What is discrete data?

Numerical data that can only take separate values, usually counted (e.g. number of siblings).

What is continuous data?

Numerical data that can take any value in a range, usually measured (e.g. height).

Is shoe size discrete or continuous?

Discrete: it only takes listed values such as 5 and 5\frac12.

A smaller group chosen from the population.

A survey of the whole population.

What makes a sample representative?

It has the same mix of characteristics as the population.

What is a simple random sample?

A sample where every member has an equal chance of being chosen.

How does systematic sampling work?

Choose every kth member of a list, starting from a random point.

How do you find a stratified sample size for one group?

\frac{group size}{population size}\timessample size

Name three causes of bias.

Unrepresentative sample, self-selection, non-response (or leading questions).

What is a leading question?

A question worded so that it suggests the answer the writer wants.

What should answer boxes in a questionnaire do?

Cover all possible answers, not overlap, and include "none" or "other" where needed.

What is a pilot survey?

A small trial of a survey to find problems before the real survey.

Collecting and classifying dataIB MYP Maths Extended: Flashcards

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What is categorical data?

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What is categorical data?: Data in words or categories, e.g. colours or favourite sports.
What is discrete data?: Numerical data that can only take separate values, usually counted (e.g. number of siblings).
What is continuous data?: Numerical data that can take any value in a range, usually measured (e.g. height).
Is shoe size discrete or continuous?: Discrete: it only takes listed values such as $5$ and $5\frac12$ .
What is a population?: The whole group being studied.
What is a sample?: A smaller group chosen from the population.
What is a census?: A survey of the whole population.
What makes a sample representative?: It has the same mix of characteristics as the population.
What is a simple random sample?: A sample where every member has an equal chance of being chosen.
How does systematic sampling work?: Choose every $k$ th member of a list, starting from a random point.
How do you find a stratified sample size for one group?: $\frac{\text{group size}}{\text{population size}}\times\text{sample size}$
Name three causes of bias.: Unrepresentative sample, self-selection, non-response (or leading questions).
What is a leading question?: A question worded so that it suggests the answer the writer wants.
What should answer boxes in a questionnaire do?: Cover all possible answers, not overlap, and include "none" or "other" where needed.
What is a pilot survey?: A small trial of a survey to find problems before the real survey.

Exam questions on Collecting and classifying data

A school survey records four pieces of information about each student: shoe size, the colour of their bag, their height in centimetres and the number of siblings.
Explain why shoe size is discrete data.2 marks
A town council wants to find out how residents travel to work. It has a list of all $8\,000$ residents, of whom $3\,200$ live in the north of the town and $4\,800$ live in the south.
A councillor suggests surveying only people who are at the railway station at 8 am on a weekday. Explain why this sample would be biased.2 marks
A student wants to find out how long pupils in her school spend on social media each day. She asks: "You spend too much time on social media, don't you?" The answer boxes are: "A lot", "Some" and "Hardly any".
Identify three faults with the question and the answer boxes.3 marks

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Written by the Exaim team, led by Shaun Daswani (Head of Upper Secondary, Improve ME Institute; MSc Financial Mathematics, Imperial College London; BSc, UCL) and Jason Daswani (operational lead, Improve ME Institute; LSE).