Lesson video

Hello everyone.

This is Mr. Millar here.

In this lesson, we're going to be looking at finding the median, mode, and range.

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

And let's have a look at this data handling cycle again.

And just as we were in the last couple of lessons, when we were looking at the mean we are staying on step three, we are processing, we are analysing the data.

This time we're going to be looking at the median, mode, and range.

Lots to do today, so let's go ahead and start.

Okay, first of all, the mode.

The mode is the piece of data that appears most often in a data set.

It is a type of average.

Three data sets for you to have a look at, what do you think is the mode in each one of them? Let's look at the first one first of all.

What do you think is the piece of data that appears the most often? Well, clearly this is going to be four.

Because I can see four, three times, but that is more than any of the other pieces of data, 'cause I can see three twice and I can see 10 and one, once each.

So four appears the most.

So the mode is four.

What about the next one? Well, in this case, all the data appears only once.

If this happens, we say that there is no mode.

All the data appears only once, no mode.

What about the next one? Well, you can see that blue appears twice and so does orange.

And if this happens, we say that there are two modes, blue and orange.

Okay, and maybe what you pausing there now to copy down the definition for mode and these examples.

So pause video now, really important that you understand this.

Pause the video and let's move on when you've done that.

Next one, median.

The median is the middle number in a list of ordered numbers.

It's another type of average.

So the mode is a type of average, the median is a type of average and so is the mean which we've looked at already.

Let's see how we do this.

So one, three, three, five, six, 11, and 13, we are looking for the middle number.

Now, you should spot that it is five and you can also have a look at this by saying, I'm going to cross off the smallest and the biggest, the next smallest and the next biggest.

I keep on going until I have found my middle number.

So the median in this case is five.

What happens though if let's say I add another number? Let's say that I add 15 here.

What do you think the middle number becomes now? Let's see what happens.

I'm going to cross out the smallest and the biggest, and I'm going to keep on going.

And now I'm left with two numbers, the five and the six.

And I'm not going to cross them off because if I did that, I would have crossed off all the numbers.

So we need to look at the five and the six.

Now to decide what my median is, I need to look at what number lies in the middle of five and six.

So what I do is I take at the mean of both these numbers, and I would find that 5.

5 lies in the middle of five and six.

So when I have an even amount of data, I'm going to have to look at the middle two numbers and take the average, take the mean of those two numbers.

Okay, pause the video to copy down this example.

Make sure you got the definition as well and then we'll move on.

Finally, the range is the difference between the largest and the smallest value.

Now, the range is a measure of the spread of the data.

So how much has the data spread out? It's not a measure of the average, like the mean, the mode, and the median, it's a measure of the spread.

What do you think the range is of this data here? You're looking for the largest and you're looking for the smallest.

Well, the largest number I can see here is nine.

The smallest number I can see is two.

So the range is going to be nine minus two equals seven.

That's what it is nice and straightforward.

Again for the final time, pause the video, get this definition down and get the example down and before we do that, let's do that before we move on.

Great.

Let's move on now.

Okay, the connect task, we are looking at the median.

So here I've got a set of data and one of the students is saying, "The median is five because that's the middle number." And the other one says, "No, you have to be careful, it's actually three." Who do you think is correct here? Well, you might be tempted to say that the first person is correct, because you can see five in the middle here.

But do you remember when we talked about the median and you might have written down the definition, the median is the middle number if the numbers are ordered.

Are these numbers in order from smallest to biggest? No, they're not.

We need to do that before we work out the median.

So starting off with the smallest one, two, another two, three, another three, five, and seven.

Now these are in order.

Now I can work out the median.

Cross off smallest than the biggest and I have the median of three.

So the second student is correct because the first student didn't organise the numbers in size order before he went ahead and took the middle one.

Okay, let's move on.

Time for some independent work.

Great.

So here are three sets of numbers, for each of these, you need to find the mean, which you've done already and in the mode, the median, and the range, which you've had to look at in this lesson.

So copy down the table.

This should take about six or seven minutes to work out all of these.

So pause the video now and have a go at this task.

Great.

So hopefully you had to go at all of these and let's go through them.

Let's do the mean first.

So sum up all the numbers.

And the first one is 30 divided by five numbers equals six.

Next one, what do I got? I've got 10, 11, 16, 17, 18, 18 divided by five, 3.

6.

Next one, some of all the numbers and they get nine, and you need to divide by six here to get 1.

5.

Some people might make the mistake that I don't need to include these zeros in my total amount of numbers.

That will be an error because you do need to include those zeros.

They are pieces of data.

So the mean for that one is 1.

5.

What about the mode? The first one is five.

No mode for the next one.

And the final one, two modes, zero and three.

They each appear three times.

Median, first one is five because they are in size order.

The next one I'm going to order them in size order before I do it.

Really important that you do that.

Median is three.

Next one, well, I'm going to cross off the smallest and the biggest, and I get these two in the middle, zero and three.

I take the number in between those and I get 1.

5.

Range, biggest minus smallest, six for the first one, six for the next one, and the final one is equal to three.

Great.

Make sure that you've got all of these fully corrected if you need to in your notes before we move on to the explore task.

Okay.

Here's explore task.

Here are five cards.

I know that there's a one on one of the cards, but the other four, I need to find out.

Can you complete the cards in different ways to get a median of four, a range of four, a mode of four, a mean of three, a median of four, a range of four, and a mode of four.

Okay.

Pause the video.

See if you can do this.

It should take about five or six minutes.

Have a go and we'll review once you've done it.

I think so, you had a good go, let's go through it.

So the first one, the median of four you just need to make sure that you have a four in the middle of that.

Then the other number, well, let's put a two here.

Put a five here, put a 10 here.

Just make sure that these two numbers are bigger than a four and this number is smaller than a four, bigger than a one.

Okay.

That's nice and easy.

Let's do the next one.

A range of four.

Well, if the smallest number is one, then the biggest number has to be five, and then the other ones can just be between one and five.

And you're fine.

There are many other possibilities that you could have here, so you could even have a zero as one of the numbers, but then you need to change the biggest one to be a four, to keep the range four.

Nice and straightforward for the range.

The mode of four, again, really straightforward.

You just need to make sure that four is the number that comes up the most times.

So if you have this, that's fine.

The mode is clearly four.

Last one is a bit of a tricky one.

So first of all, a median of four.

Let's put that in the middle.

A range of four.

So five will have to be the biggest one.

A mode of four.

So we're going to have to have another four here.

Let's put it back.

Now, the mean of three.

What does this mean? Well, if there are five numbers and the mean is three, what does the total have to be? Well, the total has to be five times by three, which is 15.

The numbers must sum up to 15.

What are the existing numbers sum up to? One plus four plus four plus five.

That equals 14.

So what's my final number have to be? Well, it needs to sum up to 15 in total, so the final number has to be a one.

Does this work? Well, this actually doesn't work.

Do you see why? If I include a one, then my mode now becomes not four but one and four.

So this final one is actually impossible.

It's kind of a trick question.

There's no way that you can get numbers to make all four of these conditions true.

So a bit of a nasty one, but there you go.

Great.

Hope you've enjoyed this lesson.

That is it for today.

Next time we're going to be looking again at these things, we're going to be considering which one is the best to use in different circumstances.

Thanks very much for watching.

Hope you enjoyed it.

See you next time.

Bye, bye.