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Hello everyone it's Mr Miller here.

In this lesson we're going to be looking at finding the mean from a set of data.

So first of all, I hope that you're all doing well.

And if you've seen the first few lessons of this unit, you know already, you would have seen this slide here.

This shows the data handling cycle, it shows us the process by which we go about conducting an experiment.

Now in the first four lessons of this unit, we were looking at step one.

So that was all about writing the hypothesis and planning the data collection.

So where are we going to collect the data and who are we going to ask? So that's all done and now we have collected the data.

So we've gone out and done step two and from now on, we are going to be looking at step three, where we've got the data and now we need to do something with it.

We need to process it and we need to represent it.

And then also analyse it and see what's going on here.

So in this first lesson, we have collected the data and we're going to to look at finding the mean.

So let's go ahead and have a look at the Try this slide.

Okay.

So let's read the Try this task together.

Year eight students are collecting soup tins for a food kitchen charity.

They're working in groups and there's a prize for the group that does the best.

Decide who should win the prize.

Give reasons for your answer.

So two groups here, Lucy's group and Harry's group.

Have a think, which of these two groups would you give the prize to.

Pause the video for a minute and have a think.

Okay, great.

So I hope you've come to an answer and one of the things that you could have done is you could have added up all the tins to see who's collected more tins.

So if you added all the people in Lucy's group, seven plus three plus two plus six, plus two, you would've got 20 tins.

Whereas for Harry's group, add them up altogether and you get 21.

So you could have said, well, Harry's group has collected more tins so I would give the price to Harry's group.

And that would be a fair enough but you could've also said, well, Harry's group has actually got more people, which gives them a bigger chance to get more tins.

So let's have a look at this in more detail.

Let's say that for Lucy's group, we represented each of the number of tins that they collected as a bar model.

So you can see Lucy's got seven tins.

Laura has got three tins, et cetera.

Now, let's have a think how many people are there in total in Lucy's group? Well, there were five people in total.

So let's imagine that we split the total number of tins equally between these five people.

On average, how many tins does each student collect? Well, there are 20 tins and five students, so 20 divided by five gives me four.

So on average, each student has collected four tins because 20 divided by five people is equal to four.

See if you can do the same thing for Harry's group.

Pause the video for a couple of seconds.

Have a think.

How many tins has Harry's group collected on average? Okay, well then if you wrote this out, now there are seven people in Harry's group.

So you could have drawn a bar model or you could have just said 21 divided by seven equals three tins.

So on average, Lucy's group has collected four tins each, on average, Harry's group has collected three tins each.

So we can say that on average Lucy's group has collected more.

And this calculation, which gives us an answer of four and three, is called finding the mean.

So we can say that the mean of Lucy's group is four and the mean of Harry's group is three.

Let's have a look at another example in the Connect slide.

Okay.

So here's a connect slide.

This time, I've got five cards that have a mean of six.

One of the cards has been covered up.

So I know that the cards are four, 10, three, four and something I don't know what that is and I need to figure out what it is.

So have a think.

How would you do this? You might want to start off by adding up all the ones that we know already.

Have a think.

Pause the video for a minute or two.

See if you can work this out.

Okay, let's go through it together.

So again, what I've done is I've used a bar model to represent the cards that I have already, so four, 10, three and four and I've also used the blue bars to represent the fact that the mean, shows how many we've got on average.

What number do we have on average.

Now I know that I've got five cards, so that's why I've got five blue bars and they have a mean of six.

So on average, each of these bars is worth six.

Okay.

So what does that tell us? Well, if I've got five bars and each of them is six, what do they sum up to in total? Well, if you're thinking six times by five gives me 30, really well done.

That is the total sum of all the cards.

How do I use this fact to work out my missing bar model there? well, I could add up all the ones that I know already, four plus 10, which is 14, plus three which is 17, plus four, that gives me 21 and I want them to equal 30 in total.

So what's the last one.

Of course it's nine.

