Lesson video

Hello everyone.

A warm welcome and a thank you for joining me Mr. Grattan for this lesson on sampling.

During this lesson, we will be looking at different types of sample and why they exist.

Pause here to have a look at some of the keywords that we'll be using today.

And note, a simple random sample is a type of sample where every item in a population has an equal chance of being selected.

So I've talked about collecting a sample, but what is a sample? And how can we go about collecting one? This lesson will focus on the collecting data part of the statistical inquiry cycle, and specifically the collection of primary data.

Sometimes you'll have to collect data from the entire population, but in other times, it'll be more sensible to only collect data from a sample of that population.

But still, what is a population? Well, a population is the entire set of people, creatures, plants, or items that make up the whole group, which is being studied during an investigation.

Collecting data on a whole population will give full insight into the habits, characteristics, or properties of that population.

But as Laura says, collecting data on potentially thousands of people or things sounds a little bit daunting, especially if the population is huge, or if it is challenging to know the size of the population, or how to acquire data on an unknown population.

A sample is a subset of a population.

It is a group of people or things selected from the wider population, usually of a size small enough to be manageable for an investigation, but big enough to be useful for an investigation.

So a sample is looking pretty reasonable right now.

Laura can just collect data from a few people in Oakfield and call them a sample, even if the investigation is about everybody in Oakfield.

But what makes a good sample? Well, the hope is that any insights into the habits, characteristics or properties of a sample can be accurately generalised to the whole population.

Which of these samples do you think have habits, characteristics, or properties that are representative of the whole population? Starting off with all of the sweets in a jar, that's the population.

An example of a sample is a random handful of sweets from that same jar.

Or what about the people who live in Oakfield? That's the population.

A sample of that population could be the pupils at Oakfield Academy.

But what if we only wanted to collect information, conduct an investigation about pupils at Oakfield Academy? Now, pupils at Oakfield Academy is the whole population.

We don't actually care about, in this different investigation, the rest of the people who live in Oakfield.

A sample of the people who go to Oakfield Academy are the pupils who are in year 11.

And lastly, our population could be all of the rabbits that live in one specific forest.

One sample from that population could be only baby rabbits that live in that exact same forest.

Okay, here is a series of check questions.

The population are the pupils who go to Oakfield Academy.

Pause here to consider which of these are samples from this population.

And so the answers are B and C.

Our population is the pupils who go to Oakfield Academy.

And so a group of these pupils could be the group of pupils on the netball team, or the group of pupils that are in year seven.

However, parents are not pupils, and so parents are not part of the original population.

Nor are the teachers, because we were specifically focusing on pupils who go to Oakfield Academy as our population.

If the population was people who go to Oakfield Academy instead, then the teachers would be a sample from that population.

Next up, an investigation is that a scientist plans to investigate what percentage of fish in Oakfield Lake are carp.

Pause here to write down the population of this investigation.

The population are the things that the scientist wants to investigate.

The scientist wants to investigate all of the fish in Oakfield Lake in order to see how many of them are carp.

Therefore, all of the fish in Oakfield Lake is the population.

For this same investigation, the scientist plans to collect some fish from several different lakes in the area, and find out what percentage of those fish caught are carp.

Pause here to choose the correct statement explaining why these fish are not a sample of the population for this investigation.

And the answer is B.

Not all the fish were from Oakfield Lake.

There is no point in collecting information from a sample that is outside of the population that you are trying to investigate.

Laura is somewhat correct.

Collecting data on the first things that you see in a population is one example of a type of strategy that you could use to collect samples from a population.

But there are many different ways, each with their own advantages and disadvantages.

For example, if Laura is trying to collect a sample of 50 people from the population of Oakfield, there are many different types of sampling methods that she could use.

Laura could stand in one spot and ask the first 50 people that she sees, or she could knock on 50 doors on one street and ask all of the residents who live at those houses.

Laura could also post a questionnaire through 50 random doors on her way to school.

Or Laura could ask the first 10 pupils that she sees, the first 25 parents that she sees, and then the first 15 elderly people that she sees.

These are just some of the many different sampling methods.

Pause here to think about or discuss, which one of these methods are most sensible? And can you think of any other ways of collecting a sample of 50 people? For this check, we have an investigation where Jacob wants to take a sample of 70 ants in his ant farm to see if they are all healthy.

Pause here to consider what the population of this investigation is.

Specifically, the population are the ants in Jacob's ant farm.

For this same investigation, pause here to choose which of these may be sensible ways of taking a sample of 70 ants.

Both A and B are correct.

C isn't a great method because you could scoop up a handful of ants and not even get 70.

And finally, pause here to choose which of these may explain why Jacob is only checking a sample of his ants and not the whole population.

And the answers are B and C.

