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I can construct bar charts from data.

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Licence

This content is © Oak National Academy Limited (2023), licensed on Open Government Licence version 3.0 except where otherwise stated. See Oak's terms & conditions (Collection 2).

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Key learning points

Data presented as a list can be represented as a bar chart
Data presented in a table can be represented as a bar chart
The type of data determines how the bars should be drawn

Common misconception

Pupils may label the vertical axis with the frequency values rather than a scale.

Remind the pupils that the scale should go up in the same jumps. i.e. 0, 5, 10, 15 etc and have them check theirs.

Keywords

Frequency - The frequency is the number of times an event occurs; or the number of individuals (people, animals etc.) with some specific property.
Bar chart - A bar chart (bar graph) is a graph consisting of bars visually representing the frequency of objects or groups.
Data - Data are a collection of information.

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Hello, I'm Mrs. Lashley, and I'm looking forward to guiding you through your learning today.

In this lesson, we're gonna look at how to construct bar charts by hand.

Here are some keywords that, hopefully, you're already familiar with.

So just take some time to refamiliarise yourself before moving on.

The lesson's got two parts.

The first part is looking at constructing and interpreting bar charts, and the second part is using bar charts within a data investigation.

So we're gonna make a start on the first part.

The screen, we've got a pictogram.

And Izzy has said that her pictogram shows the merits collected by our class each week.

The pictograms got a key to represent each icon, and it's a five-week period that she's collected that data.

I just drawn the same pictogram, got the same data, but chosen to use the icon that is a square and her reasoning for that is they are easier to draw than circles.

Jacob has also chosen to do squares for this data, but hasn't bothered with spacing, and that's just to save space.

Lucas has used the squares, hasn't used spacing either, but his quarters have been vertical strips as opposed to the squares.

Alex decided to make it easier to figure out the frequencies.

He's put the multiples of the key, so four, eight, 12, along the top.

And Izzy's then recognised that Alex's pictogram looks like a bar chart.

So Izzy has just rotated the pictogram so that the bars are now running vertically, and identifies that the pictogram that started for this data about merits now looks more like a bar chart.

Here is a bar chart made by technology for the same data.

So what are the features of a bar chart, or is a bar chart a pictogram? So the bar chart has a vertical axis and this represents the frequency.

The bars are the same width, and there are equal gaps between each bar.

Just note between the two, the pictogram and the bar chart, that the axis on the bar chart is going up in five.

Whereas our pictogram, the key was a four, which is why Alex put the multiples of four along that top.

What label is missing on this bar chart? Pause the video.

When you think you'd know what it is, press Play and check.

Hopefully, you recognise that this needs to say frequency.

So we've got one label to just tell us, which tells us the context.

So this is Types of tree, and we are missing the frequency on the vertical axis for this bar chart.

Using the bar chart, answer the question, \"How many sycamore trees were there in this woodland?\" Pause the video and then come back to check your answer.

There were nine sycamore trees in this woodland and we know that by measuring the height of the bar against the scale.

The vertical axis on the bar chart, it can be horizontal if the bars are running horizontally instead.

But most often, we're gonna be working with a vertical bar chart is our frequency.

We need to have that labelled to communicate what we are representing.

The scale is a choice and that choice is really important.

So here is a frequency table about the number of terminals at four London airports.

So you've got Gatwick that has two terminals, Heathrow has four terminals, Luton has just the one as the Stansted.

If you wish to draw a bar chart that represents the number of terminals at these four London airports, what would be a sensible vertical scale? The data here is pretty small.

The greatest number is four, so going up in ones would be fine.

And here is an example of what that bar chart might look like.

So we've got our axis labelled, we've got equal bars.

The width of each bar is the same and gaps between them.

So because the data wasn't, there wasn't much variety to the data, and the greatest number was four, going up in ones worked perfectly fine.

So the same four London airports are being used, but the data collected this time is not about the number of terminals, but instead, about the number of airlines that run or fly out of those airports.

What would the scale be this time? Would going up in ones still work? So this is gonna be a bit dependent on space.

So if you are constructing this bar chart by hand and you've only got a, you know, a fairly small piece of paper, and then you might need to change your scale.

You will need to think about all of those factors when you're choosing scales.

So depending on space, you could go up in fours, but you could go up in 10s, and the 10s would reduce the size of it.

