Lesson video

Hello everyone, it's Mr. Millar here.

In this lesson, we're going to be looking at Problem solving with the Mean.

So first of all I hope that you're doing well and first sight again is this a familiar Data Handling Cycle.

And as I said last lesson when we looked at how to find the mean? The first four lessons of this unit looked at step one in the data handling cycle.

But now we have collected the data and we are looking at analysing the data.

We're processing it, we're analysing it we're seeing what findings we can find.

So we're going to continue with that in this lesson.

And in this lesson we're going to look at more problems involving the Mean.

So let's go ahead and have a look at the Try this task.

Okay, so nice and easy to start off with, here is a set of four cards and all you need to do is find the mean of these four numbers.

Give you a few seconds to work this out.

Okay, and if you still need more time, pause the video, but you should have figured it out by now.

So to find the mean, you add up all the numbers, And may sum to 16 and then find the mean you do 16 divided by four, because there are four numbers and that equals four.

So these four numbers have a mean of four.

Okay.

Now I have added a nine to this set of cards.

So without calculating the mean, what do you think happens to the mean? Does it go up? Does it go down? Stay the same? What do you think? Well, if you're thinking it goes up, then yes, really well done.

And I could work it out, because now all the numbers sum up to 25 and 25 divided by five.

There are five numbers now, that give me five.

So by adding a nine, the mean has gone up from four to five.

What if I add another number? What if I add a two? what do you think happens to the mean? Does it go up from five, down from five? What did you think? Well, if you said down from five, then really well done, and again, I can work it out to show you.

So now the numbers sum up to 27 and I have six numbers and 27 divided by six is 4.

5.

So the mean has gone down from five to 4.

5.

Why do you think this happens? Why do you think the mean goes up when I added a nine? And why do you think it went down when I added a two? Why do you think? Well, if you're thinking that if the number that I add is above the mean, the mean goes up, but if the number I add is below the mean, the mean goes down, then really well done.

That is exactly what's going on here.

And later on in this video, we're going to see a few more examples of why this happens.

But for now let's go ahead and have a look at the Connect slides.

Let's read through.

The mean weight of a class of 35 students is 45 kilogrammes.

When the weight of the teacher is included, the mean weight increases by 500 grammes.

Find the weight of the teacher.

Okay, so what do you think is going on here? There's a suggestion for you in the box.

I can start off by working out the total weight of the 35 students.

That would be a good place to start.

How do you think you do that? Pause the video for a minute or two to see if you can work out the weight of the teacher.

Okay, let's go through this.

So the first thing we're going to do, is the total weight of the 35 students.

So the weights of the 35 students.

Well, there are 35 students and the mean is 45.

So I need to do 35 times by 45.

And when I do that, I get 1,575 kilogrammes.

What do you think I can do next? I'm including the teacher.

Well, I can work out the weight of all 35 students plus the teacher.

So lets's do that.

So the weight of the students plus the teacher.

So before that, I did 35 times by 45.

35 because there are 35 students.

What do I do now? Well, there's one more person that I have to include.

So it's going to go up to 36.

35 students plus the teacher.

Now beforehand, the mean was 45.

Now I'm told that the mean weight goes up by 500 grammes and you know, that 500 grammes is half a kilo.

So what's the new mean weight? Well now, 45.

5.

Multiply these two numbers together.

You can use a calculator to help you 1,638 kilogrammes.

Okay, so now I know the total weight of everyone before the teacher is added and after the teacher is added.

So, how did this help me find the weight of the teacher? Well, if you're thinking, I do 1,638 subtract 1,545, then that would be spot on.

I do that and I get 63 kilogrammes.

That is the weight of the teacher.

So, by finding out the totals involved, I can easily work out the weight of the teacher which is what I wanted.

Great.

Now it's going to be your turn to do some independent work when you're ready.

Okay, so there's actually going to be two different things to do in the independent tasks.

The first one is here.

