Lesson video

Hello there, my name is Mr. Tilstone.

How are you? I hope you are having a good day and that it's been happy and successful so far.

Let's see if we can make it even happier and even more successful by having a great math lesson.

So if you're ready to begin, let's begin.

The outcome of today's lesson is this, I can explain how to calculate the mean of a set of data including a value of zero.

And you might have had some recent experience at calculating the mean of a set of data, but not with zero.

Zero can be quite tricky.

So let's explore that today.

Our keywords, if I say them will you say them back? My turn, mean average, your turn.

My turn, set of data, your turn.

What did those words mean? You might have encountered them quite recently, but it's worth a reminder.

The mean average is a single number expressing the typical value in a set of data.

It's calculated by finding the total of this set of data and dividing by how many values there are.

So add first, divide second.

A set of data is a collection of facts such as numbers, words, measurements, observations, or even just descriptions of things.

Our lesson today is split into two parts.

The first will be calculating the mean average of a set of data and the second including zero in the set of data.

Let's start by calculating the mean average of a set of data.

In this lesson, you're going to meet Laura and Lucas.

Have you met them before? Well they're here today to give us a helping hand with the maths.

Laura and Lucas want to know how much everyone in their group reads each day.

Reading is fantastic, it broadens your vocabulary, it gives you general knowledge, it develops your imagination, helps you sleep better at night.

I love reading almost as much as I love maths.

"Why are we doing this, Laura?" says Lucas.

She says, "Well, reading is important," yes it is, "and we want to get an idea if we are reading a good amount." "Let's ask everyone how many pages they read yesterday." That's a good idea.

So here we've got a table showing that data.

This is a number of pages their friends read yesterday.

So in the left hand column we've got the names, and in the right hand column, the number of pages.

Have a look at that.

See what you notice.

Sofia has got quite a low number of pages.

Alex has read a lot.

He's read 58.

So quite a difference there between them.

Lucas says, "Alex really wanted to finish his book so he read more than usual." Well, it's good, isn't it, when you get a really addictive book and you just can't wait to find out what happens next.

I'm reading one of them.

And Laura says, "Sofia was really tired so only read two pages, but she says she usually reads more." Hmm, I'm not sure one day is enough to get a good picture", says Laura.

I know what you mean because if we are saying that Sofia usually reads more, then that's not typical of how much she normally reads.

And if we're saying that Alex has read more than usual, then that's still not typical of how much he usually reads.

So what would you suggest? Have you got a good idea? What could we find out? What else could we do? Well, we could look at this over a number of days.

So Laura and Lucas ask everyone to record how much they read every day for a school week.

So you can see, look, we've got Alex there.

Monday, 58 pages, Tuesday, 10 pages, Wednesday, 25 pages, Thursday, 24 pages and Friday, 18 pages.

So each of the children has got a number of pages for each day.

"So what do we do with this set of data?" asks Lucas.

Well, Laura says, "We could work out the mean average that everyone reads each week." "We could compare that with what we've read." So let's have a look.

Can you remember what the mean average is and how it's calculated? You've had hopefully some recent experience of doing this perhaps with lower numbers than this, but the same principle applies.

To calculate the mean average, find the total value of the set of data.

So what's the set of data in this case? The set of data is a number of pages read each day and then divide it by how many values there are.

So how many values are there? Well, five days, so five.

So for Alex, the total value will be 58 plus 10 plus 25 plus 24 plus 18.

You might have added those in a different order.

You might have used written methods, mental methods or combination, but either way you get 135.

Then divide by 5 as that's a number of values in the set of data.

So it's 135 pages over five days, but then divide that by 5 will give you a mean average.

135 divided by 5, you may able to do that mentally, that's 27.

So the mean average is 27.

"Alex reads an average of 27 pages each day." Sometimes it's less, sometimes it's more.

But on average, 27 pages.

Let's have a little check.

Calculates Sofia's mean average number of pages.

And Laura says, "The mean average is calculated by finding the total of the set of data and dividing by how many values there are.

So pause the video and give that a go." How did you get on? Let's have a look.

Well, Sofia, the total other set of data will be, and you might of had your own special way of adding this, but two plus 45 plus 25 plus 18 plus 30 is equal to 120.

So that's total number of pages she read over those five days.

Now we need to divide by 5 to give a mean average for each day.