So if you're limited for space, 10s would make sense.

And here is an example of going up in 10s.

Again, we've got those same four London airports, but the data's been collected about the number of destinations that they serve.

So we've got much higher values this time.

So same question, \"What choice for the scale would you make this time?\" Going up in ones is going to very easy to read, but it would take a lot of space.

So going up in ones is not one I would suggest.

So you always need to think about how high you need to get.

So the highest or the greatest value here is 224.

The lowest is 126.

That's nearly a 100 different between them.

So you could go up into steps of 25, and there's an example of going up in steps of 25.

Here is a check for you to think about why would having a vertical scale which increases by one each time not be advisable for this data? So you've got four books and the number of pages in each book.

Pause the video, have a think, and then when you're ready to check, press Play, Things that you may have considered is it would take up a lot of space.

So 73 pages is the most pages for these four books, and if you're going up in ones then you would need to go up all the way to 73.

And another reason is because the data ranges between 37 and 73.

You might want to make the increments larger, because of the space between them.

You're gonna do some practise and the first question needs you to complete the vertical scale.

So there is one number at the correct position on the vertical scale, but you need to figure out all of the other numbers that are missing.

Pause the video, and when you're ready to move on, press Play.

Question two, needs you to complete the bar chart and fill in the missing frequency on the frequency table.

Pause the video, and when you're finished, press Play.

So question one, you needed to complete the vertical scale.

What you also needed was the label of frequency, so the vertical scale needs not only the numbers but it needs that label.

Because 48 was on that fourth grid line, 48 divided by four is 12.

And that indicates that each grid line is a jump of 12.

So 12, 24, 36, the 48 was given, 60, 72.

And question two, you needed to complete both the bar chart and the frequency table.

The missing frequency was 18, the scale would've been going up in twos.

And again, you need that the label of frequency on that scale.

We're now gonna move on to the second part of the lesson, which is using bar charts within a data investigation.

So our data investigation is from a local authority and they want to know if secondary school students are eating the recommended five portions of fruit and vegetables per day.

They collect data from the four similar-sized secondary schools in their area.

About how many students are eating that recommended amount? The data that was collected is shown in the frequency table.

So we've got the four similar-sized secondary schools and the amount of students who are currently eating the recommended amount of fruit and vegetables per day.

We're gonna represent that data as a bar chart, and so we've got our scale, going up in 100s, frequency labelled, the schools is our horizontal axis, and they're named underneath each bar.

The bars are the same width and there is a gap between them.

So this bar chart is set up as it should be.

So which school do you think that local or authority is concerned about and why? So using the data that was collected and is now represented in a very simple bar chart, which school do you think the local authorities should be concerned about and why? Well, they're probably going to be worrying or concerned about Millington School and that's because the other three schools are fairly similar.

The schools were all a similar size.

So proportionally, Millington School is proportionately lower than the other three.

So in that data cycle, they've collected some data to find out about how many students are eating the recommended fruit and vegetables per day.

They represented it and have had a little bit of analysis of the data and seen that Millington School are just not quite in the same proportion of students eating that recommended amount.

So they decide the next step of the data cycle in their data investigation is that they are going to collect some further data at each school.

What data do you think they might be collecting now? What questions may have come to mind after seeing the original data? Things you may have considered is, which fruit and vegetables are they eating? Maybe they want to find out, \"Is more fruit being eaten than vegetables,\" or, \"is there specific fruit, specific vegetables?\" It might be that they want to know breakdowns per year group at each school.

They might want to see if, although one school was considerably better than another, was it one specific year group filling that data, rather than over the school as consistent approach? And perhaps, they want to know where they are eating the fruit and vegetables.

Is there consumption at home, or is there consumption at school, and maybe it's quite balanced? So they might be things that the local authority have now thought about and therefore, need to collect further data.

The local authority actually wanted to find out if the gear groups were consistently eating the recommended.

So was it one fifth of the number that are at each school in each year group? So they collect the data by year group.

Here, you've got stacked bar chart, and this stacked bar chart allows the data to be seen by year group within each school.

From the stacked bar chart, we can still see that Millington School is the school with the least amount of students each in the recommended amount.

So the height of each bar is telling us the total students from each school.

Within each bar, we can then look at the proportions of year groups.

And if you look at Oakfield, St.

George's and Acorn Park School, they seem to have about the same proportions within their year groups who are eating the recommended amount.

