Lesson video

(no audio) <v ->Hello, I'm Mrs. Ashley,</v> and I'm really looking forward to working with you throughout this lesson.

So as we make a start on this lesson, we are hoping that by the end, you'll be able to interpret both pictograms and bar charts.

On the screen, there are four words that you've met before.

Hopefully, you already feel familiar with them.

So our keyword for this lesson that's new to us is frequency and we're gonna work with that during the lesson, but the definition is, it's the number of times an event occurs, or maybe it's the number of individuals, depending on which data you are collecting.

Today's lesson has got two learning cycles.

The first one is all to do with pictograms and then we're gonna move on to bar charts in the second part.

So let's make a start on the first learning cycle.

So here, Jun is wondering how he's gonna find out about his classmates' music, and the context is that they're gonna have a party and he's in charge of putting the playlist together.

Izzy, a classmate of Jun's has said, "We'll ask the question and collect their responses." Jun wants to know from Izzy what he should do next, and Izzy suggests that then they could represent the data that they've collected from their classmates visually.

And Jun recognises that that would be really helpful for him to analyse the data.

And Izzy said, "Well, that will give you informed decisions regarding the music that he chooses for their class playlist." So just to check about what we've just went through, put the stages of Jun's inquiry into order.

Pause the video whilst you do that, and then come back for the answers.

Hopefully, you've put them in this correct order.

Here we've got the order again.

Slightly different wording, but the order that Jun went through.

So the planning was statistical inquiry.

For Jun, that was about collecting data regarding his classmates' music taste.

Then the collection of data, asking a question of his classmates and collecting it.

After that, it would've represented the data in some visual way to allow him to analyse the data, so to do some analysis.

Once he's done the analysis of that data, he needs to interpret it.

What does that tell him? What does he now know? And after that, he can come up with some outcomes and actions.

Other statistical investigations will start in exactly the same way as this, but as you work with the data further or new questions might arise, and that might mean that you need to go back through the process again.

And this is why we actually know this as the data cycle because you might go through this many times over.

So what word is missing on this data cycle diagram? This was was the analysis part of the data cycle.

So Jacob would like to know what the most common pet is within his class, so has collected data and has now represented it.

So we're at the representation part of the data cycle and he is represented it as a pictogram.

He's now at that point of interpretation and is asking, "What information does the pictogram show?" Well, the pictogram tells Jacob quite a lot.

So firstly, the most common pet is the cat.

The frequency, so remember, the frequency means the amount an event occurs or the amount of individuals.

So in this case, the amount of people that have a hamster is the same as the amount of people that have rabbits.

And you can see that on the pictogram because of the icons.

The pictogram also tells Jacob that there's the same number of fish as hamsters and rabbits combined.

Another thing that can be seen from the pictogram is there are half as many dogs as cats.

All of these are interpretations of the data by using the pictogram.

Sam studied Jacob's pictogram and has commented that it just cannot be correct.

And their reasoning is because there's 2.

5 dogs.

So if you look at that row for dogs, there's 2.

5 paw prints.

So Sam's suggesting that this pictogram just cannot be correct.

Is Sam correct with their observation? Well what Sam has assumed is that each paw print represents one pet.

And if that was the case, then Sam would be correct.

You couldn't have 2.

5 dogs.

If we had a key, we'd know the value of each icon and that way Sam wouldn't think that one paw print was one.

Classmates of Jacob have decided they think they know what it must be worth.

So Laura believes that one paw would be worth four.

Sam has recognised their error in thinking all of them represented one so now thinks that they must represent 10.

And Lucas, he believes that they must represent five.

Who cannot be correct? Lucas cannot be correct.

So Lucas said that each paw would be five and that would cause the same issue as each paw representing one because if each paw represents five, then going back to the dogs because there is that half paw, then that would mean that there is 12.

5 dogs represented on this pictogram, which clearly can't be true.

So unfortunately Lucas is not correct with his choice of five.

