# Use Populations and Sampling

In this worksheet, students practise finding samples.

Key stage:  KS 4

GCSE Subjects:   Maths

GCSE Boards:   AQA, Eduqas, Pearson Edexcel, OCR

Curriculum topic:   Statistics

Curriculum subtopic:   Statistics, Sampling

Difficulty level:

### QUESTION 1 of 10

What are populations?

Populations in maths describe a situation where you are referring to a whole group of people.

i.e. All the pupils in a school is the population of the school, all the people on a train is the population of the train.

What is a sample?

A lot of the time, when you are trying to find something out in statistics, it isn't sensible to ask everyone, instead, you ask some of them and use that as a statistical representation of everyone. This is a sample.

i.e. If I want to find out about the lunch habits in a school, instead of asking everyone, I might only ask 50 and assume this represents the views of everyone.

How do I find a sample?

Samples are given as percentages.

Example 1: I want to find a 10% sample of pupils in a school. If the school has 400 students, how many do I need to speak to?

I need to find 10% of 400, this is 40 students.

Example 2: I ask 150 students in a school with 1000 students about their favourite crisps. What sample size is this?

We are trying to find out what percentage 150 out of 100 is, this can be written as a fraction. We can then multiply by 100 to get a percentage.

 150 1000
x 100 = 15%

Primary Vs Secondary Data.

This sounds more complicated than it is. Primary data is simply data you have collected yourself (ie questionnaire or survay) , secondary data is data you have found somewhere else (i.e. house prices)

Bias

Sometimes if you are collecting primary data, you can introduce a bias (unfairness)

For example, if you asked people coming out of a gym how long they spent exercising, this is biased because you don't haeve people who don't exercise)

If you wanted to find out the favourite subjects of pupils in a school. You would have to ask tgesame number of boys as girls to make it fair.

For each of these situations, select if you would collect primary or secondary data.

There are 1500 students in a school.

How many students do I need to speak to to get a 12% sample

Complete the following sentence.

In a company of 2000 people, 240 are asked about their working hours.

What is the sample size?

I'm investigating the favourite flavour of crisps in my school. Is asking 10 of my friends a fair sample or a biased sample?

Fair

Biased

In a school, there are 160 students in Year 11 and 140 in year 10.

If I want to take a sample of 60 people, how many do I speak to from each year group?

Fair

Biased

For each of these situations, say if the data collection is biased or fair.

I sample the number of students in a 6th form. If there are 2000 students in total. How many girls are in year 13?

 Year 12 Year 13 Boys 30 20 Girls 25 25

James is surveying the time people spend on a train getting to work.

If 6000 people use a the train each week, how many people foes James need to ask each day to get a 10% sample.

A questionnaire is given to everyone on a bus.

Is this a population or a sample?

Population

Sample

• Question 1

For each of these situations, select if you would collect primary or secondary data.

EDDIE SAYS
You would use secondary data if it isn't really possible to collect the data yourself. The only one where you could really do your self is the estimation. This would use primary, all of the others would use secondary data.
• Question 2

There are 1500 students in a school.

How many students do I need to speak to to get a 12% sample

180
EDDIE SAYS
We need to find 12% of 1500. 10% is 150 1% is 15 We can make 12% by adding 10% + 1% + 1%.
• Question 3

Complete the following sentence.

EDDIE SAYS
Just remember that a population describes a whole group and that a sample is part of a population Population > sample
• Question 4

In a company of 2000 people, 240 are asked about their working hours.

What is the sample size?

12
12%
12 %
EDDIE SAYS
Our first step here is to find this as a fraction. We then multiply this by 100 to find the percentage (samples are given as percentages) 240/2000 x 100 = ...
• Question 5

I'm investigating the favourite flavour of crisps in my school. Is asking 10 of my friends a fair sample or a biased sample?

Biased
EDDIE SAYS
There's a couple of reasons this is biased. 1) Does it represent everyone in the school? 2) Have I asked enough people?
• Question 6

In a school, there are 160 students in Year 11 and 140 in year 10.

If I want to take a sample of 60 people, how many do I speak to from each year group?

EDDIE SAYS
This is a bit more complicated. I have 300 people in total and I want to ask 60. This works out as a sample of 20% But, I don't just ask 30 of each as year 11 is bigger than Year 10. I have to ask 20% of year 11 and 20% of Year 10.
• Question 7

For each of these situations, say if the data collection is biased or fair.

EDDIE SAYS
The first option is fair because the people you are asking represent the whole school. The second one is unfair as it doesn't include people who don't use supermarkets.
• Question 8

I sample the number of students in a 6th form. If there are 2000 students in total. How many girls are in year 13?

 Year 12 Year 13 Boys 30 20 Girls 25 25

500
EDDIE SAYS
In total we have asked 100 students (just add together the numbers in the table). 25 of these are year 13 girls This means that 1/4 of the pupils I asked are Year 13 girls So we can say that 1/4 of all students are year 13 girls
• Question 9

James is surveying the time people spend on a train getting to work.

If 6000 people use a the train each week, how many people foes James need to ask each day to get a 10% sample.

120
EDDIE SAYS
If we're looking for a 10% sample, this is 600 people in the week. But, the question asks for each day! As the question is about work, we say that we have to split this into 5 equal parts.
• Question 10

A questionnaire is given to everyone on a bus.

Is this a population or a sample?

Population
EDDIE SAYS
The key word here is \'everyone\'. Anything that has the word everything has to be a...
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