Lesson video

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Hello everyone, it's Mr. Millar here, and in this lesson we're going to be representing bi-variate data.

So, first of all, I hope that you're all doing well, in this lesson we're going to be looking at how we represent bi-variate data by looking at scatter graphs.

And before we have a look at any scatter graphs, here is the try this task.

So are the following statements true or false? You need to look at the table on the left hand side, which has age of cars in years is in one column and price of the car in thousands of pounds in the other column.

And you have got seven statements to decide if they are true or false.

Pause the video now for four or five minutes, see how you get on.

Okay, great, so let's have a look at these statements and go through them very quickly.

So the first one at the table gives information on 20 different cars, well, this is false because each row of course represents a different car.

So the first car is one year old and costs 6,000 pounds and in total there are 10 rows, so 10 different cars.

Next one, the modal price of a car is 5,000.

What we can see that we've got one, two, three fives here, which is the most number of fives so that is true.

The range of ages of the cars is 10 years, well, this one is false, because the oldest car is eight years, and the youngest or the youngest car is zero years so the range is going to be eight.

The brand new car costs 6,000 pounds more than the car, which is four years old.

While, the brand new car is the one that is zero years old, so that is 10,000 pounds.

The one wishes four years old is 4,000.

So this one in the middle is true.

The cars, which costs 4,000 pounds are the same age, well, no, one of them is four years old, the other one is five years old, so that is false.

The two threes in the table have the same meaning.

Well, this was false as well.

Because one of the threes means three years old, the other three means at 3000 pounds.

So they mean different things.

And the final one, the value of the car decreases as the age increases.

Well, this is an interesting one and this is what we're going to be coming back to.

But if you said true, then I would agree with you because overall, if we have a look at the, the cars, which are for younger, they tend to have a higher value than the cars, which are older.

But of course this isn't true for every single car, but in general, this seems to be the case.

And this is, the key idea of for today's lesson, which is that if we have bi-variate data, we can use a scatter graph to look at the relationship between the two variables a lot more easily.

Let's have a look at the next slide.

Okay.

So here was the connect slides and it says that representing binary data on a scatter graph can help us see connections more easily.

So again, we have got a data table showing the age of car and the price of the car.

And on the right hand side, we have got a scatter graph, which is showing that same data.

And first of all, we can really easily understand what the scatter graph is showing.

So we have got the age of Carl on the X axis and the price on the Y axis.

So if, for example, we were looking at this point here, the one I've circled, we can see that the car, which is a six years old, has got a price of 4,000 pounds.

So it's really easy to, to read off the graph, to read values off the graph.

Now, the scatter graph is really interesting because it really clearly shows us a relationship between the two variables.

So have a think, how would you complete this sentence here to describe the relationship between the age of the car and the price? Well, if you're thinking something like the scatter graph shows that as the age of the car increases, the price decreases then really well done, because you can see that as the age of the car increases, the price tends to go down.

You could have also said the other way around.

So as the age of the car decreases the price increases, that is absolutely right as well.

But that is the key here.

We can see that there was a relationship between these two variables and that is why a scatter graph is so useful.

Now this is one other thing I want to say on the slide.

And you could have seen it already that you've got this one point out here, this, car, which is seven years old and is more expensive than the others.

And you could say, well, doesn't that mean that there isn't a relationship.

And the answer to that is if we just have one piece of data, which is outside the rest of them outside of the trend, then we can say that this is an outlier and you might've come across that expression before an outlier.

And what we say as well, yes, although this is outside of the other piece of data, we can, you know, we can ignore it or we can say it doesn't fit with the general trend.

The general trend that the age of the car increases, the price decreases is still true, despite this an outlier.

So anyway, hope that is very clear.

Now let's have a look at the independent task.

Okay.

Let's look at the independent task now.

So for this task, we've got a scatter graph showing the relationship between shoe size and height.

And you have got five different questions to answer.

Pause the video now, for five or six minutes to have it go to at these five questions.

Okay, great.

Hopefully you had a good go at these.

Let's go through them.

So first of all, explain what point A means.

Well, here is point A here and we can say, we can see that the shoe size is full and the height is 155 centimetres.

So, that means that the person with a shoe size of four is 155 centimetres.

Next one, what shoe size does the student who is 160 centimetres tall have, well, let's have a look where 160 centimetres is.

We'll go across to this point here.

And then we'll read down to a shoe size of six.

Next one, what data point is the outlier? So the outlier is the data point, which is outside the general trends.

And we can see that at this point here looks like it's outside the trends, because it's someone with quite a small shoe size who is quite tall.

What fraction of the people in the sample have a shoe size of six or more? Well, we need to look at all the people that have a shoe size of six or more.

So it would be all of these people.

That's one, two, three, four, five, six, seven, eight, so eight people out of a total of eight, nine, 10, 11, 12, 13, and 14.

So eight fourteens.

And finally write a sentence, explaining what this graph is showing.

Well, if you wrote something like in general, as the shoe size goes up, so does the height or as height increases? So does shoe size then, really well done.

That shows this scatter graph is sharp.

So anyway, I hope that you did well with these questions.

Let's have a look at the explore task definition.

Okay.

So here is the explore task.

And in this task, we have got three different scatter graphs.

And that, each of these, what I want you to do is have a think about the different, the possible connections between the two variables.

So what connection is there between age and height, between math test score and how far you can run and the number of photos taken and the battery life.

So for each of these graphs, I want you to write one or two sentences explaining each of these.

Pause the video now to give yourself time to do that.

Okay, great.

So let's go through these and for the first one, height and age, where we can clearly see that, as age increases, so does height.

Which shouldn't be surprising because we know that as you get older, you grow, you get taller.

So that is nice and straightforward.

The next one maths test score and how far you can run.

Well, we can kind of see in this one that the data is all over the place.

There's no real clear trend in the data.

And that shouldn't really surprise us because how far you run, and your test score in maths shouldn't really be related because there's going to be some people who are good at maths and can run really far.

And also some people who are good at maths, you can't get very far.

So there's no real relationship between the two of them.

You can't really make a connection.

But the final one you definitely can, because we can see that as the number of photos that you take increase your battery life decreases.

Which shouldn't be a surprise because taking photos obviously takes up battery life.

So we can expect that we have this relationship.

And in the next lesson, we're going to be taking this a little bit further, because what this comes down to is this idea of correlation.

So two variables are correlated.

There's a relationship between them.

So we're going to have a look at that in the next lesson, but as for today, that is it.

So thanks so much for watching.

Well done for completing this video, hope you enjoyed it.

See you next time, have a great rest of your day.

And bye bye.