Define sampling frame .

A sampling frame is a list of all the members of the population, such as a company's list of its employees' names. It is essential for a simple random sample, because you cannot give a unique number to members you cannot list. Where no such list exists, a genuinely random sample is very hard to take.

What is the difference between a population parameter and a sample statistic?

A population parameter is a numerical value describing a characteristic of the whole population, such as the mean height of all 16-year-olds, and it is usually unknown. A sample statistic is a value computed from the data in a sample. Statistics exist in order to estimate parameters, which is the whole reason for sampling at all.

How do you use random numbers to take a simple random sample of 20 from a club of 50 members?

Give each member on the register a unique number from 1 to 50, which is the sampling frame. Read the random digits in pairs , taking the member whose number comes up when the pair is between 01 and 50, and ignoring the pair otherwise. Carry on until 20 different members have been selected, ignoring any repeat.

Why is it more efficient to assign two numbers to each of 50 members rather than one?

Two-digit random numbers run from 00 to 99, so with one number each, half of every set of digits generated is wasted. Giving each member two numbers uses all 100, so no draw ever has to be discarded. The same reasoning gives five numbers each for 200 mice with three-digit numbers, since 1000 divided by 200 is 5.

Why would you take a sample instead of carrying out a census?

A census is time-consuming and expensive, and it can be impossible when testing destroys what is tested, as with the lifetime of every lightbulb a factory makes. A sample is quicker and cheaper, and leaves far less data to analyse. The price paid is that a sample might not represent the population, whereas a census is fully accurate.

True or False? Asking people in a cinema is a good way to estimate what proportion of people enjoy watching films.

False. People who are in a cinema are far more likely than average to enjoy films, so the sample is biased and the estimate will come out too high. A sample has to be representative of the population, and simply making it larger would not fix this one.

A question describes a sampling method and asks you to criticise it. What should you look at?

Look at how much data was collected, which means considering the sampling fraction , since most methods improve with a larger sample. Then look at whether the method could introduce bias , because randomness is what keeps bias down. A method that is not random in some respect is usually the thing worth challenging.

What does a sample strictly tell you about, and what follows for two different samples?

Strictly a sample tells you only about the members that were actually selected, and its results are then used as estimates for the population. It follows that two different samples from the same population can lead to different conclusions. That is why a single sample is evidence rather than proof, and why the wording of a conclusion matters.

A LevelMathsCambridge (CIE)Probability & Statistics 2FlashcardsStatistical Sampling & EstimationSampling & Data Collection

Sampling & Data Collection (Cambridge (CIE) A Level Maths: Probability & Statistics 2): Flashcards

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Define sampling frame.

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Cards in this collection (10)

Define sampling frame.
A sampling frame is a list of all the members of the population, such as a company's list of its employees' names.
It is essential for a simple random sample, because you cannot give a unique number to members you cannot list.
Where no such list exists, a genuinely random sample is very hard to take.
Fill in the three terms:
the whole set of things you are interested in: $______$
a subset of it that you collect data from: $______$
a collection of data from every single member: $______$
The completed terms are:
the whole set of things you are interested in: population
a subset of it that you collect data from: sample
a collection of data from every single member: census
A census and a sample are two ways of getting at the same population, and the choice between them is a practical one.
What is the difference between a population parameter and a sample statistic?
A population parameter is a numerical value describing a characteristic of the whole population, such as the mean height of all 16-year-olds, and it is usually unknown.
A sample statistic is a value computed from the data in a sample.
Statistics exist in order to estimate parameters, which is the whole reason for sampling at all.
Fill in the two probability conditions:
In a random sample, every member of the population has a $______$ probability of being selected.
In a simple random sample, every member has an $______$ probability of being selected.
The completed conditions are:
In a random sample, every member has a non-zero probability of being selected.
In a simple random sample, every member has an equal probability of being selected.
A simple random sample asks for more than that as well: every possible sample of that size must be equally likely.
How do you use random numbers to take a simple random sample of 20 from a club of 50 members?
Give each member on the register a unique number from 1 to 50, which is the sampling frame.
Read the random digits in pairs, taking the member whose number comes up when the pair is between 01 and 50, and ignoring the pair otherwise.
Carry on until 20 different members have been selected, ignoring any repeat.
Why is it more efficient to assign two numbers to each of 50 members rather than one?
Two-digit random numbers run from 00 to 99, so with one number each, half of every set of digits generated is wasted.
Giving each member two numbers uses all 100, so no draw ever has to be discarded.
The same reasoning gives five numbers each for 200 mice with three-digit numbers, since 1000 divided by 200 is 5.
Why would you take a sample instead of carrying out a census?
A census is time-consuming and expensive, and it can be impossible when testing destroys what is tested, as with the lifetime of every lightbulb a factory makes.
A sample is quicker and cheaper, and leaves far less data to analyse.
The price paid is that a sample might not represent the population, whereas a census is fully accurate.
True or False?
Asking people in a cinema is a good way to estimate what proportion of people enjoy watching films.
False.
People who are in a cinema are far more likely than average to enjoy films, so the sample is biased and the estimate will come out too high.
A sample has to be representative of the population, and simply making it larger would not fix this one.
A question describes a sampling method and asks you to criticise it. What should you look at?
Look at how much data was collected, which means considering the sampling fraction, since most methods improve with a larger sample.
Then look at whether the method could introduce bias, because randomness is what keeps bias down.
A method that is not random in some respect is usually the thing worth challenging.
What does a sample strictly tell you about, and what follows for two different samples?
Strictly a sample tells you only about the members that were actually selected, and its results are then used as estimates for the population.
It follows that two different samples from the same population can lead to different conclusions.
That is why a single sample is evidence rather than proof, and why the wording of a conclusion matters.

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