Lesson video

Hello there.

My name is Mr. Tilstone.

I'm a teacher.

I just love maths, so it's a real pleasure and a real privilege to be here with you today to teach you this lesson, which is all about mean averages, and that's something that you might be getting quite confident with.

Let's see if we can teach you even more today.

If you're ready, let's begin.

The outcome of today's lesson is this.

I can explain why the mean is useful and when it is not appropriate.

We've got some key words.

If I say them, will you say them back please? Are you ready? My turn, mean average.

Your turn.

My turn, set of data.

Your turn.

And my turn, outlier.

Your turn.

Now, that last word in particular is quite unusual.

Let's explain what that means.

Well, let's start with mean average.

That's a single number expressing the typical value in a set of data.

It is calculated by finding the total of the set of data and dividing by how many values there are.

And I'm sure you've done that lots of times very recently.

So we add first and divide second.

A set of data is a collection of facts such as numbers, words, measurements, observations, or even just descriptions of things.

An outlier is a value that lies outside.

It is much smaller or larger than most of the other values in a set of data.

And we're going to be looking at lots of examples today of outliers.

So by the end of the lesson, I'm sure you're going to be very confident about that.

Our lesson today is split into two cycles, two parts.

The first will be outlying values.

So we'll explore that concept of outliers.

And the second.

is the mean average useful? 'Cause it isn't always.

Let's start by thinking about outlying values.

And in this lesson, you're going to meet Laura and Lucas.

Have you met them before? They're here today to give us a helping hand with the maths.

Here is a graph showing Oak's football team results.

Laura says, "That match three data stands out a bit from the rest." Doesn't it just? Look at the number of goals there, 11 goals scored by Oak in that match.

That's a lot, isn't it? It's very unusual.

And compared to the others, it really does stick out.

"Yes," says Lucas, "It was a high scoring game for both teams." And sometimes, just sometimes, that happens in football.

You get these kind of really unusual matches and strange scores.

"Do you think it should be included in the mean average?" He asks.

Hmm, that's a good question.

Laura says, "I think we could describe it as an outlier." An outlier is a value that lies outside as it is much smaller or much larger than most of the other values in a set of data.

So what's this? Is that much smaller or much larger than the other values? It's much larger, much larger.

Where else might an outlier make a difference? Well, let's have a look at this table.

This has got the heights of some children, five children.

"We calculated the mean average height of the members of the Class 6 5-a-side football team." And Laura says, "I can't see any outliers here, can you?" I can't either.

None of those really stick out.

None are either much smaller than the others or much bigger than the others.

"Then we decided to include our coaches, Dr.

Shorrock and Mr. Tazzyman.

They are important members of the team." So let's have a look.

So Dr.

Shorrock has got a height of 165 centimetres, quite a lot taller than the others, and then Mr. Tazzyman, 193 centimetres, quite a lot taller than that.

Ah, they are a bit taller than the children.

Yes.

What is the mean average height of the team without Dr.

Shorrock and Mr. Tazzyman? 120 Plus 130 plus 135 plus 127 plus 140 is equal to 652.

The total of the heights is the total of the set of data.

And then what do we need to do with that to find the mean average? We divide, in this case, by five.

So 652, those combined heights, divided by five, the number of people, is equal to 130.

4.

So we're dividing by five.

The mean average height of the team we can say is 130.

4 centimetres.

And that seems reasonable, doesn't it? Some are a bit less than that, some are a bit more than that.

That seems like a reasonable mean average.

Let's do a little check.

Calculate the mean average height of the team, including Dr.

Shorrock and Mr. Tazzyman.

Pause the video.

How did you get on with that? Let's have a look.

Well, first of all, did you add together all of their heights? If you did, that gave you 1,010.

So the total height of the team is a total of the set of data.

And then 1,010 divided by 7.

Why by seven? Because now there are seven team members if you include the two coaches.

So 1,010 divided by 7 is equal to 144.

3.

So the mean average height of the team is now 144.

3.

Let's do another check.

What do you think about the two mean averages calculated? Do they both give a representative value for the height of the team? Well, Laura says, "The mean average height of the children is 130.

4." And Lucas says, "The mean average height of the team, including the coaches, Dr.

