7.5 Sampling

A free GCSE Maths Foundation lesson for Edexcel (9–1) from OBA School: types of data, populations and samples, bias, and estimating from a sample. Watch the video, read the explanation and worked examples, then try the revision questions. You can work through the full lesson, with interactive activities, practice quizzes and printable worksheets, in our free online course.

What you will learn

• Describe data as qualitative or quantitative, discrete or continuous, primary or secondary
• Explain the difference between a population and a sample, and why we use samples
• Describe how to take a random sample and recognise when a sample is biased
• Use the results from a sample to estimate for the whole population

Key words

• Population: The whole group you want to find out about, such as all 900 pupils in a school.
• Sample: A smaller group chosen from the population, whose results are used to represent it.
• Random sample: A sample where every member of the population has the same chance of being chosen.
• Biased: A sample is biased if it is likely to give results that are not typical of the population.
• Primary / secondary data: Primary: data you collect yourself. Secondary: data someone else collected (books, websites, databases).

Types of data

• Qualitative; Meaning Described in words, not numbers.; Examples Eye colour, type of car, favourite sport
• Quantitative; Meaning Numbers: counts or measurements.; Examples Number of siblings, height, time
• Discrete; Meaning Quantitative data that can only take certain values (often counted).; Examples Number of goals, shoe size, number of pets
• Continuous; Meaning Quantitative data that is measured and can take any value in a range.; Examples Mass, length, time, temperature

Worked example: classifying data

Decide the type of each: (a) the number of texts sent in a day (b) the time taken to walk to school.
(a) It is counted and can only be whole numbers. (b) It is measured and could be 12.37… minutes.

Answer: (a) quantitative, discrete (b) quantitative, continuous

Populations and samples

Asking or testing the whole population is often too slow, too expensive or impossible (you cannot test every match by striking it!). So we take a sample.

• Small; Advantage Quick and cheap to collect.; Disadvantage Results may not represent the population well.
• Large; Advantage Results are more reliable.; Disadvantage Takes longer and costs more.

Worked example: identifying the population

A leisure centre has 2400 members. The manager asks 120 of them about new opening hours.

Answer: Population: all 2400 members. Sample size: 120

Random samples and bias

To take a simple random sample: list and number every member of the population, then use a random number generator (or names drawn from a hat) to pick the numbers. Ignore repeats.

Worked example: spotting bias

A council wants to know how often people in a town use buses. Jen asks 30 people at the bus station on Monday morning.
Everyone she asks is about to use a bus, so they probably use buses more than most people. She also misses people who work or travel at other times.

Answer: The sample is biased: it is not representative of the whole town

Key fact: A sample can be biased because of where or when it is taken, who is asked, or because it is too small.

Estimating from a sample

Assume the population behaves like the sample. Use the same fraction (or proportion) of the population.

Worked example: walking to school

In a random sample of 50 pupils, 18 walk to school. The school has 750 pupils. Estimate how many walk to school.
Fraction in the sample = 18/50. 18/50 × 750 = 18 × 15 = 270

Answer: About 270 pupils

Worked example: quality control

A machine makes 4000 bolts a day. In a sample of 200, 6 are faulty. Estimate the number of faulty bolts each day.
6/200 = 3%. 3% of 4000 = 0.03 × 4000 = 120

Answer: About 120 faulty bolts

Common mistakes

• Saying “ask people at random” without explaining how they are chosen (number them and use a random number generator).
• Calling shoe size continuous: shoe sizes can only take certain values, so they are discrete.
• Giving a reason for bias that is not linked to the context of the question.
• Using the wrong total when scaling up, for example multiplying by the sample size instead of the population size.

Revision questions

Try these, then check your answers below each one.

Question 1. Which of these is continuous data? (Choose from: The number of goals scored, Shoe size, The mass of a baby, Favourite colour.)

Answer: The mass of a baby

Working: Mass is measured and can be any value, such as 3.42 kg. The others are counted, set sizes or words.

Question 2. A council wants to know how often residents use the library. Which sample is least likely to be biased? (Choose from: Ask people inside the library, Ask 50 residents chosen at random from the list of all residents, Ask your friends, Ask people at a bus stop at 8 am.)

Answer: Ask 50 residents chosen at random from the list of all residents

Working: Only the random sample from a full list gives every resident an equal chance.

Question 3. In a random sample of 40 pupils, 14 have a pet dog. The school has 600 pupils. Estimate how many pupils in the school have a pet dog.

Answer: 210

Working: 14/40 × 600 = 210.

Related lessons

• Previous lesson: 7.4 Estimating the Mean
• Next lesson: 8.1 Rectangles, Parallelograms and Triangles
• In this chapter: 7.1 Mean and Range
• In this chapter: 7.2 Mode, Median and Range
• In this chapter: 7.3 Types of Average

Continue in the full course

This lesson is section 7.5 (EGCMF0705) of our free GCSE Maths Foundation course. In the full course you get every video for this section, an animated interactive lesson, a self-marking practice quiz, a printable worksheet with a mark scheme, and your progress saved. Go to the full GCSE Maths Foundation course.