So we can use the fact that we know what the mean is to work out the missing card here.

Let's have a look at the independent task now.

Okay.

Let's have a look at the independent task, you've got two questions to do.

The first one, You need to find the mean of these sets of numbers.

So remember how we find the mean, we need to add up all of the numbers.

So three plus six plus four plus five plus seven and then divide that by how many numbers there are.

In this case, there are five numbers.

That has to do the first one.

Question two, these seven cards have a mean of two.

Two of the cards have been covered up.

What are all the possible positive whole number values on the missing cards.

So pause the video now.

Make sure that you are writing your answers.

You should be working on this for about six or seven minutes.

Pause the video and have a go at these two questions.

Great.

So hopefully you have done that.

Let's go over them nice and quickly.

So the first one, if I add up all of those numbers, I get 25 and 25 divided by five gives me five.

So the mean is five for the first one.

For the second one, the mean is also five.

The third one the mean is 35.

And the fourth one the mean is minus five.

And you could have noticed that there's actually some similarities between these questions.

So the last one, the one with negative numbers is the same as the first one but all the numbers are negative.

And the third one, is also the same as the first one but all the numbers are multiplied by seven.

So therefore the mean is also multiplied by seven, which is interesting.

Question two.

Hopefully what you noticed is that if I've got seven cards with a mean of two, I know that all of them must add up to seven times by two which is 14.

What are the ones that I know already add up to? Well, one plus four plus zero plus three plus one sums up to nine.

So the two missing cards must sum up to five.

So therefore I need to make a total of five from these two missing cards using positive whole numbers.

So it depends if you think that zero is a positive number or not, that's debatable, but if you do, you can have zero and five, you could have one and four.

Can you think of the other ones in case you haven't got it yet? Well, they're two and three and then just using them the other way round so a five and zero four and one and three and two.

So six possible answers there.

When you're ready, let's move on to the explore task.

Okay, so let's have a read through the explore task.

So imagine you have a large supply of three kilogramme and nine kilogramme weights.

So an unlimited supply, can you find combinations of these different weights whose mean weight is a whole number of kilogrammes.

So we're combining different numbers of three kilogramme weights and nine kilogramme weights to find a mean weight whose weight is a whole number of kilogrammes.

So in the green boxes, there are some suggestions for the things that you could find out.

So pause the video now and see how far you get with the explore task.

Okay, let's go through it.

So the smallest mean that you can get, this is actually quite a straightforward one.

Do you think you know what the smallest mean weight that you can get is? Well, if you only use three kilogramme weights, your mean is going to be three kilogrammes because the moment you start adding some nine kilogramme weights, your mean is going to get bigger.

What about getting a mean weight of six kilogrammes? Did you find a way how to do this? Well, if you spotted that the mean of three and nine is six.

So if you had one lot of three kilogramme weights and one nine kilogramme weights, the total in terms of the weight would be 12 kilogrammes.

And if you had two weights, 12 divided by two gives you a mean of six kilogrammes.

So any combination of the same number of three and nine kilogrammes would give you a mean weight of six.

The smallest number is one of each.

Okay.

The final one is a little bit tricky.

You could have tried some different combinations, but you would have got the answer if you had set two lots of nine kilogramme weights and one lot of three kilogramme weights because the two lots of nine kilogramme weights would give you a total of 18 kilogrammes and then you've got three kilogrammes for the one, three kilogramme weights.

So in total, you've got a total weight of 21 kilogrammes and three different weights and 21 divided by three gives you seven.

So that is one way how to get the mean weight of seven kilogrammes.

Even for free, if you can find the other whole number weights so see if you can find eight kilogrammes as a mean, see if you can find four kilogrammes, et cetera.

Feel free to do that in your own time.

But in terms of this lesson, that is all we are doing today.

So thanks very much for watching.

Hope you enjoyed the video.

Next time we're going to be looking at more problems involving the mean.

So am looking forward to seeing you next time.

Have a great day.

Take care and Bye bye.