Discrete or continuous: the number of goals scored in a match?

Discrete: it is counted and takes separate values.

Discrete or continuous: the time taken to run 100 m?

Continuous: it is measured and can take any value in a range.

What is a random sample?

One where every member of the population has an equal chance of being selected.

Give two causes of bias in a sample.

For example: some members have no chance of being chosen (convenience sampling), non-response, or leading questions.

What is convenience sampling?

Choosing the members that are easiest to reach. It is quick but often biased.

How do you take a systematic sample of n from a list of N?

Find k=\frac{N}{n}, pick a random starting member in the first k, then take every kth member.

How does stratified sampling work?

Divide the population into groups and sample each in proportion to its size: \frac{group}{population}\timessample size.

How does quota sampling differ from stratified sampling?

Quota sampling fills fixed numbers from each group but the members are chosen non-randomly; stratified sampling selects randomly within each group.

Give two ways of dealing with missing data.

Follow up non-respondents or choose replacements; report the issue and treat conclusions with caution.

State the rule for an outlier.

More than 1.5\timesIQR below Q1 or above Q3.

Can an outlier be a valid data value?

Yes. In context it may be a genuine extreme value; it is only removed if it is an error.

How are outliers shown on a box and whisker diagram?

As crosses beyond the whiskers.

4.1 Sampling, data quality and outliersIB Maths: Applications and Interpretation HL: Flashcards

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What is the difference between a population and a sample?

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What is the difference between a population and a sample?: A population is the whole group being studied; a sample is a part of it used to draw conclusions.
Discrete or continuous: the number of goals scored in a match?: Discrete: it is counted and takes separate values.
Discrete or continuous: the time taken to run 100 m?: Continuous: it is measured and can take any value in a range.
What is a random sample?: One where every member of the population has an equal chance of being selected.
Give two causes of bias in a sample.: For example: some members have no chance of being chosen (convenience sampling), non-response, or leading questions.
What is convenience sampling?: Choosing the members that are easiest to reach. It is quick but often biased.
How do you take a systematic sample of $n$ from a list of $N$ ?: Find $k=\frac{N}{n}$ , pick a random starting member in the first $k$ , then take every $k$ th member.
How does stratified sampling work?: Divide the population into groups and sample each in proportion to its size: $\frac{\text{group}}{\text{population}}\times\text{sample size}$ .
How does quota sampling differ from stratified sampling?: Quota sampling fills fixed numbers from each group but the members are chosen non-randomly; stratified sampling selects randomly within each group.
Give two ways of dealing with missing data.: Follow up non-respondents or choose replacements; report the issue and treat conclusions with caution.
State the rule for an outlier.: More than $1.5\times\text{IQR}$ below $Q_1$ or above $Q_3$ .
Can an outlier be a valid data value?: Yes. In context it may be a genuine extreme value; it is only removed if it is an error.
How are outliers shown on a box and whisker diagram?: As crosses beyond the whiskers.

Exam questions on 4.1 Sampling, data quality and outliers

A council wants to find out how its residents travel to work. A researcher stands outside the main railway station one morning and questions the first 80 people who walk past. The council has 12 000 residents on its electoral register.
Describe how the council could take a simple random sample of 80 residents from the electoral register.2 marks
A sports club has 600 members: 240 juniors, 210 adults and 150 seniors. The club takes a stratified sample of 80 members for a survey about its facilities.
Explain why a stratified sample is more suitable than a simple random sample for this survey.2 marks
Eleven students record the time, in minutes, they take to finish a puzzle: 12, 14, 15, 15, 17, 18, 19, 21, 22, 24, 41. The student who took 41 minutes says she forgot to stop her timer. Use your GDC to find quartiles.
Find the interquartile range (IQR) of the times.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).