So 120 divided by 5.

Well you could do 100 divided by 5, that's 20.

And 20 divided by 5, that's 4.

Add them together, that's 24.

So Sofia reads an average of 24 pages a day.

So a little bit less than Alex.

Do you think Jacob or Sam will have higher or lower mean average number of pages? What do you think? As they all have five values in this set of data, we can think about their totals.

Jacob's total is this 5 plus 25 plus 40 plus 33 plus 22 is equal to 125." And Sams total is 24 plus 30 plus 21 plus 90 plus 36, which is equal to 130.

"125 and 130 will mean they are in between Alex and Sofia's mean averages." And you are going to find out what they are now.

So let's do some practise.

Calculate the mean average number of pages read by Jacob and Sam.

And number two, who reads the most and what's your reason for choosing them? Number three, use Lucas and Laura's information to complete the table.

So Lucas says, "My mean average number of pages is 28.

How many pages could I have read each day?" And there are lots and lots of possibilities there.

So you might want to explore more than one.

And Laura says, "My mean average is one less than Sofia." Now we know Sofia's mean average.

Laura's is one less.

"How many pages did I read on Friday?" You're going to have to do a couple of steps to get there.

Okay, if your teacher is okay with you working with somebody else, I can always recommend that because then you can share ideas with each other and help each other out.

Pause the video and away you go.

Welcome back.

How did you get on? So number one, the total of Jacob's set of data.

We add all those numbers together, 5, 25, 40, 33 and 22.

And that is equal to 125.

And there are five values.

So five days.

So you divide by five.

So 125 divided by 5 is equal to 25.

And the total of Sam set of data is 24 plus 30 plus 21 plus 19 plus 36, which is equal to 130.

And there are still five days, five values.

So you divide 130 by 5 or 100 divided by 5 is 20 and 30 divided by 5 is 6.

So there's 26.

26 for Sam.

Now you could say that Alex reads the most as his mean average is the highest and he has the highest value at 58 pages for one day.

So two different reasons to justify saying Alex there.

And number three, use Lucas and Laura's information to complete the table.

While Lucas says, "My mean average number of pages is 28, how many pages could I have read each day? So my set of data must have a total of 140 because 28 multiplied by 5 is equal to 140.

So we already know is mean average, we're multiplying it by five.

So my daily numbers must have a total of 140 pages.

So something plus something plus something plus something plus something is equal to 140.

So many possibilities here.

Here's just one of them.

You could say 28 plus 36 plus 20 plus 30 plus 26 is equal to 140.

And, "My mean average is one less than Sofia," says Laura.

"How many pages did I read on Friday?" Well, we know Sofia's mean average is 24, so Laura's must be 23.

So we're multiplying 23 by 5 to give us 115.

That's a total number of pages.

So we know the mean average, we know the Monday, Tuesday, Wednesday, and Thursday values.

We just need to find the Friday value.

"So 17 plus 41 plus 12 plus 30 is equal to 100.

So I must have read 15 pages on the Friday", 'cause that equals 115.

You're doing really, really well and you're ready for the next part of the lesson, which is those tricky zeros including zero in the set of data.

Lucas and Laura are interested to find out more.

They keep collecting data, but this time for 10 days and they include a weekend that's gonna give a really fair representation of how much they read.

I read more at the weekends personally.

Lucas says, "Alex didn't read anything on day 6 and 7." I wonder why.

"He said it was a weekend and he was busy playing football so he didn't read." Well, that's fair enough, isn't it? Lucas says, "Let's calculate his mean average for the 10 days." To calculate the mean average, find the total value of the set of data and divide it by how many values there are.

Now that's a rule, that's a generalisation that you've applied lots of times now.

Let's see how it applies this time now we've got the zeros in there.

"Can you fill in the gaps in the sentence?" To calculate the mean average, find the total value of the hmm, and divide it by how many hmm there are.

"So he only read on 8 days.

So do we divide the set of data by 8 this time?" Hmm, what do you think? Is that fair? "No," says Lucas, "you have to include all the data even if the value is zero." So it's still 10, there's still 10 days that we're considering, even though on two of those days he didn't read anything.

That's going to affect his overall mean average.

So we're still dividing by 10 even though two of them were zero.

So to calculate the mean average, find the total value of the set of data and divide it by how many values there are.

