A census involves collecting data from every member of the population, rather than from a subset of it. Its advantage is that it gives fully accurate results. Its disadvantages are that it is slow and expensive, and that it is impossible where testing uses up what is tested: a firework manufacturer cannot test every firework it makes.

How do you classify a set of data as qualitative, quantitative, discrete or continuous?

Qualitative data describes something, and is usually given in words rather than numbers, such as the colour of a car. Quantitative data uses numbers, and splits in two: Discrete data is counted , and takes specific values from a usually finite set, such as the number of pets a student has Continuous data is measured , and takes any value in a range, such as the height of a student The same quantity can fall either side of that line: age is discrete if you mean how many whole years old someone is, and continuous if you mean how long they have been alive.

Define sampling frame .

A list of all the members of the population , such as a list of every employee's name in a company. Whether or not one exists is what decides which sampling methods are available to you.

True or False? In both stratified and quota sampling, the members taken from each group are chosen at random.

False. Only stratified sampling selects randomly within each group. In quota sampling the members do not have to be chosen randomly, and if someone declines to take part they are simply replaced by someone else. That is the main difference between two methods that otherwise look alike: both split the population into groups, and both match the sample's proportions to the population's.

A researcher stands by the office door for ten minutes one morning and asks workers how long their journey was as they arrive. Which sampling method is this, and what is its main weakness?

Opportunity sampling, also called convenience sampling: a sample formed from whichever available members of the population happen to fit the criteria. Its main weakness is that it is unlikely to be representative of the population: here it reaches only the people who arrive during those ten minutes, a group already selected by how long their journey takes. It is used when a sample is needed quickly, or when no list of the population is available.

Which sampling methods do not select their members at random, and why does that matter?

Quota sampling and opportunity sampling do not select their members at random: in both, the members are chosen by whoever is collecting the data rather than by chance. That matters because a non-random sample is more likely to be biased and cannot reliably be used to make inferences about the population, which is the disadvantage to give when comparing quota sampling with simple random sampling. Simple random, systematic and stratified sampling are all random, provided the list they work from is itself random.

You cannot list or number every member of a population, for example the fish in a lake. Which sampling methods does that rule out, and which are still available?

Ruled out: simple random , systematic and stratified sampling, all of which work from a sampling frame. Still available: quota and opportunity sampling, neither of which needs a list. This is why the answer is so often quota or opportunity when a question makes a point of saying that no list exists.

Why can two people sampling the same population reach different conclusions?

Because a sample only gives information about the members actually in it, and two samples contain different members. This is why sample size matters: taking a larger sample is the improvement that applies to almost every sampling method. So, for example , a sample of 10 from a population of 800 is only 1.25% of it.

A LevelMathsEdexcelStatisticsFlashcardsStatistical SamplingSampling & Data Collection

Sampling & Data Collection (Edexcel A Level Maths: Statistics): Flashcards

Exam code: 9MA0

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FrontSampling & Data Collection
Complete the two key terms:
A $______$ is the whole set of things you are interested in. A $______$ is a subset of it that you actually collect data from.
FrontSampling & Data Collection
How do you classify a set of data as qualitative, quantitative, discrete or continuous?
BackSampling & Data Collection
Qualitative data describes something, and is usually given in words rather than numbers, such as the colour of a car.
Quantitative data uses numbers, and splits in two:
Discrete data is counted, and takes specific values from a usually finite set, such as the number of pets a student has
Continuous data is measured, and takes any value in a range, such as the height of a student
The same quantity can fall either side of that line: age is discrete if you mean how many whole years old someone is, and continuous if you mean how long they have been alive.

