Lesson video

Hello, and welcome to this lesson on drawing Venn diagrams. For today's lesson It would probably help if you do get a pencil and a physical paper and pen, or something that you can write on and with.

Should you need to pause the video at any time during this lesson, then please do so, as this could come across as a very new concept, so, if you need to rewind the video, pause the video, anything for your convenience, feel free to do so.

It would help if you put your phone on silent to avoid distraction or noise, and if you can get into a space with less noise as well.

When I tell you to pause the video and attempt a task, it would be for your own good if you actually do that.

Because you can check, before you get to the independent task, whether or not you understood the concept I have just taught.

So now, pause the video should you need to get into a space with less noise, or if you need to go get your equipment and press resume when you're ready to begin the lesson.

Okay.

Let's think about our try this task, looking at the Venn diagram on your screen, what is different about this type of Venn diagram, and the Venn diagram that we've been looking at in the previous lessons? So, pause the video and think about that question.

Once you've thought about it, can you then find the probability of B.

Pause the video, answer those, and then press resume to proceed with the lesson.

So, hopefully you found out.

Hopefully you found out B by adding 0.

2 and 0.

4 and then adding 0.

6 all together we got 0.

9.

We know that probability must always be equal to one or a hundred percent.

So, as a decimal it must be equal to one.

If we subtract 0.

9 from one, we are left with 0.

1.

So, the probability of B is 0.

1.

So, what's different is, we're filling in the information.

Usually when we did Venn diagram before, we had to either draw in our Venn diagram and fill in our Venn diagram from scratch.

Usually they wouldn't just leave a space for us to fill.

Also this is decimal, and usually we've been working with either elements from a list or fractions.

Okay.

Let's think about this question then.

We are wanting to fill in a Venn diagram.

A group of friends have been surveyed.

38% have been to the UK.

80% have been to Norway, 11% have been to neither the UK or Norway, find the percentage of the group that have been to the UK and Norway.

Let us start by drawing our base or rather our outline for our Venn diagram.

So, this set here would represent the UK, and this set here would represent Norway.

38% have been to the UK.

Well, that doesn't really tell me much 'cause, I could write 38% here, or I could write something like 30% here and 8% here.

I don't really know.

So whatever I write, I would really be guessing.

Let's draw that back.

I would really be guessing.

So, what information can I use, to help me to fill in this Venn diagram? Well, I'm going to look for information that tells me something about both.

Now, since 11% have been to neither the UK or Norway, so that means 11% is here.

Okay? So, now I'm working from the outside-in.

So, 11% not been to the UK, our whole probability, our whole percentage is a hundred, so, if I've got 100% percent and I'm taking away from that 11%, that have never been to either the UK or Norway, I am left with 89%.

So, now I know that my UK and Norway, the total data must be 89%.

Well, how much do I currently have? I've got 38% for the UK, and then, adding that to 80% for Norway.

I have 118%.

That is a lot more than 89%.

So, that tells me that, if I subtract 118%.

if I subtract 89% from 118%, that would give me the middle section.

That would give me my intersect here.

Because, I know that this full thing, all of the UK is 38% and all of Norway is 8%.

However, I have this extra, if I do 118 takeaway 89, it is 29%.

So I have this extra 29%.

So, therefore, it must be for the overlap here.

So, if the overlap is 29%, so, 29%, have been to both the UK and Norway, what number, what percentage would I write here? Is going to be 9%.

Isn't it? Because this whole region must be equal to 38% and 29 plus nine is 38%.

What of for this region here, I've got 29%.

The whole of Norway region was equal to 8%.

So, this region here must be? 51%.

Because, 51 plus 29 is 80%.

So, find the percentage of the group that've been to the UK and Norway, that is 29%.

So, where we have information like this, and we're told to draw a Venn diagram, we usually work from the outside-in, information we know for both, and we use that to fill in the other regions.

Let's try this one.

People were asked the newspaper that they read.

40 people read the Metro, 30 people read the Guardian, 25 people read the Independent 15 people read both the Metro and the Guardian, 12 people read Metro and the Independent 10 people read the Guardian and the Independent, and four people read all three newspapers.

So, if I draw my outline for my Venn diagram, because I've got three different sets, I would have three circles.

I'm going to label this Metro, Guardian and the Independent.

If I start from my first line, 40 people read Metro.

Again, that doesn't really give me information about specifics.

So, even if I write 35 here, one there, one there, and then I write three here.

Again, I'm just guessing.

I don't really know.

So, I need to start with information that I do know, and then work my way out.

What information would provide me with a good base to start from? Let's start from the bottom.

Four people read all three newspapers.

That's a good place to start.

I could put that in this region here, cause this region here counts for all Metro, Guardian and the Independent.

So, four people read all three newspapers.

Okay.

Now let's go to the 10.

Let's go to this information.

10 people read the Guardian and the Independent.

So, if I just changed the colour of my pen to green, 10 people read the Guardian and the Independent.

So, that means this region here, must be equal to 10.

Because, this is the guardian, and this is the independent, but I've got four here already, so, this must be six.