So we've got Laura, we've got Sam's suggestions.

Who is correct out of those two suggestions? Well, both of them could be correct.

Both of them wouldn't give us a fractional amount of pet as five did and as one did.

But only one of them seemed sensible for the size of data that we would've collected.

And that's because Jacob collected his data from the class.

So if each paw represented 10, there'd just be too many pets on this pictogram.

So Laura's suggestion of four is more reasonable for this dataset.

So now we can see the pictogram fully completed with the key.

How many more cats are there than dogs? But now we're using the value of each icon to get a frequency from this pictogram.

So we know that there are 20 cats and we know that by each paw representing four.

There are five paws and five times four is 20.

If we do the same for the dogs, the dogs would represent 10 and that's because there is 2.

5 paw prints.

So 2.

5 times four is 10.

So how many more? Well, we need to do a subtraction there to look for the difference? And so there were 10 more cats than dogs in this data.

Can you think of an alternative way to get to that same answer? The alternative would be to just focus on the icons and not the value until you needed it at the very end.

So what I mean by that is there are five paws on the cats and 2.

5 paws on the dog.

So that's a difference of 2.

5 paws.

So we now know that there are 2.

5 more paws on the cats, and 2.

5 paws represents 10.

And so there is 10 more cats than dogs.

So what was the frequency of each pet that Jacob collected the data about? Well, that's a case of just now going back to the key and how many multiples of the key you have on each row to get the frequency.

So for the dog, we've already figured the dog out.

The dog, you've got four on the first paw, four on the second paw, and two on the half paw, and so that's a total of 10.

For hamster we've got one four paw.

So one four means it's just a frequency of four.

And this is how you're gonna do it for the rest of the pictogram.

There's the 20 that we worked out previously.

And so the data collected by Jacob is in the frequency table and then he would've represented it as a pictogram.

So just to check on that, the key has changed.

So now what are the two missing frequencies from the frequency table? Pause the video whilst you're calculating it, and when you're ready to check your answers, press play.

This time the key was 10 per paw, so there was still 2.

5 paws on the dog row.

So 2.

5 times 10 is 25.

Cat, there were five paws, 10 per paw, 50.

So here on the screen we've got Jun, another member of the class, and they've drawn some data up into a pictogram as well.

Jun checks his data and sees that from his collection of data that there were 30 more green sweets than yellow.

So how much should his icon be worth? Well the 30 more is represented by the three more icons and that represents 30, so that's 10 per icon.

So we've got another pictogram here and pictograms are great representations of data because they're so visual.

So here we have a really good example of a pictogram where it's about books.

We know it's about books without really reading any information because the icon is a book.

It is about the amount of books of each genre and the key tells us that each full book is worth 10.

So they're fairly easy to understand and you get a good feel for the data.

So pictograms are brilliant for that.

We want to draw a pictogram regarding rainfall, total rainfall from four places within the UK for April, 2010.

And therefore we need to go through, before we start constructing it, we need to go through that thought process of a good icon.

Sofia's gonna suggest that a good icon for this data would be an umbrella.

There's an example of what that icon might look like for Sofia.

Izzy says she was used a welly boot.

And lastly, Jun suggests that he would use rain droplets.

All of them are representative of the data.

The umbrella makes sense, welly boots make sense and rain droplets make sense, but is one better than the other? So firstly, Izzy's welly boot, it's gonna be very difficult to split it up, to divide it up.

We know that often on a pictogram we might need to put halves or quarters, and where would you make that division on a welly boot? Would it be understandable to the reader that it means half or a quarter? So the welly boot doesn't quite fit.

For simplicity, yes, but not for division.

The umbrella could be split in half quite easily.

You wouldn't have to have the sort of turned handle, you could have a straight handle and then half would be very easy to represent and to understand.

But then it'd be very difficult to go any further than the half.

So it'd be hard to divide it up much further than just into two equal parts, and therefore it's not gonna fit a whole host of data.