And this touches on what we did in the Try this task.

So let me explain, the mean of two, four, four, seven, eight is five.

Predict whether the mean of the following sets of numbers is less than, equal to, or more than five.

So, I'm not saying to work out the mean of this sets of numbers.

I'm saying that, compare the new sets of numbers to the original and predict if the mean goes up, down or stays the same.

Let's do the first one together and then you can do the remaining ones.

Two, four, four, seven, nine.

Okay.

What I want you to do is, I want you to compare this sets of numbers with the original.

What's the same, what's different? Well, the first four numbers are all the same, but the last number is a nine rather than an eight.

What do you think that does to the mean? Well, if you're thinking that it makes the mean more than five because my total has increased, well done.

So I'll tick this, the column here.

Okay, now it's your turn.

Pause the video, have a go at the remaining four, take about three or four minutes to do this.

Great, let's go through this very, very quickly.

So the second one down, this is going to be less than five because the first number has gone down.

The next one, well the two and the four are the same and the final eight is the same.

And instead of the four and the seven, I've got a five and a six.

So, actually the mean is going to stay the same because the four's gone up by one, the seven has gone down by one, overall my sum hasn't changed.

And by the way, you can check any of these by working out the mean yourself.

Next one.

Okay, this time I added a number.

My numbers are the same, but I've added a five.

And because I've added a number, which is the same as the original mean, my mean will stay the same.

Finally.

What have I done here? Well, similar numbers to before, but there's a nine instead of an eight and there's a six.

So my mean is going to increase because my numbers are getting bigger.

Let's have a look at the second Independent task when you're ready.

Here it is.

Timothy's mean score on the first three tests was 75.

On the next five tests his mean score was 85.

What was his mean score on all eight tests? Now, you may be tempted to say, well, in some of the tests, he got 75, some of the tests he got 85.

So I'll just take the average is going to be 80.

But you'd actually be wrong.

And your job is to find out what the mean actually is.

Suggestion for you in the box.

I can start off by working out the total score from the first three tests.

Start there, I'll continue from there.

Pause the video for three or four minutes, see if you can work out this one.

Great, let's go through it.

So, the first three tests.

The total is going to be three times by 75 equals 225 marks.

The last five tests, it's going to be five times by 85, 425.

What about the total? Well, in total I've done eight tests, three plus five, and the total number of marks that I've got, I do 225 plus 425 and I get a 650.

How do I find the mean from that? Well, that's really easy.

The mean is the total number of marks 650, divided by eight, which is 81.

25.

So it's not actually 80.

Why do you think is actually a bit more than 80? Why do you think it's more than 80? If you're thinking that there were more tests that he got more than 80 than less than 80.

So five tests, he got 85 and only three tests he got 75.

So my average is actually a little bit more than 80, really well done.

Okay, finally, let's go to the Explore task.

Okay, here it is.

It's a nice one.

Here are five cards.

One, two, three, four, and five.

One card is removed and the mean is now 3.

25, which number has been removed? Should be pretty easy to understand.

So I want you to pause the video, see if you can find out which number has been removed.

Great, okay.

So hope that you worked it out and if you've got the answer two, then really well done.

Let's just check to see if we're right.

If we have removed two, the sum of my numbers is now one plus three, plus four, plus five, that's 13.

And the mean 13 divided by four, because there are four number left is, 3.

25.

So, things to just find out how you did this, but if you spotted that the original mean was three.

And now the mean is 3.

25.

So I must have removed a number which is lower than the mean for the mean to go up.

So I must have removed either one or two then really well done.

That would have helped you work this out a bit quicker.

Anyway, the number that you moved was two.

So, well done if you've got that and well done for completing assessment, because that is all for this lesson.

Thanks so much for watching, I hope you enjoyed it.

Next time we're going to look at a few more different measures of data.

So, Median, Mode and Range.

So I look forward to doing that one for you.

See you next time, have a great day.

Bye bye.