Shorrock and Mr. Tazzyman, is 144.

3." So do they both give a representative value for the height of the team? Pause the video and discuss.

What do you think? Well, when we include the adults, the mean average height is taller than any of the children.

So that 144.

3 centimetres is taller than any children.

So it's not really very representative is it? I think the heights of the teachers, especially Mr. Tazzyman, are outliers as they are taller than any of the children.

They really stand out and they change the data, don't they? Considerably, in fact.

So the mean average height without the adults is a better representation of the height of the children in the team.

Let's have a little practise.

Let's see if you've understood that concept of outliers.

So number one, identify the outlying values in these sets of data.

So the first set of data is looking at pages read.

So one date was 24, the next 31, the next 167, the next 18, the next 38, and the next four.

You think there you can see any outliers? What about goals scored per match? And then what about cards in each pack? And spelling test score out of 40.

So number two, explain why these values are outliers.

What would they do to the mean average if you use them in the calculation? If you are allowed to work with a partner, please do.

Pause the video, and away you go.

Welcome back.

How did you get on with that? So we're looking at outliers.

Let's look at the pages read.

We've got two outliers here, 167 and four.

One's much higher than the rest, like much, much higher, and one's much lower than the rest.

Much, much lower.

And the next one, 10 goals is a lot of goals scored per match.

What about cards in a pack? Well, it's unusual for zero cards to be in a pack, isn't it? And then 38, much higher than the other values.

It sort of sticks out, doesn't it? And then the spelling test scores, well, that zero sticks out, that week that the person was absent, so we can say that's an outlier.

So zero is not an outlier in the goals scored per match because it's very common to see zero goals scored in a football match, as any football fan will tell you.

And number two, the outliers are much larger or smaller than the other values.

They would make the mean average a less accurate representation of the set of data.

Well, let's move on to the next cycle.

That's, is the mean average useful? It's important to know when the mean average is a useful piece of information.

So we've got five people here and their ages, one's 32, one's 10, one's nine, one's nine, one's 10.

What could you say about those ages? Would you say that one of them is an outlier? What's the mean average age of this group? Well, if we add them together, that's 32 + 10 + 9 + 9 + 10, and that gives us a total of 70 if we add all those years together.

And there's five people in that group.

So 70 divided by 5 is equal to 14.

So the mean average of this group is 14 years.

Hmm, what could you say there? Are most of the people in the group around 14 years old? No, not really.

Nobody's around 14 years old.

We've got the first person who's much, much older than 14 and the rest are younger than 14.

So no member of the group is 14 or very close to 14.

So it's not a good value to represent the age of the group.

What would give a more accurate mean average for the group? Let's do a little check.

Calculate the mean average age of the group without the teacher.

So we've taken away the outlier, now we've just got the children.

Can you work out the mean average of their ages? Pause the video.

Did you remember how to do that? Did you add them all together? That would give you 38 years.

And then did you divide, in this case, by four? And if so, that would give you 9.

5.

So 9.

5 is a good representation of the age group of the children.

They're all either that or a bit younger or a bit older than that.

Is the mean average always a useful piece of information? The local shoe shop has sold out of Jacob's shoe size again.

He takes a size five.

He says, "I found the mean average shoe size for our class.

It's 4.

75.

I'm going to tell the shoe shop." And Laura says, "I'm not sure what they would do with that data.

Hmm.

How would it help them to order the right sizes?" He says, "Yeah, you have a point there.

I think the most popular shoe sizes would be more useful." Mm, I do too.

Sometimes a mean average is not the most helpful piece of information, you need to think about how it could be used.

Let's do some practise.

Number one, calculate the mean average with and without the outlying values.

What do you notice? So again, we've got the pages read, again the goals scored per match, again the cards in each pack, and again the spelling test score out of 40.

Take away those outliers and see what happens.

So with and without please.

Number two, how could you use the mean average value in each case? Pause the video.

Good luck.

And off you go.

Welcome back.

How are you getting on? Are you feeling good? Are you feeling confident? Are you getting to grips with the idea of outliers? Well, let's give you some answers and you can check.

Number one, calculate the mean averages of the sets of data with and without the outlying values.

