3 2 2 2 3 3

Find the mean goals scored per game.  Give your answers to 1 decimal place.

 Player A Player B Mean
EDDIE SAYS
Did you remember how to find the mean? Add up all the numbers and divide by how many numbers there are. Both of these payers scored, on average, the same number of goals per game. So how does the manager pick?
• Question 4

Two strikers are on trial at a football club. They both play six games before the manager makes a decision on who to sign.

 Game 1 Game 2 Game 3 Game 4 Game 5 Game 6 Week 1 2 3 6 1 2 1 Week 2 3 2 2 2 3 3

Find the range of goals for each player.

 Player A Player B Range
EDDIE SAYS
Did you remember how to find the Range? We just subtract the smaller one from the larger one Player A had a range of 5 and player B had a range of 1. This means player B is more consistent because his range is smaller.
• Question 5

Two strikers are on trial at a football club. They both play six games before the manager makes a decision on who to sign.

 Game 1 Game 2 Game 3 Game 4 Game 5 Game 6 Week 1 2 3 6 1 2 1 Week 2 3 2 2 2 3 3

Which player should the manager choose?

Player B
EDDIE SAYS
We know that both payers scored 2.5 goals per game but player B had a smaller range so he is more consistent.
• Question 6

Chloe and Rob play five rounds of golf together and get the following scores.

 Monday Tuesday Wednesday Thursday Friday Chloe 72 80 56 86 86 Rob 74 78 80 72 76

Find the mean for each player.

 Chloe Rob Mean
EDDIE SAYS
Did you remember how to find the mean? Add up all the numbers and divide by how many numbers there are.
• Question 7

Chloe and Rob play five rounds of golf together and get the following scores.

 Monday Tuesday Wednesday Thursday Friday Chloe 72 80 56 86 86 Rob 74 78 80 72 76

Find the range of scores for each player.

 Chloe Rob Range
EDDIE SAYS
Did you remember how to find the Range? We just subtract the smaller one from the larger one Rick had a range of 30 and Rob had a range of 8. This means Rob is more consistent because his range is smaller.
• Question 8

Chloe and Rob play five rounds of golf together and get the following scores.

 Monday Tuesday Wednesday Thursday Friday Chloe 72 80 56 86 86 Rob 74 78 80 72 76

If there was one spot on the golf team, who should the manager give it to?

Rob
EDDIE SAYS
We know that both payers scored 76 per round but Rob had a smaller range so he is more consistent.
• Question 9

Andy and Kate both take five maths tests. These are their scores.

 Test 1 Test 2 Test 3 Test 4 Test 5 Andy 45 56 47 77 82 Kate 39 78 32 92 62

Find the mean and range for both students.

 Andy Kate Mean Range
EDDIE SAYS
Did you remember how to find the mean and range Mean: Add up all the numbers and divide by how many numbers there are. Range: Biggest - Smallest
• Question 10

Andy and Kate both take five maths tests. These are their scores.

 Test 1 Test 2 Test 3 Test 4 Test 5 Andy 45 56 47 77 82 Kate 39 78 32 92 62

Who do you think is better at Maths?

Andy
EDDIE SAYS
Andy has the higher average score and the lowest range. This means he gets better scored and is more consistent.
---- OR ----

Sign up for a £1 trial so you can track and measure your child's progress on this activity.

### What is EdPlace?

We're your National Curriculum aligned online education content provider helping each child succeed in English, maths and science from year 1 to GCSE. With an EdPlace account you’ll be able to track and measure progress, helping each child achieve their best. We build confidence and attainment by personalising each child’s learning at a level that suits them.

Get started