It'll be very limited to quite rounded numbers.

Whereas the droplet could be used in groups and so that would fit more data.

And here's an example of using the rain droplets to represent that data.

If we look at the bottom row is Lowestoft.

You've got three groups of six and then one droplet spare.

So that's representing a total of 19 millimetres.

When we are coming to the construction part of a pictogram, an icon needs to be carefully selected.

It needs to represent the data, the context of the data so that it really is impactful visually.

But the icon needs to be able to be divided up, needs to be quite simple to reproduce, especially when you're constructing by hand, you need to make them similar.

And so that is a limitation of a pictogram, that it can be quite difficult to find a good icon that can represent and fit a real data set.

So thinking about all of those issues and problems, which of these three frequency tables would be easily represented as a pictogram? Pause the video whilst you're making your decision, and then when you're ready to have a check, just press play.

I'm hoping that you've come up with B.

So although those numbers are relatively large numbers, they are multiples of 10 and that would therefore allow you to choose an icon that could be worth 40, and a quarter would be a 10, a half would be 20, and the full icon would be 40.

So because they are large but rounded values, then more icons would be able to fit them.

Aisha has collected data about the number of leaves on a plant over one month period and then presented it in this pictogram.

So Aisha has done things well within this pictogram.

What are they? Well, she's chosen a very simple and representative icon.

This data was collected about the number of leaves, so she's chose a leaf, and that leaf is fairly simple and can be halved.

Her one leaf icon is worth two, so she doesn't need to worry about quartering it or any other fractional amount.

One half of it is all that she needs and it's fairly simple that she can do that.

So that's a well chosen icon.

And I've just referred to it already, there is a key, so we know the value of each leaf.

So each leaf that I see within the pictogram is worth two.

Unfortunately she hasn't done everything correct and they need to be corrected.

Can you see what they are? So there's two more things that she needs to rethink and that's the size of the icon.

So the size of the icon needs to be consistent throughout the pictogram and that's to not cause confusion.

Because if the key tells us that one leaf of one size is worth two, then people might start to question, well, if it's a smaller icon, is it worth less? If it's a bigger icon, is it worth more? So being consistent with the icon size.

And the second thing is the space between them.

And that's really because it's such a visual diagram that allows us to very quickly see and get a feel of the data by seeing which one's the most common, which one's the least common.

But if the spacing is not consistent, then that can be misleading because the one that feels like the icons go on the furthest might not actually be.

It might be there's just a very large gap between two of them.

So we need to be really careful that the sizing and the spacing does not cause confusion or to be misleading.

And so here is what we would hope her pictogram would've looked like from the beginning.

So she has her key, it's a well chosen icon, the spacing and the sizing is all the same.

So just to check on everything we've been going through, what are the characteristics of a good pictogram, and choose all that apply? Pause the video whilst you're thinking for your answers, and then when you're ready to check them, just press play.

We've spoken about this a couple of times.

We need to have simple representative icons to really show that context of the data very quickly to the reader.

But the icon is only useful if we also have that key.

The key will then tell us what each icon is worth.

We're now up to the part of the lesson where you're gonna do a bit of practise on pictograms. So on this first question, you need to interpret the pictogram that's given and complete the missing words within each.

Pause the video whilst you're having a go at that.

So here's question two.

For this question, you need to complete the pictogram, and that's only on Izzy's row.

Pause the video whilst you're having a go at that.

This pictogram is nearly complete.

The only thing that's missing is the value of the icon.

The key needs to be completed.

Use the statement about the total to figure out what each apple is worth.

Pause the video whilst you're having a try of that, and then when you're ready we're gonna come back and go through the answers.

Question one needed you to interpret the pictogram.

A key wasn't given, so this was not a complete pictogram, but it does allow you to do a little bit of interpretation even without the numbers, the data and the frequency.

So you can quite easily see that most people play football.

Golf is the least played sport.

Twice as many people play hockey than rugby.

And lastly, the same amount of people play football as hockey and rugby combined.