What do you notice? So let's start by including the outliers.

That's 24 + 31 + 167, the outlier, + 18 + 38 + 4, that other outlier, is equal to 282.

And 282 divided by 6, which is the number of days, is equal to 47.

So that's got a mean average of 47.

Now, if we ignore those really strange values, and maybe on that day that we read 167 pages, maybe it was like a day where we were travelling to a holiday destination so had more time, and maybe the four was a day where maybe you were feeling a bit poorly and weren't able to read, something like that, but if we take away those two outliers, that gives us 24 + 31 + 18 + 38 + 4, and that gives us a total of 115 pages.

115 Divided by 5 is equal to 23.

What about the goals scored per match? Let's start by including the outliers.

And in this case, that's that unusual match where there was 10 goals scored.

So 2 + 1 + 2 + 0 + 3 + that 10, the outlier, + 4 + 3 + 2 is equal to 27.

So 27 goals were scored across those matches.

And 27 divided by 9 is equal to 3.

So a mean average of three goals per match.

And then ignoring that unusual result, that's 2 + 1 + 2 + 3 + 4 + 3 + 2 is equal to 17.

Now, this time we're not dividing by nine because we're taking out that outlier day.

We're dividing by eight.

So 17 divided by 8 is equal to 2.

125.

So we can say just a bit more than two goals scored per match.

And the cards in each pack.

Well, let's do it including the outliers.

So that's 19 + 21 + 17 + that 0, the outlier, + 38 + 12 + 24 + 13.

So 38 was also an outlier, we did include it this time.

So that gives us 144 in total, the number of cards.

And then we dividing by eight, that's the number of packs, including the outliers.

144 Divided by 8 is equal to 18.

And then, ignoring those outliers.

So 19 + 21 + 17 + 12 + 24 + 13 is equal to 106.

So 106 cards.

And this time we're not counting eight packs, we're counting the six packs.

So 106 divided by 6 is equal to 17.

667.

So we can say just a bit less than 18 cards.

And then what about the spelling test? Let's include the outliers to start with.

Let's include the absent week, so 29 + 0 + 31 + 30 + 27 + 37 + 35 is equal to 189.

And that's 189 over seven weeks.

So we're doing 189 divided by 7, and that's equal to 27.

Or we could ignore the outliers, that's 29 + 31 + 30 + 27 + 37 + 35.

So this time it's not seven weeks, we're thinking about six weeks.

So we're doing 189 divided by 6 this time, and that gives us 31.

5.

That's ignoring the outliers.

Which one do you think's fairer? Which one do you think's more representative? So number one, what did you notice? You might have noticed that including the outliers meant that the mean average was sometimes outside the range of the other values in the set of data.

So it's not helpful to include it because it sort of skews the data, it makes the final mean average not very representative of anything.

And number two, how could you use the mean average in each case? You could use the mean average to set a reading target for children in the class.

How could we use the mean average in the next one? You could use the mean average to track the performance of the team from term to term or year on year.

And removing that outlier, I think, helps in that case because it's just an unusual score.

How could you use the mean average here? Well, there's not much use for this mean average as the number of cards is not that important or that useful.

What about this one? You could use the mean average to track the performance of the class and see how their spelling is improving across the year.

And when we take out the outlier, the mean average is much more representative and fairer, I would say.

We've come to the end of the lesson.

Today we've been explaining why the mean is useful and when it is not appropriate.

Hopefully you've learned lots of new things such as outliers.

An outlier is a value that lies outside.

It is much smaller or larger than most of the other values in a set of data.

And we've seen both kinds today.

Sometimes when it's much smaller and sometimes when it's much larger.

Some sets of data had two outliers in 'em, one that was much smaller and one that was much larger.

It can make a mean average value less accurate as a value to represent the whole set of data.

So sometimes, sometimes, it's useful to exclude the outlier.

You have to make that decision.

Sometimes the mean average of a set of data is not very useful.

It's important to spot this.

You will learn about different kinds of averages at some point in the future.

Well, I've really enjoyed spending this math lesson with you, and I hope you've enjoyed it too.

I hope you have a fantastic day and whatever you've got in store, you are the best version of you that you can possibly be.

Take care and goodbye.