Millington School doesn't seem to have quite the same proportions as the other three.

The same data is represented with a comparison bar chart as well.

And so this comparison bar chart allows you to compare the year groups between the schools more easily.

It's not as obvious that Millington School is much lower than the others overall, but it does allow us to see that in every school year sevens are the ones that, who are eating the recommended amount of fruit and vegetables per day the most.

That's consistent through the, all four schools.

Which school's Year eight students are eating the recommended fruit and vegetables the most? And that would be Acorn Park Academy.

So because if we just are focusing on Year eight, we're just focusing on the second bar of each group and that's the blue checked bar.

And so if we wanna know which school's Year eights eat the most, then we're looking for the tallest.

And the tallest one is the Acorn Park.

So that's where the comparison bar chart is helpful 'cause we can make comparisons about the year groups within each school.

So here we've got the two bar charts side by side.

So you've got the stacked bar chart, which shows us that Millington School is not performing to the same amount, regarding the amount of students eating the recommended fruit and vegetables, whereas, the comparison bar chart allows us to compare year groups within each school.

So using the further data, which year group do you think the local authority will focus their efforts at Millington School? They're concerned about Millington School, they can see the Millington School, which is a similar size to the other three is not getting their students or their students are not eating the recommended amount.

Which year group do you think they should focus on? So what actions and outcomes will come out of doing this data investigation? They're probably gonna focus on Year 10, because within Millington School, so using the comparison bar chart on the right, you can see that the fourth bar, the Year 10, the purple one, is much shorter than the other four bars.

So Year 10s are the ones that need a little bit more focus perhaps.

All right, a check for you.

So using this bar chart, which grade has decreased in frequency every year? Pause the video so that you can study the bar chart, and then when you think you've got an answer, press Play.

Hopefully, you went for Grade B.

There are three years represented on here.

And if you get to the Grade B bars, they are on the declines.

There's getting less each year, and so that's decreased every year.

We have a bar chart now that represents the number of children with each shoe size in a year eight class.

So we're in a year eight class, we've tallied up or we've collected the data about what shoe size they are wearing.

No half sizes, just you're either a size four or you're a size five.

If you look along that horizontal axis, the shoe sizes are in a random order.

So they're size eight, then there's size four, then there's size 10.

Does that matter? Regardless of what order it is, we can see that size six is the most common within this year eight class, because it's got the tallest bar.

If we order the bars from the smallest shoe size to the largest shoe size, is it clearer? Well, the use here is that it allows you to see the distribution more easily.

And because this data is all about year eights, and year eights are all the same age, we would expect this shape.

There is going to be some students with smaller feet within the class.

There are gonna be some students with larger feet within the class, but there will be a size that is a majority and that's because of age, and therefore, height and all those other factors.

So this shape is probably what you would expect.

So having them ordered from the smallest shoe size to the largest shoe size, does give you some additional insight to the data.

So data that's collected and represented on a bar chart is often non-numerical.

And examples of that are colours, favourite colours, for example, or colours of cars, animals.

It might be, you go to a zoo or you go to a farm, it might be pets, or food, favourite foods, favourite flavours of foods.

And so should the bars, if the data that we've collected is non-numerical, be put into some sort of order? And so here is an example of a bar chart that is non-numerical.

Pets, we've got dogs, we've got cats, we've got fish, hamster, rabbits and other.

And for this type of data, the order isn't, there isn't a relevant order.

So it doesn't need to be in an order, you can decide the order that you put them in.

We're not expecting some shape to the data.

So on this check, is it True or False? The bars of a bar chart always need to be in a particular order.

So True or False? Hopefully, you went False.

So now a justification as to why.

Is it false because the same data is being represented regardless of order? Or sometimes there is a known relevant order and then you will, but not all things do.

Pause the video whilst you consider that justification, and then when you're ready to check, press Play.

So it's the second one.

So there are some things that do have a known relevant order and if that's the case, then you would order them.

It makes sense to order them.

So the shoe size was one of those that ordering it from smallest shoe size look to the biggest or biggest to the smallest.

Because there is an order, then you would order it.

Non-numerical often doesn't have a relevant order, but some of them will do.

You're now gonna do some practise to do with bar charts in data investigation.

So question one, you need to decide whether each data set should be ordered or not.

