Lesson video

Hello everyone is Mr. Miller here, in this lesson we're going to be be finding the median from the frequency table.

So, first of all I hope that you're doing well, and just to start off with the data handling cycle again, the last couple of lessons, we have been looking at how we represent the data.

So we start off by looking at what a frequency table was.

And then last lesson we looked at finding the mean from a frequency table.

This lesson listen we're going to continue with frequency tables.

This time we going to be finding the median.

So without further ado, let's check out the Travis slide.

Okay, Yasmine asks 15 students in her year, how many siblings they have? Here are her result.

How would you find the median? Now there's a number of ways that you could do this, One thing that you could do is you could list out all the data.

So what that means is you can see that there were three people with zero siblings.

So you can write that out as zero, zero, and zero, and then you can keep on going, you can see that six you will have one sibling, et cetera.

And then you could find the median from that list.

So feel free to pause the video now for a couple of minutes, to try to find the median either by using this method, the listing methods or another method.

Pause the video now.

Great.

So I hope that you have had a go at working out the median.

Let's keep on going with this method and then we'll talk through another way we can do this.

So six people have one sibling, one, two, three, four, five, six.

Three, people have two, two, two one, three, and two people with five minutes.

And then because the data is in size order I don't to worry about putting it in size order it's there already.

I can take the smallest and the biggest off, and then keep on going until I find my middle number.

So I'll get there eventually, as long as I'm careful, this is fine.

And there we go, there is my middle number, so my medium is a one.

So you could do it that way, but what happens if there were a lot more than 15 students, what happens if they were 60 or 80 pieces of data? Well,doing this method would not work very well.

It would take a very long time to list out all the data.

So there must be a quicker way to work this out.

Can you think of a quicker way to work this out? Okay.

Well, first of all, you know that there are 15 pieces of data, so you need to try to find the piece of data that is in the middle.

Now, you know that if there are 15 pieces of data, you're going to have seven pieces of data that are below the median and then the median, and then seven pieces of data which are above the media, seven plus one, plus seven gives me 15 pieces of data.

Therefore in what position is this median a piece of data? Well, it's an eighth position.

So, knowing that I'm looking for the number in the eighth position, I can quite easily find this from my frequency table, simply by counting the number of tallies until I get the eighth piece of data.

So, one, two, three, four, five, six, seven, my eighth piece of data is still in that one.

So, another way I could look at it is if I complete the frequency column, So three, six, three, one, zero and two.

I know I'm looking for my eight piece of data, So is it in this first row here.

Well, no, because I've only got three pieces of data in it.

What about this second one here? Well, three plus six is going to give me nine, So there are nine pieces of data within those first two rows.

So my eighth piece of data is definitely going to lie in there as well.

So I can use the frequency table, if I know what position the median is in to work out the median really easily.

Let's have a look at a few more examples.

Okay, this time two students are discussing how to find the median from this frequency table.

The first student is saying, "Since there are eight pieces of data in total, the median is the fourth, which is two." The other student is saying, "No you don't take the fourth piece of data." So who do you agree with? Feel free to pause the video for a minute or two, have a think, which of these students do you agree with? Okay, great let's go through this, First of all, I'm just going to write up all the pieces of data so I can explain this really clear.

So I've got one piece of data, which is zero is two piece of data which are one, one, two, two threes, and two fourths.

And now I can cross off the data, the smallest and the biggest.

And now I need to pause because I noticed that I've got two pieces of data here because I've got an even number of starting piece of data.

I can't cross them both off, so what do I do? Well, I take the average of that two and the three.

So the median is not going to be two, it's going to be 2.

5, but why is that the case? Why do I take, why is it not the fourth piece of data? Well, if there are an even amount of data, I need to split the data into two.

So four pieces of data and four pieces of data.

And the median, this one here is going to be between the fourth piece of data and the fifth piece of data.

So I need to be careful sometimes when I'm, I have an even amount of data, sometimes the median is going to be a decimal because it lies between two different pieces of data.

So the median here is going to be 2.

5 because I'm looking between the fourth and the fifth piece of data.

Okay, let's go on to the next slide.

All right, so two different independent tasks for you to do, here's the first one, I got three frequency tables, and I want you to tell me which of these frequency tables has the same mode and median? So you used to work out for both of these.

What's the mode? what's the median? And is it the same.

Pause the video for a couple of minutes and let's see where you get to.

Great.

okay.

So let's go through this and I need to, of these cases it's really easy to find out what the mode is.

So the first one, the mode is going to be two 'cause are 50 pieces of data which are two.

The next one, the mode is going to be zero.

And the final one, there are actually two modes here, One and two.

Let's have a look at the median.

Well, the first one we could count up the number of pieces of data that we've got, two plus three plus 50 plus, plus four it's going to give me 59.

So I could find out that I'm looking for the 30th piece of data.