What of if I say, 12 people read Metro and the Independent? So, Metro and the Independent is here for 12, so, if I take this whole region, must be equal to 12.

So, this would be? It would be eight.

Wouldn't it? Cause eight plus four is 12.

I think we're doing well so far.

Let's go to 15.

15 people read the Metro and the Guardian.

So again, this whole region, this is the intersection for the Metro and the Guardian, but this whole region.

Cause I already have a four in that region, this whole thing must be equal to 15, so this would be 11.

Right? Now, 25 people read the independent, 25 people read the Independent.

So, I've got six, four, eight, and this number must add up together to give me 25.

So what must this number be? Seven.

Okay? Now, 30 people read the Guardian.

30 people read the Guardian.

This whole region here, must be equal to 30.

So, I've got 10 and I've got 11 that's 21.

So therefore this must be nine.

And 40 people read the Metro.

So I've got 15 add eight, that's 23.

And, just so I don't make a mistake, that is 17 over here.

And this is how we draw a Venn diagram to represent this information.

Okay.

Let's ask some questions with our Venn diagram.

How many people read at least one newspaper? How many people read at least one newspaper? So, essentially we're asking for the probability of the number of people that read the newspaper.

So, it's going to be M union G union I.

So, essentially we're adding all of it together.

And I think if you add everything together, you get 62 people.

Second question.

How many people read only Guardian? So that means the probability of G, and, not M and not I.

So, not the Metro, not the Independent, and that is only nine people read just the Guardian.

Only.

That's the keyword here, only Guardian.

The last one, we want the number of people that read exactly one newspaper.

So, that means we're in this region, 17 people only read the Metro, nine people only read the Guardian and seven people only read the independent.

So, how many people read exactly one newspaper? Well, it's going to be 17 plus nine plus seven, and that is 33.

It is now your turn.

An exam has two sections, theory and practical.

And then it proceeds to give you some more information.

Pause the video now and attempt to represent the information on your screen on a Venn diagram.

Pause the video, and then resume after you've had a go at the task.

Okay.

Hopefully you had a go at that.

It says, everyone in a class who took the exam, passed at least one section.

I know that the total amount of percentage, the total percentage in my Venn diagram, should be a 100%.

So, I'm going to add 64 and 82 together.

64% plus 82%, well, that gives me 146%.

So, I should have a 100% in my Venn diagram, but I have 146%.

So I am going to subtract a hundred percent from 146%, and I am left with 46%.

This four to 46% that I have excess, where should that go in my Venn diagram? It should go in the middle, shouldn't it? It should go in the overlap cause it represents, people that have passed at least one section.

So, it represent people that pass the theory and people that pass the practical.

That just say 46 not 64.

So, let's do that again.

46%.

Right.

If the theory we want 64% all through, what should be in this region over there? Well, we'll go into subtract, aren't we? So, over here I would have 18%.

And for the practical, if the total region for the practical is 82%, and I already have 46%, what should be in my region here? Again, we subtract.

So, it's going to be 36%.

Okay.

It is now time for your independent task.

So, pause the video and attempt all the questions on your worksheet.

So, pause your screen now, and attempt all the questions on your worksheet, and then return, and we can go through the answers together.

Okay.

How did you get on with your task? For your ease, I've drawn my Venn diagram, and I hope you're checking to see if yours is like that.

When I drew this Venn diagram, I realised that I wasn't given the data for students who only like hippos.

So, I had to add all my values together and subtractive it from 80, which was the total number of students I asked.

And then it was 26.

So, check in yours.

For the next one, these ticks were just me ticking off when I was doing it.

So, again, I wasn't given the information for students who only liked tennis.

So, I had to add all my information together and took it away from a hundred, which gave me 10.

So, remember that we start with the intersection, we start with the information that.

With the section, with the region, with the most information.

So, it was six students liked all three sports.

So, I started with six here, and then I worked my way out for each one.

Lastly, again, I started with the one that gave me the most information, which is seven played neither instruments.

So, I put my seven here, I took it away from my total, which is 27, I added my two information that I know 17 and 15, that gave me 32 Which is more than what the information in my Venn diagram, the total information in my Venn diagram should add up to.

So, I took it away from.

I took 27 away from 32, that's the five in the middle, and then I use that five to fill in my region for C and for F.

Okay.

You may be looking at your explore tiles thinking, why is it so long? It is not long.

Take a moment to read the sentences, and also the numbers, numbers one to eight.

And then based on this information, you have on your screen, you are to represent this information on a Venn diagram.

So, think about it, think about what we did in today's lesson.

Going and starting with the region with the most information and then working your way out.

So, start that, and then I would put an answer up for you to see.

Pause the video, complete your explore task, and then resume the lesson, and I will put a possible solution up for you to see.

I wonder how you got on with yours, this is a solution for populated event diagram, using the information you were given on the previous slide.

Okay? We've now come to the end of this lesson, I hope you're able to take something away from how we fill in a Venn diagram.

Venn diagrams are really useful when you're representing information visually, as you saw in the lesson.

And before you go, do complete the quiz just to consolidate your learning from today's lesson, and I will see you at the next lesson.

Goodbye.