Question two, you needed to complete the pictogram and that was by adding the three cog icon onto Izzy's row of the pictogram.

And the reason you knew that she needed three is because the statement said that Jun has six more cogs than Izzy.

Jun had five icons and we know that he has six more cogs, and each icon was worth three cogs, so therefore there was two extra on Jun's row than on Izzy's.

And so that's why Izzy only has three.

Question three, it was a mostly complete pictogram except from the missing value on the key.

There was 280 apples represented across the whole pictogram because it told you there is a total of 280 apples.

So the total frequency is represented by all of the rows, week one, week two and week three.

And so by doing a calculation, dividing the total by the amount of icons, you should have got 20 apples.

So each apple is worth 20.

So we're now up to the second part of the lesson and this part is all to do with bar charts.

So we're gonna think about Laura's new marketing campaign.

She's collected data regarding people's favourite colours and that's now represented on part of a bar chart.

It's not a complete bar chart.

Why is this not yet a bar chart? What is missing from Laura's bar chart? Well, we're missing the vertical axis.

She knows that the frequencies are 10, 12, 12, 16, 16 and 22, but she can't remember which frequencies match with which bar.

Can you match the frequencies to the correct colour? You're thinking about the greatest frequency, the least frequency, and then those ones in the middle that are the same or there's a pair of them and comparing them to each other.

And that would allow you, hopefully, to get the 10 on the shortest bar, which is blue, the 22 on the tallest bar, which is purple.

And then as I say, we've got some pairs, we've got two twelves and two sixteens.

Well, 16 is a greater number than 12.

So the taller pair represents the sixteens and the shorter pair represents the 12.

Just to check.

Frequency is shown on a bar chart by, the height of the bars.

the labels of the bars, or the vertical axis scale? Well, the height of the bars definitely is where we represent frequency on a bar chart.

But you're not gonna know that frequency unless you have the vertical axis scale.

So we need to have both to be able to read off the frequency.

Often our bar charts are drawn sort of vertical axis is our frequency, but that doesn't have to be the case.

You can have horizontal bar charts as well, and then the horizontal axis would be the frequency.

On the screen, there's a bar chart that represents the amount of trips abroad by UK residents.

Sofia commented that without the axis or frequency you cannot read this bar chart.

So in that last check we discussed that you can't get frequency unless you've got the vertical axis.

So we don't have the vertical axis here, we don't have a frequency table or the numbers associated with each one.

So we don't have that information.

Sam's response to Sofia is that we can comment on the most popular time to travel or the least popular time to travel even if we do not have the frequencies associated.

And Sam's correct with that observation.

So when do most UK residents travel abroad? Most UK residents travel abroad between July and September, and we can see that from that incomplete bar chart from just the fact that that bar is the tallest.

By being the tallest we know it will have the highest frequency.

Can you think of reasons why the UK residents travel the most in July to September? I'd imagine you've thought of things like when your school holidays are, the six-week summer holidays in the UK happen between July to September.

It might be to do with the weather, that people travel in the summer months to other places where the weather is is also nice between July to September.

So they might be in some of the reasons that you thought of about why people travel between July and September most.

We've got the same information here but we've now got our complete bar chart.

So we've now got a scale up on the vertical axis and it's labelled as frequency.

So remembering that frequency is all to do with the number of times an event occurs or the number of individuals.

So approximately how many residents travelled abroad during the months of July to September? So using the vertical axis, read off the approximate amount.

About 25 million.

So about 25 million UK residents are travelling abroad between July and September.

When we discuss the data cycle at the beginning and why it's quarter cycle, it's common that you're gonna get to a point where you've collected data and you start to analyse the data that further questions might come up that you want to then investigate.

And that might be that you want to consider why the UK residents are travelling abroad, not just between July and September, but just across the whole 12 months of the year.

So can you think of any reasons that people are travelling abroad? You may have thought of holidays.

So often you're gonna travel abroad because you're having a break and going on holiday.