It is impractical and time consuming to check potentially hundreds or thousands of ants, and it's definitely difficult to guarantee that you've checked them all, when each ant is very small.

Laura says that if a population is really big, you know that you need to collect a sample.

But she also says if a population is small, she has to collect data on the whole population, right? Well, Laura isn't quite correct.

We have definitely covered the idea that samples are helpful to get a picture of the whole population if the population size is large.

But this isn't the only time samples can be useful.

Samples are also incredibly useful even with small populations if an investigation means that the population will be damaged or destroyed.

Then it makes no sense to investigate a whole population just to see it all get destroyed.

For example, imagine you had a bunch of grapes.

You want to give it to a young child, but you want to test if the bunch is sour or not before you give the grapes to that child.

The population is the bunch of grapes and the investigation is to see if the bunch is sour or not.

Eating all of the grapes will obviously leave none left for the child.

However, taking a sample of two or three will give you an idea for whether the rest of the grapes are sour or not.

Taking a sample of the grapes makes far more sense than testing or eating the whole population.

Okay, here's a quick check.

An engine company produced 20 engines for sports cars.

The investigation is the engineer wants to see if the engines will break or survive when they reach 15,000 RPM.

Pause here to consider, how many engines should the engineer test for this investigation? Testing all 20 of them seems like a bit of a waste if all 20 of them break, and one may not be enough to get a picture of the whole population.

So about three or four is sensible, because if all of them break, then likely the other ones will break as well.

For this practise, we have question one.

Pause here to give an example of a sample for each population, and for the last row, suggest a population that that sample could belong to.

And pause here for questions two and three where you have to write an explanation for whether the sample the headmaster of Rowanwood or Oakfield Academy took is more sensible.

And for question three, explain why Laura investigating the whole population is not sensible, and suggest a more suitable sample.

And that is great work so far in considering the flaws and qualities of all of these scenarios.

Here are the answers to question one.

Pause here to look through the examples of samples.

And note, there are many, many possible samples that could have been taken from all of these populations.

And for question two, the sampling method of the headmaster of Oakfield Academy is much more sensible.

Pause here to check if the explanations given match your own.

And for question three, well, there's no point in testing the lifespan of all 10 batteries, as Laura will not have any batteries left to use herself.

It is much better to take a sample of one or two batteries and make an assumption that the majority of the other batteries will have a similar lifespan.

We've looked a little bit into a lot of different sampling methods.

But now let's dig into a lot more detail about one specifically, the simple random sample.

Laura correctly notices that there are lots of different sampling methods, but Laura also notices that a lot of them are pretty bad.

Parts of the population may be over or underrepresented, making the sample very unrepresentative of the whole population.

And we want a representative sample, otherwise the information that we gain from the sample can't be generalised to the whole population, making an investigation pretty useless.

These unfair sampling methods are called biassed samples.

A biassed sample is when a member or group of members from a population are more or less likely to be chosen for a sample compared to other members of that same population.

On the other hand, a simple random sample is a sample where every member of the population has an equal chance of being chosen for a sample.

For a small population, we can perform a simple random sample by putting the names of each member of that population into a hat once each, and then randomly picking names from that hat until you have enough for your sample.

But note, each name picked from the hat should result in exactly one member being chosen for the sample.

So no name should be used more than once to create your sample.

Okay, here's a set of checks.

A teacher wants to select a simple random sample of six pupils from a class of 15 pupils by putting names into a hat.

Pause here to think how many names should be in that hat? 15 pupils means a population of 15, therefore 15 names should go into that hat.

That same teacher chooses these five random names Andeep, Sofia, Alex, Sam, and Laura.

Based on the sample so far, pause here to consider which of these names cannot be the final one chosen to create the full sample of six.

A and D are correct.

Andeep and Sam should not be able to be chosen, because they have already been chosen as part of the other five names.

Oh, that's interesting, the final name is Andeep.

Each pupil in the class has a unique name.

So what does this mean? Pause here to look through all three of these options.

Well, it's pretty clear that Andeep's name was put into the hat more than once, at least twice.

Because of this, this is no longer a simple random sample.

Laura is very much correct here.

Picking names out of a hat is time consuming, especially for large populations.

Computers and calculators can be used to help collect a simple random sample.

Both can generate random numbers through the use of an RNG, which means random number generator.

Every number an RNG generates has an equal chance of being generated.

Here's an example of an RNG, a random number generator in action.

You can assign every member in a population a unique number.

This can be done in a time efficient manner, such as going one, two, three, four to the names on a register, or as students enter a classroom.

Then the computer or calculator uses a random number generator to generate a random number in the range that you give it.

So in this example, the integers between one and six can be generated.

So if the RNG machine generates the number two, then we know that Andeep has been chosen for the sample.