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Cards in this collection (12)

Complete the two key terms:
A $______$ is the whole set of things you are interested in. A $______$ is a subset of it that you actually collect data from.
The completed sentences are:
A population is the whole set of things you are interested in. A sample is a subset of it that you actually collect data from.
You sample because a population parameter, such as the mean height of all 16-year-olds in the UK, is usually unknown. A value worked out from a sample, called a sample statistic, is used to estimate it.
Define census.
A census involves collecting data from every member of the population, rather than from a subset of it.
Its advantage is that it gives fully accurate results.
Its disadvantages are that it is slow and expensive, and that it is impossible where testing uses up what is tested: a firework manufacturer cannot test every firework it makes.
How do you classify a set of data as qualitative, quantitative, discrete or continuous?
Qualitative data describes something, and is usually given in words rather than numbers, such as the colour of a car.
Quantitative data uses numbers, and splits in two:
- Discrete data is counted, and takes specific values from a usually finite set, such as the number of pets a student has
- Continuous data is measured, and takes any value in a range, such as the height of a student
The same quantity can fall either side of that line: age is discrete if you mean how many whole years old someone is, and continuous if you mean how long they have been alive.
Define sampling frame.
A list of all the members of the population, such as a list of every employee's name in a company.
Whether or not one exists is what decides which sampling methods are available to you.
How do you carry out a simple random sample?
Give every member of the population a unique number, then use a random number generator or a lottery method to pick $n$ different numbers.
What makes it simple random sampling is that every possible group of $n$ members has an equal probability of being chosen, not merely every individual member.
True or False?
In both stratified and quota sampling, the members taken from each group are chosen at random.
False.
Only stratified sampling selects randomly within each group. In quota sampling the members do not have to be chosen randomly, and if someone declines to take part they are simply replaced by someone else.
That is the main difference between two methods that otherwise look alike: both split the population into groups, and both match the sample's proportions to the population's.
How do you decide which members to include in a systematic sample?
To decide which members to include in a systematic sample, work out the size of the interval:
$k = \frac{size of population (N)}{size of sample (n)}$
Then choose a random starting point between 1 and $k$ , and take every $k$ th member after it.
The starting point has to be random, and so does the order of the list: a systematic sample taken from a list that is itself ordered in some meaningful way is not random.
A population of $N$ members is divided into strata, and a stratified sample of $n$ members is taken. Complete the formula for the number sampled from one stratum:
$number from a stratum = \frac{______}{______} \times size of that stratum$
The completed formula is:
$number from a stratum = \frac{n}{N} \times size of that stratum$
So, for example, sampling 10 mice from a population of 800 that contains 540 field mice gives $\frac{10}{800} \times 540 = 6.75$ , which rounds to 7 field mice.
This formula is not in the formulae booklet.
A researcher stands by the office door for ten minutes one morning and asks workers how long their journey was as they arrive.
Which sampling method is this, and what is its main weakness?
Opportunity sampling, also called convenience sampling: a sample formed from whichever available members of the population happen to fit the criteria.
Its main weakness is that it is unlikely to be representative of the population: here it reaches only the people who arrive during those ten minutes, a group already selected by how long their journey takes.
It is used when a sample is needed quickly, or when no list of the population is available.
Which sampling methods do not select their members at random, and why does that matter?
Quota sampling and opportunity sampling do not select their members at random: in both, the members are chosen by whoever is collecting the data rather than by chance.
That matters because a non-random sample is more likely to be biased and cannot reliably be used to make inferences about the population, which is the disadvantage to give when comparing quota sampling with simple random sampling.
Simple random, systematic and stratified sampling are all random, provided the list they work from is itself random.
You cannot list or number every member of a population, for example the fish in a lake.
Which sampling methods does that rule out, and which are still available?
Ruled out: simple random, systematic and stratified sampling, all of which work from a sampling frame.
Still available: quota and opportunity sampling, neither of which needs a list.
This is why the answer is so often quota or opportunity when a question makes a point of saying that no list exists.
Why can two people sampling the same population reach different conclusions?
Because a sample only gives information about the members actually in it, and two samples contain different members.
This is why sample size matters: taking a larger sample is the improvement that applies to almost every sampling method. So, for example, a sample of 10 from a population of 800 is only 1.25% of it.

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