Lesson video

Hello there, my name is Mr. Tilstone.

I'm a teacher and I just love maths.

I hope you're in fine form today, that you are focused, and that you are ready for today's challenge.

If you are, let's begin.

The outcome of today's lesson is this.

I can explain how to use the mean to make comparisons between two sets of data.

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

Your turn.

And my turn, set of data.

Your turn.

I'll bet you've encountered these words quite a lot in recent lessons, but let's have a little reminder about what they mean.

The mean average is 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.

So we add and then we divide.

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

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

The first will be comparing data and the second, finding the missing values in the set of data.

Let's begin by comparing data.

Today, we've got Laura and Lucas, and you might notice they're carrying flags.

Laura says, "Go Oak Netball." And Lucas says, "Go Oak Football." So let's find out what that's all about.

Oak Academy has a netball and a football team, does your school? Laura and Lucas are discussing which team is the most successful.

Laura says, "I think the netball team has won more matches than the football team." Well, that could be a reason to say they're more successful.

Lucas says, "I think they've played more matches, so that's not a fair comparison." Hmm, that's a good point, Lucas.

So Laura asks, "How can we compare the teams?" Can you think of a way? How could we compare the teams? What ideas have you got? Lucas says, "We could compare the mean average number of goals they score each match." That's not a bad suggestion, is it? She says, "Okay, let's collect the data." So here we go, here is some Oak Academy football team data.

Here are the Oak Football team results.

And the purple bars show the goals scored and the green bars the goals against.

So in match number one, there was one goal scored and two goals conceded.

So they lost that one, 2:1.

In the second match, there were four goals scored and one goal conceded.

So they won that one, 4:1.

What about the third match? What could you say about that? What was the score there? Well, there were two goals scored and one goal conceded.

So it was 2:1 to Oak.

What about the fourth one? Two goals scored, three goals conceded.

So they lost 3:2 in that one.

What about the fifth one? Match number five? Well, four goals were scored and two were conceded.

So that means that Oak won 4:2.

What about number six? In that case, Oak won 3:2.

What about seven? Oak won again, 6:3.

And what about that final match, match 8? Well, that was a draw.

Two goals scored, two goals conceded, it was 2:2.

So what could we look at? How could we compare this data? "There is a lot that we could discuss and calculate," say Lucas, there is.

What do you notice? You might like to have a little think about that.

And here are the Oak Netball team results.

So let's have a look.

In match number one, four goals were scored and five conceded.

So they lost that one 5:4.

What about week two? What could you say there, did they win or lose? Yeah, they won that one.

They won that one 3:2.

What about week three? Did they win or lose? They won again.

They won that one 5:4.

What about number four, match number four, win or lose or draw? Well, they actually lost that one.

They scored two goals but conceded three.

So they lost that one 3:2.

What about week five? Well, six goals scored, and then three conceded.

So they won that one 6:3.

That was a good match for them.

What about number six, week six? Well, three goals were scored and two were conceded.

So that was 3:2, so they won that one.

What about week seven? Four goals scored, one conceded.

That was 4:1, what about week eight? Four goals scored, three conceded, that was 4:3.

And what about week nine? Five goals scored and four conceded.

So another win for the netball team there.

What do you notice? What could you say? How could you or would you compare the football and netball team data? What ways have you got? "Let's calculate," says Lucas, "The mean average goals scored per match." Okay.

Well, if we add all of those together, so 1 plus 4 plus 2 plus 2 plus 4 plus 3 plus 6 plus 2.

So that's all the purple bars essentially added together.

That equals 24.

So they scored 24 goals over the eight matches.

Now divide the value of this set of data by the number of values.

Well, 24 is the number of goals scored and 8 is the number of matches.

So 24 divided by eight is equal to 3.

The mean average goals scored per match is 3.

Sometimes they scored more than that, sometimes fewer than that, but on the whole, the average is 3.

Let's have a little check.

Calculate the mean average number of goals scored by the Oak Netball team now.

So look at those blue bars.

Can you calculate the mean average number of goals? Pause the video.

Well, when you add all of those goals together, it does equal 36.

And then we need to divide by 9.

36 divided by 9.

Hopefully, that's a known times tables factor or related fact that is equal to 4.

The mean average goals scored per match is 4 for the netball team.

So Laura says, "I think the netball team is best as their mean average score is 4." But Lucas says, "I still think the football team is best with a mean average of 3 as you don't get as many goals in football." Hmm, they've both got good points here, haven't they? Can you use the mean averages to compare the teams? You can use mean averages to compare the teams, but you need to choose the right data.

"Could we look at the goal difference," wonders Laura.

"That might make it fairer perhaps." Hmm, "Yes," says Lucas.

"If the team wins, the difference is positive and if they lose it's negative." Let's do some practise.

Number one, calculate the mean average difference in the goals scored and goals against for the Oak Football team.

Laura says, "In the seventh match it is plus 3." So let's have a look at that match number seven.

So six goals scored.

3 conceded the difference between 6 and 3.

Well, they won, so it's a positive 3 difference.

And then Lucas says, "Look at the first match.

The difference is negative 1." There was a 1 difference between the goals scored and the goals conceded, but they lost that one.

So that's negative 1.