I can then activate the machine once more, this time giving me six, and so Jun has been selected for my sample instead.

Okay, grab a calculator, and I can show you how to use it to generate some random integers.

First up, press the catalogue button, then scroll down to probability, and then scroll down again to select random integer, and press okay.

After pressing okay, you should go back to this screen where it says RanInt# and then open bracket.

The first number that you type is the smallest integer the RNG can generate.

Then type in a comma that is shift, close bracket, and then the next number is the largest integer that the RNG can calculate.

Don't forget the closed bracket, and then press execute to generate your random integer.

You do not need to type all of this again to generate another random number.

All you need to do is press execute again and it will generate another random number.

Keep generating numbers until you get four different integers.

The four pupils with these numbers will be your sample.

If the maximum or minimum number has already been generated, you can change the parameters of the RNG in order to avoid duplicating some of the numbers that have already been chosen.

In this instance, nine was already selected, so we can change the parameters to one to eight rather than one to nine.

And please note, when a pupil whose number isn't the maximum or minimum has been chosen already for a sample, they cannot be selected again, even if their number appears a second time from the RNG.

So just repeat the generation process again until a non chosen number is generated.

Okay, here's a set of similar checks all about using a random number generator.

Pay attention to all of the details very carefully for each check.

For this first one, can you explain why this is not a simple random sample? Pause here to think about or discuss an answer.

The RNG has a minimum value of three, meaning one and two cannot be generated.

Aisha and Andeep have a 0% chance of being chosen for this sample, making it a biassed sample, not a simple random one.

For this check, everyone has two numbers.

Pause here to choose the correct statement.

Is this a simple random sample or not? It is, but remember, it is only a simple random sample if a pupil will not be selected twice, once with each of their two numbers.

If, for example, Aisha has been chosen because the RNG selected one, she cannot be chosen again if the RNG then selects 10.

If the random number generator does choose 10, then generate another random number until you do not get one of Aisha's numbers.

Okay, what's changed this time? Pause here to look through all of the details and consider if this is a simple random sample or not.

The answer is D, no.

Some pupils are less likely to be chosen because the RNG only goes up to 15.

So 16 for Lucas, 17 for Alex, and 18 for Sam cannot be chosen.

Oh, Jun now has four numbers for some reason.

Pause to consider if this is a simple random sample or not.

And the answer is definitely no, answers C and D.

Jun has a more likely chance of being chosen than the rest of them, and therefore the rest of them have a less likely chance of being chosen than Jun.

Note how B is not a correct answer though, and the reason for that may be in this last check.

Pause now to consider all of the details in this scenario to see whether it is a simple random sample or not.

Yes, it is because even though Jun has more numbers than the rest of them, 19 and 20 are in no way included in the RNG.

Because 19 and 20 aren't included, Jun functionally only has two numbers that can be used for the sample, the 6 and the 15.

He has the same chance of the RNG choosing one of his numbers compared to the rest of the population.

And now onto the practise.

For question one, describe how a simple random sample could be collected by the football manager.

And for question two, explain why names in a hat is not practical for the headmaster's investigation.

And then describe how a random number generator could be used instead to generate a simple random sample.

Pause now for these two questions.

And finally for question three, in order for this to be a simple random sample, what range of numbers should Jun be assigned? And what would be typed into a calculator to generate a simple random sample from this population? Test this for yourself.

Who gets generated by the code that you suggest for part B? Pause now to try this question.

Great effort everyone in considering the suitability of different types of simple random sample.

The answers for question one.

The names of each football player could be put into a hat.

But alternatively, if every football player has a unique number on their football shirt, the manager could use a random number generator to generate a sample from those preassigned football shirt numbers.

For question two, is there even a hat big enough to fit 960 names? And even if there was, you cannot guarantee that all of the names would be in the hat.

It's just not very practical.

The headmaster could assign a unique number between 1 and 960 to all students from a list or a register given in alphabetical order.

That RNG can then be used at least 80 times to generate a sample of 80 students.

And finally, for question three, Jun should be assigned the integers between 26 and 30.

And this is what the code should look like when the RNG is typed into your calculator.

Were you able to successfully generate some random numbers to choose some of these students? And if you did, a very well done.

That is all for this lesson.

I appreciate the attention to fine detail across all of the subject methods that we have covered.

Throughout this lesson, we have considered an effective sample aims to provide the same insights into the habits, characteristics, or properties as when investigating a whole population.

We've also considered different advantages and disadvantages of different sampling methods.

And finally, a simple random sample is a fair or unbiased way of choosing a sample, as each member of a population has an equal chance of being selected for that sample.

An RNG or random number generator can be used to help collect a simple random sample.

Once again, thank you all so much for your attention and effort during this lesson.

I'm Mr. Grattan, and until next time, have a great rest of your day.