But do I really need to know exactly what piece of data I'm looking for? Or can I tell what the median is going to be from this table? Well, it's sort of obvious, isn't it? That the median is going to lie in this category here because I don't have that many pieces of data below that category.

And I don't have that many pieces of data above that category.

So the middle piece of data is certainly going to lie in the two as well.

What about for the middle? Well, let's count up the number of pieces of data I have.

So if I added up the frequencies 20 plus 15 plus 10, plus five, that's going to give me 50 pieces of data.

So I know I'm looking around the 25th, the 26th, is it going to be in the first one? No, because that's only 20, but what about the second one here? Yes.

My median is going to to lie in the second row, one bottle because again, I'm looking at the 25th and 26th,this is the data, and it's definitely going to lie in this one here.

What about the final one? Can you see very easily what the median is going to be here? Well, because I know that the median is the middle number, I can see that if I took, if I went between the one and the two, I have the same number of pieces of data above and below that in between level, So the median is going to be 1.

5.

So only in the first frequency table is the mode and the median the same and in the other two, it's different.

So what this tells us is that sometimes I need to be pretty careful when I'm working out the median, but other times I can look at the data and I can realise quite quickly what the median is going to be.

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

Okay Leela asked a sample of her year group how tall they are, here are the results.

Put the following data into a frequency table and find the mode and median.

Great pause the video here, copy down this frequency table, put the data into it and find out the mode and the median let's go through this together, You should have had three pieces of data which were at 140 four piece of data which were 145.

And then two pieces of data which are 50 piece of data, and one piece of data which is 155 What's the mode? Well, the one with the highest frequency is 145.

And what's the median? Well, I could list them out as I did before, there's not that many pieces of data, so it might be worth it, but there are 10 pieces of the data.

So I'm looking at between the fifth and the sixth piece of data.

And I can see quite straightforwardly that is going to to lie again in the 145 centimetre category.

So let's move on now to the explore task when you're ready.

Okay, so here is the explore task, Antoni has collected the shoe sizes of his class but he's lost some of his results.

He's lost four pieces of data.

So we're going to need to find four missing piece of data.

Here are of the results that he's got so far, it does know that with all the different included his mode is 4.

5, his media is five, and the highest is six.

Fill out what you can on the table already and find out what the missing four pieces of data are.

So again, I want you to copy down this table, fill out the results that we know so far, put them into the table and then see if we can work out the four missing pieces of data.

Pause the video for a couple of minutes to explore this task.

Okay, let's go through this then.

So first of all, I'll fill out my table.

So I got a 5.

5, five, 4.

5, another 4.

5 another five, four, another 5.

5, four, 3.

5, And finally another 5.

5.

I hope that you got that far that's nice and straightforward.

Now let's have a think about what else I need to have here.

So, first of all, I'm told that my highest shoe size is 6.

0.

I don't have a 6.

0 already, so I'm going to to need to make another category, and I know that I'm going to have at least one person with at 6.

0, So that's the first thing that I know.

Next I know that the mode is 4.

5, So what do I need to do here? Well, at the moment only two people have a shoe size of 4.

5 and three people have issue size of 5.

0 and 5.

5, so I need at least two more people that have a shoe size of 4.

5, so that it's the mode.

So I've dealt with that, And now finally, I need time to look at where my final missing piece of data is going to go by investigating the media.

Okay, so first of all, let's count out at the number of pieces of data that I have already, So I've got one, two, three, four, five, six, seven, eight, nine, 10, 12, 13, 14 piece of data.

And with one more piece of data, I'm going to have 15 pieces of data.

So I know that if I've got 15 pieces of data, I'm going to have seven below the median, and then the medium is going to be eight piece of data and then seven above the medium.

And I know that my eight piece of data is going to be 5.

0, let's see what the eighth piece of data is already.

So if I count up, I've got one, two, three, four, five, six, seven, and eight.

So my eight piece of data is 5.

0 already.

What does that mean? Well, what tells me is that if my final piece of data is below 5.

0, then the median is going to be pulled down to a 4.

5.

'Cause I have eight pieces of data, which are 4.

5 or lower.

So my median has to be 5.

0 or higher.

So what does that have to be? Well, if it's 5.

0 or 5.

5, then we will have four pieces of data for those, so that will be the mode along with 4.

5.

So it can't be 5.

0 or 5.

5.

So I therefore know it has to be another 6.

0 and you can check it out, you can check that the mode is still 4.

5.

The median is 5.

0 and the highest is still 6.

0 So hopefully that was a fun one to investigate, and I hope that you got somewhere with that.

Thanks very much for watching the video.

That is it stay for today And next time is going to be our final lesson for this unit, Where we're going to to be looking at bar charts to finish things off.

Thanks very much for watching yes again, hope you have a great day, take care and bye.