It might be that you are going abroad to visit family or friends.

It might be that you're travelling abroad for work or for business.

If we were to collect further data, not about just the amount of times people are travelling but why they are travelling, if we collected that data, then we can show that and represent that as a comparison bar chart.

It's still a bar chart.

You're still gonna find the frequency by looking at the height of the bar and using the vertical axis scale to read it.

But this time we've got groups of bars within each timeframe.

So January to March, et cetera.

There is a key similar to the pictogram.

You're not gonna know what each bar is representing without the key.

So the key here is telling you the reason.

So we've got holiday, business, visiting and other.

So you may have come up with other reasons people travel abroad and they would be represented on the other bar.

On the right-hand side, this is a stacked bar chart.

So again, it's showing you exactly the same data but just representing it in a different bar chart.

And so this bar chart has got the four categories as well.

Again, there's a key to tell you the colour and the shading combinations so that you can identify each part.

But the stacked bar chart is each of those bars that you can see on the left hand side have been put on top of each other.

So what is the same and what's different about these two types of bar charts? So they're both showing you the total trips abroad and the breakdown by reason.

So because they've both got those colours and shading, we've got the key, that's the reason part that they're showing.

You can find the totals on both of those bar charts.

The comparison bar chart is easier to analyse the reasons why people are travelling.

The stacked bar chart is much easier to see which months were the most popular, and that's because they've all been stood on top of each other so it looks like the original bar chart that we can just see which bar was the tallest.

On the comparison bar chart you can calculate that, but it is a calculation.

It is not a case of just being able to visually see it.

So just to check, match up the types of bar chart to their name.

Pause the video whilst you're doing that.

So the standard bar chart maps to the middle example, then we've got the comparison bar chart and that maps with the last image, and that's where you'll have groups of bars at each category.

There needs to be a key in order for you to understand it and know which one represents which.

Which leaves the last one to be a stacked, and the stacked one is where all those bars have been put on top of each other.

So on the screen we've got the pictogram to represent the same data as we've got as a bar chart.

So what's the same with a pictogram and a bar chart? Well, they both are representing frequency visually.

They both represent that information.

Because they're fairly simple and visual, they give you a snapshot of the shape and nature of the data.

So you can see which one is the most common or the least common, how the data has been distributed across the categories.

And they're both simple to read and understand.

So you don't need to have a huge amount of mathematical knowledge to be able to read them and understand what the data is that they are representing.

Be some differences, otherwise why would we have the two different types of charts? Well, bar charts do not use icons.

They use rectangles and so they're not as visually appealing as a pictogram.

The context of the data does not come across as easily on a bar chart as it does a pictogram.

And in the first part of the lesson where we spoke about icons and choice of icons, pictograms have limitations with which frequencies they can represent easily because you need to get an icon that can be a value that can be divided up easily.

If the frequencies are are really random and not very rounded values, they're gonna be more difficult to show on a pictogram.

And that's where a bar chart is much more useful.

So is one better than the other? Really it all depends on the context and the need for the chart to determine which one is better.

In some instances a pictogram will be better than a bar chart, and in other instances a bar chart will be better than a pictogram.

Larger data sets, they're going to tend to be presented on a bar chart.

What makes a good bar chart? What makes a bad bar chart? What do they need? Are some things optional or are there certain things that you have to have? Like on a pictogram you need to have a key, is there something on a bar chart that you must have? So here we've got two bar charts, and Jacob and Alex have constructed these bar charts for the same data.

And the data is regarding ice cream sales and the flavour.

So the frequency is the amount of sales of that flavour ice cream.

The flavours are vanilla, strawberry, chocolate and other.

And on the horizontal axis you've just seen the initial of the flavour.

If we compare their two attempts at a bar chart for this data, what is the same? Well, the heights of the bars.

So neither of them have disagreed with the frequencies per flavour.

Their vertical scale.

They made a choice that their vertical scale was going to go up in twos, and they've done that correctly.