So the set of data was all of those different pages and then how many values there are.

That's how many days there are.

So that's 10.

So the total of the set of data, when you add all of those numbers together, you get 207.

So over those 10 days he read 207 pages, impressive.

"I can use my place value understanding," says Lucas, "to divide by 10." 207 divided by is equal to 20.

7.

You can't really read 20.

7 pages, can you? "His mean average is not a whole number.

So we can say he read 20 to 21 pages a day on average." Let's do a check.

Calculate the mean average number of pages that Sofia read over the 10 days.

And Lucas says, "Remember that the set of data includes all values, even those that are zero.

And you might notice there is a zero in there for Sofia.

Okay, pause the video.

To calculate the mean average.

Find the total value of the set of data and divide it by harmony values there are.

So you're adding those numbers.

That's 2, 45, 25, 18, 30, 50, 48, 0, 8 and 12 and then dividing by 10.

So when you add those together, it's 238.

She read 238 pages.

And there are 10 values, so 10 days to consider.

So 238 divided by 10 is equal to 23.

8.

So we can say 23 to 24 pages is her mean average.

Why is it important to include the zero values when you calculate the mean average? So let's have a look, so you can see Jacob's got a zero value on day six.

You can see Lucas has got two zero values, day seven and eight.

And you can see that Laura has got a zero value on day seven.

So those were days when they didn't do any reading at all.

Lucas says we have to include the zero values as we are calculating the mean average for 10 days.

If we didn't include the zero days, we would not be dividing the totals by 10.

So it wouldn't be a fair comparison.

We wouldn't be able to compare the mean averages of the children.

Let's do some final practise.

Number one, complete the table to calculate the mean averages for Jacob, Sam, Lucas, and Laura.

And you might notice some zero values in there.

Lucas says, "Remember to include the zero values as we are calculating the mean average over 10 days." So that's what we're dividing by.

Number two, Lucas wants to increase his mean average over 10 days to 25, good for you Lucas.

He still can't read at the weekend though, he is a busy boy.

He likes his football, he can't do that.

So how many pages should he plan to read in the next 10 days to do this? Hmm, that's going to take a little bit more thinking about.

So do take your time on that.

And as always, share ideas with a partner if you can.

Righty-o, pause the video and away you go.

Welcome back.

How are you getting on? How are you feeling? Are you feeling confident? Are you feeling good? Let's give you some answers and you can compare.

So to calculate the mean average, find the total value of this set of data and divide it by how many values there are.

You've done that lots and lots of times now.

So for Jacob, when you add all those together, including the zero, it gives you 210.

And 210 divided by 10 is equal to 21.

For Sam, if you add all of those values together and there is no zero this time that gives you 265.

265 divided by 10 is 26.

5.

So on average you reach 26 or 27 pages a day.

Lucas add all of those values together, including those two zeros, and that gives you 230.

230 divided by 10, gives us 23.

And Laura, if you add all of those values together, including the zero that gives us 231.

And 231 divided by 10 is equal to 23.

1.

So we can say she read on average 23 or 24 per day.

Number two, Lucas wants to increase his mean average over 10 days to 25.

He still can't read at the weekend.

How many pages should he plan to read in the next 10 days to do this? While the total for his set of data was 230, so his mean average was 23 and he is trying to increase that.

For his mean average to increase to 25, the eight days of reading for his set of data needs a total 250 pages.

So there's so many possibilities for this as long as they equal 250.

So this is one possibility he could do 30, 31, 32, 35, 34, 20.

Still zero and zero, it's got to be that way for him 'cause of his football, 18 and 50.

Add those together and we get 250.

250 divided by 10 gives us a mean average of 25.

He's done it.

We've come to the end of the lesson.

You've been incredible.

Today, you've been explaining how to calculate the mean of a set of data, including a value of zero.

That zero can be tricky.

The mean average of a set of data is calculated by finding the total of the set of data and dividing it by the number of values.

It is important to include any zero values in the set of data when you calculate the mean average.

Otherwise, it's just not a fair comparison.

Well done and your accomplishments and your achievements today, give yourself a very well deserved pat on the back and say, "Well done me." I really do hope I get the chance to spend another math lesson with you at some point in the near future.

But until then, have a fantastic and successful day and whatever you do, be the best version of you that you can possibly be.

Take care and goodbye.