Lesson video

Hello, everyone, it's Mr. Millar here.

In this lesson, we're going to be looking at finding the mean from a frequency table.

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

And let's start the lesson again by having a look at the data handling cycle.

last lesson, we looked at representing our data in a frequency table, which was useful because we could easily find the mode and the range.

And also useful because we could easily find the total from that table.

In this lesson, we're going to find the mean from a frequency table, which is something that is really, really important.

So let's go ahead and check out how we do that.

Okay, so Cala asks 25 students in her year, how many bottles of water they drank yesterday.

Here are her results in a frequency table.

Find the mean? Great, So this is actually the same table that we had look at the last lesson and Cala is saying I can find the total number of bottles drunk first This is actually something that we did last time around.

So go ahead, pause the video and do this, I've given you a third column to help you do this.

So pause the video and find the total number of those drunk first, and then see if you can use that to find the mean.

Great, so I hope that you had a go at doing this.

And what you should have done is done one times by nine, two times by six, three times by four.

And then the rest of the table that is straightforward.

So that's the first step.

How do we find the total number of bottles drunk? Well, we are going to need to add up all of these numbers.

And if we do that, we get 43.

So that is the total number of bottles drunk.

How do we find the mean? Well, to find the mean, we know that we have to do the total divided by the number of pieces of data.

How do we get the number of pieces of data? Well, we're actually told that there are 25 students, so we know that it's 25.

And we can check that by summing up all of these numbers in the frequency column.

And that also is 25.

So how do we find the mean? 43 divided by 25.

Put that in a calculator, and you get 1.

72.

So it turns out that we can use a frequency table to really easily find the mean, by doing these steps like this.

I'd recommend that you pause the video to make sure that this is down in your notes if it isn't already.

It's going to be useful when we look at further examples.

So pause the video and get this down into your notes.

Okay, the Connect task.

Two students are discussing how to find the mean number of books read.

How does Cala know that Binh must be wrong.

So below that is the frequency table Binh is saying I can add up the frequencies and divide by five.

So the mean is 57 divided by five equals 11.

4.

So, just to be clear, this 57 is the sum of all the frequencies.

And Carla's saying 11.

4 can't possibly be the mean.

So, what do you think? How does Cala know that Binh must be wrong? What mistake Has she made? And how would you do this correctly? Pause the video for a couple of minutes to have a think about this one.

Okay, great, so this is a really common misconception that I actually see a lot of students make all the time.

So what's happened here is we've added up all the frequencies 57.

And then divided by the number of rows there are.

So I can see there's one, two, three, four, five rows in this table, and you'll get 11.

4.

But 11.

4 can't possibly be the mean, why not? Well, if I look at the number of books read, the maximum number of books read is four, 12, people have read four books.

So the average number of books that someone's read can't possibly be 11.

4.

Because that is a lot higher than four.

The mean is going to have to be somewhere between zero and four, probably around two because that looks like around the middle of my data.

So make sure that you don't make this mistake.

You're going to have to do something different to find the mean.

So in case you haven't done it already, what you need to do is do a new column.

I call that the number of books times by the frequency.

And I do zero times by 10.

One times by 11, two times by 13, three times by 11.

and four times by 12.

Then what do I do? I need to add up all of these numbers, and I get a 118.

And now to find the mean, I do 118 divided by 57 and I get a nasty decimal 2.

07.

You needed a calculator to do that.

Anyway, 2.

07, does that sound like a reasonable answer? Well, yes, it does.

'Cause if you look at the data, it looks as if the mean is around two.

So, this raises the really important point that when you get an answer, like 11.

4, you should always look at your original data in the table to check, does this actually make sense? If it doesn't make sense, then you probably made a mistake somewhere.

So you need to go back and check.

Alright, let's now move on to the independent task.

We've done a couple of examples now.

So you should be able to feel comfortable finding the mean yourself.

Great, so here are two frequency tables.

Use the third column to help you find the mean.

I picked some numbers here where you don't actually need a calculator.

So you should be fine without one.

So pause the video now, copy down both of these tables into your notes and find the mean in both cases.

Okay, great, well done for doing that.

And here are the answers you should have got.

So third column.

We'll just do that.

And I think quickly.

Actually, I've give out the answers already.

So I'll show you.

So this is what the third column should have look like.

And then what do we do next? Well, we need to add up all of these numbers here, to get 30.

Add up all of the frequency here to get 15.

So the mean, of the first one is 30 divided by 15, which is two.

And then the next one, I add up all of these numbers, and I get 585.

Add up all the frequency to get 10.

And in the mean 585 divided by 10 gives me 58.

5.

And let's just check in both of these cases, does my mean actually makes sense? Well, yes, I think it does.

I think this makes sense in both cases, so I'm happy with my answer.

Okay, great, make sure that you're really comfortable with this.

This is a really important skill.

Really important, you know how to do this.

So when you feel ready, let's move on to the Explore task.

Okay, so let's read through this together.

Anthony has recorded the number of books that 20 students in his class have read, but one of his numbers got smudged! So that is this number down here.

He knows that the mean is six, can you help him find the missing number? Okay, so what are we going to do here? First of all, we're not just going to guess this number, we're not going to guess is a five or guess is the six.

We're going to do this in a logical manner.

And a good place to start, I think, would be to complete what you can of this column.

So zero times by one equals zero.

Start from there complete what you can you're also going to have to use the fact that we know the mean is six, we going to have to use that.

Anyway, see how far you can get.

This is a nice problem, a tricky one.

So pause the video for a few minutes to copy down the table.

See how far you can get with the problem, and then we'll go through it together.

Okay, great, so let's go through this together, I can complete the rest of the table as much as I can.

So four times by five is 20.

I can't complete the next row.

It's going to be something times by five is something but I don't know what that number is.

And got eight times by four which is 32 and nine times by three, which is 27.

Great, Okay, what's next? Well, I now need to use the fact that I know that the mean is six.

I know the mean is six.

And I also know that my total frequency, the total number of students is 20.

How does that help? Well, if I know the mean, and I know the frequency, I know what the total number of books that have been read is this number here.

That is going to be 20 times by six, which is 120.

So I know that the sum of all of these numbers here is going to be 120.

Okay, what's next? Well, I can add up all the numbers that I know already.

They sum up to 85.

So the missing number here is going to be 120 minus 85, which is 35.

Then my final step is, what does my missing number here have to be? Well, obviously, it has to be a seven, because seven times by five is 35.

So I know my missing number.

Great, well done for having a go at this problem.

I hope that you enjoyed it.

Thanks very much for watching this lesson.

Next time we're going to be looking at finding the median from a frequency table.

So thanks very much for watching.

See you next time.

Have a great day, bye bye.