That is going up in twos each time.

The gap doesn't change between any of those values, so it's multiples of two.

And the order of their ice cream flavours is the same.

So to compare, we can do that very easily because they are in the same order.

If they were in different orders, it wouldn't matter.

But to compare them, we'd need to be very careful that we were comparing vanilla to vanilla.

Unfortunately, both of the boys have made mistakes when they've constructed their bar charts.

And what mistakes have they made? So Alex is missing the axis titles, whereas if you look at Jacobs, he has correctly identified and labelled the axis.

So the vertical one is his frequency and the horizontal is about the ice cream flavours.

Without those labels, without those titles, we won't understand context of the data.

Glaringly obvious difference between the two is that Alex's has gaps, whereas Jacobs do not.

And so Jacob is incorrect with that.

Jacobs should have had gaps as well.

So bar charts need to have gaps between the bars.

Jacob's a little bit confused as to why.

He doesn't quite understand why that is something that his bar chart had an error on.

So Alex has asked Jacob to consider a number line.

So think about a number line.

Hopefully we're all very familiar with number lines.

Obviously you could write them vertically.

This one is horizontal.

And so Alex is asking, "Does anything exist between seven and eight?" Are there anything that we know lies between number seven and number eight on a number line? Jacob says, "Yeah, there's lots of numbers," and he's given some examples.

7.

2.

7.

85.

Alex says, "Okay, but what if you were counting how many shirts you owned?" Would there be anything that exists on that number line between seven and eight? And the answer is that, well, no, I'd either have seven shirts or I'd have eight shirts.

So those examples of numbers that lie between seven and eight no longer work in the context of number of shirts.

You can't have 7.

2 shirts or 7.

85 shirts.

You either have seven shirts or you have eight shirts.

Because certain contexts, there isn't things between.

So if it was non-numerical data, and his example is animals in a farm, the bars would need to be separate.

Jacob has understood this now and has said rightly so that nothing would exist between goat and horse.

So depending on the type of data you're working with and the type of data that has nothing in between, so the shirts example, you either have seven shirts or eight shirts, or here with types of animals at a farm you either have a goat or you have a horse, there isn't anything that exists in between them, they would be represented on a bar chart and they therefore need to have gaps.

Check for understanding on that.

True or false, bar charts should have gaps between each bar? And then a justification.

Pause the video whilst you're thinking through that one, and then when you're ready to check it, just press play.

Hopefully you went for true.

And that is because the data, there isn't data between the two categories.

They are separate categories.

So always think back to that idea of shirts.

You either have seven shirts or you have eight shirts.

And think back to the idea of animals.

You either have a horse or you have a goat.

We're now up to the part where you're gonna do a bit of practise on on all of that that we've just done on bar charts.

So for question one, you answer the questions.

Pause the video whilst you're doing that, and then when you're ready for the next question, come on back.

Question two is more of a puzzle question.

Make sure you read through all five clues before you head straight in.

And then when you're ready to come and check the answers, press play.

So 1a, which was the most popular colour in each year? So because we're asking for the most popular, we're therefore looking for the highest frequency, and that will come from the tallest bar.

So in year seven, the tallest bar was the red colour.

And for year tens, that was the black.

Part b, compare the number of students who liked yellow best in each year group.

There was one more student in year seven that preferred yellow.

For question part c, how many more year sevens than year tens liked green, well, actually there was no more 'cause they both equally liked green.

And then d, how many students were in each year group? To get a total, you needed to do some maths by adding up the totals of each bar.

And so 192 for year seven and 191 for year 10.

Question two.

So this was the one that you needed to use the clues to build up to the bar chart.

So this lesson we have been checking the understanding of pictograms and bar charts.

Pictograms and bar charts both represent data through frequency.

Pictograms use icons to show the frequency and you must have the key in order to support your understanding of frequency on a pictogram.

Bar charts represent frequency using the height and there needs to be gaps between the bars.

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