Okay? Number two, calculate the mean average difference in the goals scored and goals against for the Oak Netball team.

And number three, look at the two mean averages.

Which team do you think is best? Can you justify that? Laura says, "Look at the matches they lost." And Lucas says, "Which matches have a negative score difference?" So the ones they lost are a negative score difference.

The one they won are a positive score difference.

Pause the video and away you go.

Welcome back, how are you getting on? How are you feeling, are you feeling happy? Are you feeling confident? Would you like some answers? Let's do that.

Number one, we needed to use a little bit of knowledge about negative numbers here.

We've got 8.

The total goal difference score is a total of the set of data and that's 8.

And then there were eight matches played.

So 8 divided by 8 is equal to 1.

The mean average goal difference per football match is 1.

And then for number two, do the same thing again and that gives us 9.

So the total goal difference score is the total of the set of data.

So 9 divided by 9.

So the second 9 is a number of matches and that equals 1.

So the mean average goal difference per netball match is also 1.

So look at the two mean averages.

Which team do you think is the best? Well, the mean average goal difference for football is 1.

And the mean average goal difference for netball is 1.

So the mean average goal difference for both teams is 1.

And Lucas says, "I think we can say from this data that the teams are both as good as each other." So yes, I agree, there's lots of ways to look at it, but on goal difference alone, we can say they're equally good.

So, go, team netball, whoop-whoop.

And go, Team football, whoop-whoop.

It's time for the second cycle.

That's finding the missing values in the set of data.

The score for match three for the football team was wrong and has been removed from the graph.

You can see that empty space here.

Netball had a mean average of four goals per match.

I wonder what score we would need in match three to beat that.

There are eight matches.

So the total of the set of data needs to be more than 4 multiplied by 8, or in other words more than 32.

So how many goals would the team need to score in match three for the mean average to be greater than 4? The total number of goals scored in the seven matches is 22.

If we add them up now, the team would need to score 11 goals in match three to give a total of 33.

No pressure then, hey? "That's a lot of goals," says Lucas, "We could make the score 11:8, and say that it was a high-scoring game for both teams." Let's check that this does give football a winning mean average goals scored per match.

Well, let's do a check.

Calculate the mean average goals scored per match with a new data for match three.

Pause the video.

So the purple bars are showing us the goals scored.

And when we add all of those together, that gives us 33.

33 divided by 8 is equal to 4 remainder 1.

So the mean average goals scored per football match is just over 4.

That mean average goals scored per match is now just higher than the netball team's teeny-tiny bit.

Go, Oak Football.

It's time for some more practise.

Add the data for the missing matches for the netball team.

Find different ways to complete the data so that the netball team has number one, a mean average number of goals per match that is between 4 and 5.

Number two, a mean average number of goals per match, that is less than 3.

Number three, a mean average goal difference that is greater than 1.

And number four, a mean average goal difference that is less than 1.

Now in these cases, there may be more than one answer.

So when you've got one, don't stop there.

See if you can find a different one.

Pause the video.

Very best of luck with that.

I'll see you soon for some feedback.

Welcome back.

How did you get on? Let's have a look, let's give you some answers.

So this is the Oak Netball team results and we are finding different ways to complete the data so that the netball team has.

So number one, a mean average number of goals per match, that is between 4 and 5.

Well, the total number of goals or total of the set of data must be between 36 and 45 to give a mean average of between 4 and 5.

So the missing data must total between 6 and 9.

So lots of possibilities there.

Number two, a mean average number of goals per match that is less than 3.

So for the mean average to fall to less than 3, the total number of goals scored over the nine matches must be less than 27.

This is actually not possible as the seven matches with scores have a total number of goals of 31.

So well done, if you said that's not possible.

Well done if you figured that one out.

Number three, a mean average goal difference that is greater than 1.

So the goal difference for the seven matches with results is 9.

So it needs to be above 9 for the mean average difference to be greater than 1 with the other match scores.

The team could have had two winning matches with any score for the mean average to remain greater than 1.

If the team didn't win both the matches, they could have won one match by one goal and had a draw.

So for example, the scores could have been 3:2 and 1:1.

Which possibilities did you come up with? Number four, a mean average goal difference that is less than 1.

So the goal difference for the seven matches with the results is 9.

So it needs to be below 9.

For the mean average difference to be less than 1, the team must have a negative goal difference across the missing data of 1 or more.

So they must either have lost both matches or have lost one by one goal and drawn the other one.

So again, some different possibilities there.

Well done if you came up with more than 1.

We've come to the end of the lesson.

It's been my favourite kind of math lesson today, one where we've had to do lots of thinking and lots of persevering, so well done if you did that.

Today, we've been explaining how to use the mean to make comparisons between two sets of data.

And in today's example, we've been comparing the Oak Football team with the Oak Netball team.

You can use the mean average of sets of data to make comparisons, but you must make sure that you are comparing similar data.

Small changes to data can make a big difference when making comparisons.

And you've seen some examples of that today.

You need to think carefully about what you are comparing.

E.

g.

, the goal difference was perhaps a more accurate way of comparing different sports than the number of goals scored just because football and netball are so different.

Very well done on your accomplishments and your achievements today.

I hope you've enjoyed the lesson as much as I've enjoyed teaching it.

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

Take care, and goodbye.