S1 Maths Revision- Statistics

This study pack contains revision work for statistics

We have some reminders to help you remember how to do the calculations. Have a look through them then have a go at the questions in the revision exercises. They are at Extension, Core and Groundwork levels.

Choose the exercise that suits you best. You may wish to try more than one of them. Always try the easier one first. Answers are at the end so that you can check how you get on.

Good luck.

Reminders

Revision Topic – Statisitics

Groundwork – Revision

Statistics

1. A class carried out a survey to find

the pupils’ favourite type of pet.

Results are as follows:

Dog Cat Dog Fish Dog

Cat Hamster Fish Cat Dog

Cat Dog Fish Hamster Rabbit

Dog Dog Rabbit Rabbit Dog

a) Copy and complete this frequency table to

show the results:

Colour Tally FrequencyDogCatFishRabbitHamster

b) Show your results in a bar chart.

c) What is the most popular type of pet?

2. The pictograph below shows the favourite ice cream for a class.

Vanilla ☺☺☺☺☺☺

Chocolate ☺☺

Cherry ☺

Mint ☺☺☺☺

Caramel ☺☺☺☺☺☺☺ ☺ = 2 pupils

a) What is the favourite flavour?

b) How many chose cherry (not one!)

c) How many chose mint?

No of Pupils

Type of

Ice Cream

3 Senga’s test scores are as follows:

6 3 8 3 10

a) Calculate her mean score.

b) Kerry has only sat three tests.

Her scores are as follows:

7 10 7

Calculate her mean score and compare with Senga.

Core – Revision

Statistics

1. A class are asked how many hours of

exercise they took in the previous weekend.

The responses are listed below.

2 1 4 1 0 5 4 6 4 2

3 0 4 1 1 2 1 0 3 2

1 3 1 2 5 6 0 1 4 0

a) Draw a frequency table to show these results.

b) Use your frequency table to draw a bar graph.

c) It is recommended that teenagers exercise for at

least 2 hours each weekend.

Comment on how this applies to the results here.

d) Is there anything to consider when collecting the

data here?

2. Mr Teacher does a survey with his class.

The results are shown below.

No. of PupilsEnjoy school all of the time 4Enjoy school most of the time 10Enjoy school some of the time 7Do not enjoy school very often 8

a) Draw a pictograph to show the results.

b) Point out anything you think is wrong with the

questions Mr Teacher asked.

3. Mr Teacher does another survey to find out

what the favourite vegetable of his class is.

He draws a pie chart to show the results.

a) What is the least popular vegetable?

b) If 28 pupils had been asked, how many chose corn?

b) Anything wrong with Mr Teacher’s survey this time?

4. a) Sam’s test scores are as follows:

10 8 7 12 8

i) Calculate his mean test score.

ii) Calculate his range.

b) Linda has only sat three tests.

Her mean score is 9.

What is her total score?

Extension– Revision

Statistics

1. A survey is to be carried out in Wallace Hall

Academy to find the favourite subject

of the pupils.

Results are shown below:

Subject No. of ChildrenPE 18Art 12

Science 6Other 24

a) If you were drawing a pie chart to show these

results, calculate the size of angles for each sector.

b) Only a sample of the pupils were asked.

How can you tell this from the results?

c) What should be done to make it a fair sample?

d) Is there anything wrong with the way the survey

was carried out?

How would you describe the results?

2. Sally is a keen athlete.

Her favourite distance is the 200m.

She records her times for her most recent race

Time (seconds)

31 28 30 32 29

a) i Calculate the mean of these times.

ii Calculate the range.

Sally’s friend Brenda is also a 200m runner.

Her mean time is 29 seconds.

Her range is 6 seconds.

Make two statements comparing the data for

Sally and Brenda.

3. Three friends add up all the money that

they have between them.

They calculate that the mean amount of

money per person is £8.

How much money do they have altogether?

4. Sandy is a keen darts player.

He calculates that for his first five throws

his mean score is 40.

Unfortunately, after his sixth throw his mean

goes down to 35.

What was his score with his sixth throw?

1 .a) Colour Tally FrequencyDog IIII III 8Cat IIII 5Fish III 3Rabbit I 1Hamster II 2

b)

2. a) Caramel. b) 2 c) 7

3. a) 6 (30 ÷ 5)

b) 8 , Kerry has performed better than Senga as she has a higher mean

score.

Type of Pet

F

r

e

q

u

e

n

c

y

Core

No of Hours Frequency

0 41 72 53 44 55 46 1

0

1

2

3

4

5

6

7

8

0 1 2 3 4 5 6

No of Hours

1. a) b)

No of Hours

Frequency

c) While quite a lot of pupils had done less exercise

than 2 hours, most of them had done at least 2

hours.

d) Not a good idea to just take results of just one

weekend.

2. a) All of the time: ☺☺

Most of the time: ☺☺☺☺☺

Some of the time: ☺☺☺☺

Not very often: ☺☺☺☺ ☺ = 2 pupils.

b) The categories are not very clear. (They are vague)

3. a) Celery (no surprise there!)

b) 14

c) There are only 4 options, and no option if you like

another vegetable or do not like any. (Mr Teacher

needs to get a grip!)

4. a) 9 (45 ÷ 5) b) 27 (3 X 9)

1. a) PE 1080, Art 720, Science 360, Other 1440

b) There are only results of 60 pupils, much less than

are in the school.

c) Make sure all year groups are equally represented

and that there is gender equality.

d) Too few options for answers. This has meant that a

lot of results are “Other” which means the results

are vague.

2. a) i 30 secs ii 4 secs

b) Brenda is slightly faster on average as her mean

time 29 is lower than 30.

Sally is more consistent as her range 4

is less than 6.

3. £24

4. 10 (210 – 200)