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Use Statistics to Compare Distributions

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

'Use Statistics to Compare Distributions' worksheet

Key stage:  KS 4

GCSE Subjects:   Maths

GCSE Boards:   AQA, Eduqas, Pearson Edexcel, OCR

Curriculum topic:   Statistics

Curriculum subtopic:   Statistics, Analysing Data

Difficulty level:  

Worksheet Overview

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...

Jhonny records the number of school papers he sells in 2 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

 

Give your answers to 1 dp

 Week 1Week 2
Mean

Two strikers are on trial at a football club. They both pay 6 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 dp

 Player APlayer B
Mean

Two strikers are on trial at a football club. They both pay 6 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 APlayer B
Range

Two strikers are on trial at a football club. They both pay 6 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

Rick and Rob play 5 rounds of golf together and get the following scores

 

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

 

Find the mean for each player

 

 RickRob
Mean

Rick and Rob play 5 rounds of golf together and get the following scores

 

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

 

Find the range of scores for each player

 

 RickRob
Range

Rick and Rob play 5 rounds of golf together and get the following scores

 

  Monday Tuesday Wednesday Thursday Friday
Rick 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?

 

Rick

Rob

Andy and Alex both take 5 maths tests. These are their scores.

 

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

 

Find the mean and range for both students

 

 RickRob
Mean
Range

Andy and Alex both take 5 maths tests. These are their scores.

 

  Test 1 Test 2 Test 3 Test 4 Test 5
Andy 45 56 47 77 82
Ales 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...

CORRECT ANSWER
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

Jhonny records the number of school papers he sells in 2 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

 

Give your answers to 1 dp

CORRECT ANSWER
 Week 1Week 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 pay 6 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 dp

CORRECT ANSWER
 Player APlayer 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 pay 6 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

CORRECT ANSWER
 Player APlayer 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 pay 6 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?

CORRECT ANSWER
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

Rick and Rob play 5 rounds of golf together and get the following scores

 

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

 

Find the mean for each player

 

CORRECT ANSWER
 RickRob
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

Rick and Rob play 5 rounds of golf together and get the following scores

 

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

 

Find the range of scores for each player

 

CORRECT ANSWER
 RickRob
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

Rick and Rob play 5 rounds of golf together and get the following scores

 

  Monday Tuesday Wednesday Thursday Friday
Rick 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?

 

CORRECT ANSWER
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 Alex both take 5 maths tests. These are their scores.

 

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

 

Find the mean and range for both students

 

CORRECT ANSWER
 RickRob
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 Alex both take 5 maths tests. These are their scores.

 

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

 

Who do you think is better at Maths?

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

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