Lesson video

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Hello, my name is Miss Parnham.

In this lesson we're going to learn about stratified sampling.

In this example, we have 200 workers in an office divided into three departments, but those departments are different sizes.

So it is a good idea to take a stratified sample, so that we can take a proportion of each group and it will be representative of the whole population.

So if the sample size for HR is eight, that means eight 20th, or two fifths or 40% of the population from HR is in the sample for HR.

So we will use that same fraction or percentage to work out the numbers in the sample for sales and for marketing.

So 40% of 120 is 48.

The other way you could look at it is, the Sales team is Six times bigger than the Human Resources team.

So the sales team sample is six times bigger than the Human Resources sample.

And the marketing 40% of 60 is 24.

Again, you could think of it as marketing is half the size of the sales department.

So the sample is half the size of the sales department sample.

Adding those numbers up, gives us a total of 80.

And if you've already noticed, this is 40%, or two fifths of the total population of 200.

Here's a question for you to try.

Pause the video to complete the task and restart the video when you're finished.

Here are the answers totaling up the number of workers should get you 300.

So 30 is 10% or one 10th of this.

So all your sample sizes for each area of the workforce should be 10% of the populations.

And a good double check is that the all add up to 30.

Here is a further question for you to try.

Pause the video to complete the task and restart the video when you're finished.

Here with the answers 15 is one fifth of 75 or 20%.

So you need to find one fifth of all the other populations from the other year groups in order to get their sample sizes.

And then if you add them up, you should find that that's 80 just a good double check.

one fifth of 400 the whole population size is 80.

So that's where that answer comes from.

In this example, the entire population is 271.

and the sample size is 50.

So the sample size as a proportion of the population is 50/271, or 18.

5% when it's rounded, but we must not work with a rounded answer when we use this in calculations.

We're going to multiply this fraction by each of the populations from the different age groups.

In order to work out the sample size, we will have to round our answers to the nearest integer because we can't ask a decimal number of people.

So multiplying each of these numbers by 50/271, produces the following answers.

What you may notice by looking at these numbers is that when they are summed, they only give an answer of 49 and not 50.

This is because of the rounding process.

When we're calculating problems involving stratified sampling, it's often best to jot down more accurate versions of the numbers that we get from our calculator.

Usually two decimal places will be enough.

So if we look at these numbers, these are more accurate answers 250/271 multiplied by each of the populations.

One of these numbers needs to be rounded up so that the sample size becomes 50.

And the one that has the strongest case for being rounded up is the 6.

46.

Because the decimal part is the greatest, so we're just comparing the digits after the decimal point.

This is the greatest.

So we will exchange six for seven so that the sample size is 50.

Here's a question for you to try.

Pause the video to complete the task and restart the video when you're finished.

The total population size here is 521.

So forming a fraction of 50/521 gets you 9.

60% to three significant figures, but you must calculate with the accurate value for this.

And even though Eva done that, because she's got to round at the end to the nearest integer, because she can't ask a decimal number of people, then it's led to a sample size of 49 because of the rounded.

So looking at the more accurate results and comparing the decimal parts of them, we can see that 11.

42 has the weakest case for being rounded down, because it's got the greatest decimal part.

So this number is going to be adjusted up to 12 to make the sample size 50.

Here's a further question for you to try.

Pause the video to complete the task and restart the video when you're finished.

We've got a total population of 450 here.

And if the sample size four is 40, then 440 fifths is going to give us the sample size for each part of the population.

Now doing that produces 1714 and 10, which actually add up to 41.

And we need a sample size of 40.

53, 13.

51 and 9.

96.

So the one that has got the weakest case for being rounded up is 13.

51, because it's got the smallest decimal part to its number.

So we're going to take that 13 and round it down to 30 in order to balance that out to a sample size of 40.

That's all for this lesson.

Thank you for watching.