So when you draw a bar chart, would the order of the bars matter? Pause the video, and then when you're ready to move on, come back.

So for question two, Jacob has collected data and he wants to see if there's a trend to his step count.

He collects data over a two-week period.

Week one has already been constructed on the bar chart.

Week two, the data is on, in the data table, and you need to add it to the bar chart.

So this is gonna be a comparison bar chart.

So draw the bars beside the given Week one data.

Pause the video, and when you finish comment, when you finish doing that, come back.

The next part is to comment on what you can see from your comparison bar chart.

So what comments can you make regarding Jacob's daily step count, and justify your comments.

Pause the video whilst you do that and then when you're ready, come back for the answers to these questions.

Question one.

This question was all about working out whether when you construct a bar chart, your bar should be in any order, or if there is a specific relevant order you should have given them.

So part A is the colours of karate belts.

Well, there is an order because there's some sort of rank system and it would make sense, therefore, to order the colours in the same ranking system.

If a data was being collected about animals at a zoo, there isn't an order.

So the order wouldn't matter.

If it was about types of pen, again, there isn't an order, so it wouldn't matter.

Movie genres.

There isn't an order to that, so it wouldn't matter.

If your data was about clothing sizes, then it would be ordered.

So if we went for, for example, on the screen, if Extra Small, Small, Medium, Large, Extra Large, et cetera, then you would put them in that order.

Question two, you needed to complete the bar chart, adding the data for Week two to make a comparison bar chart.

You clearly didn't need to do orange, but it needed to be different to the original bars.

The question 2b, was making some comments about Jacob's daily step counts.

And so things you may have said, \"His daily step count is lower at the weekend,\" and that might be, and a justification of that is, it might be, because he's not walking around a school building.

The daily step counts are similar between the two weeks, and that might be due to him following a timetable at school, Monday to Friday, and having the same hobbies at the weekend.

So by him doing the same things week by week, then his daily step count will not fluctuate too much between the weeks.

So during this lesson we have looked at constructive bar charts by hand.

So bar charts are data representation.

They're part of the data cycle.

When you've collected your data, you organise it and then you represent it.

They are fairly simple to understand, which is why they are often used.

The vertical axis represents frequency and the bars have to have an equal gap between them.

If the data has a relevant order, then the bar should be put in that order.

Well done today.

I look forward to working with you again soon.

(metal clanking).

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"https://www.thenational.academy/_next/image?url=https%3A%2F%2Foaknationalacademy-res.cloudinary.com%2Fimage%2Fupload%2Fv1697783339%2Fdfwjcrqsuimhmnubued5.png&w=640&q=75", "imageKey": "4bf3547a-cce2-4b8a-43ea-422ddbac9a72/question/cd7ddcdf1cfe2bb29f7ccfd28811bd54.png" } ], "id": "59645604-4366-6b04-81b2-8aea3f17062a", "lessonId": "6f956a2d-4e50-d834-38b3-7b87114c117b" }, { "type": "Question", "question": { "text": "Some things are measured and some are counted. Which of these are counted?" }, "questionType": "Multiple choice", "correct": [ { "text": "number of cars that drive past" }, { "text": "photographs with an elephant on them" }, { "text": "number of odd socks" } ], "choices": [ { "text": "heights of a group of people" }, { "text": "number of cars that drive past" }, { "text": "photographs with an elephant on them" }, { "text": "weights of some pet dogs" }, { "text": "number of odd socks" } ], "id": "3d1db70f-4329-d00b-8a87-f919fd306e35", "lessonId": "6f956a2d-4e50-d834-38b3-7b87114c117b" } ], "lessonId": "6f956a2d-4e50-d834-38b3-7b87114c117b", "meta": { "gradeStageId": "ks3", "subject": "Maths", "grade": "Year 8", "topic": null, "unit": "Graphical representations of data", "lessonCount": "11", "age": [ 12, 13 ], "gradeId": "age_12_13", "gradeStage": "Key Stage 3", "lesson": "Securing constructing bar charts by hand" } }, { "id": "99fd7af1-047a-b185-0a4c-b78e655662d3", "type": "Resource", "resourceType": "Quiz", "title": "Securing constructing bar charts by hand", "quizType": "Exit quiz", "items": [ { "type": "Question", "question": { "text": "The total frequency for this data set is ______.", "image": "https://www.thenational.academy/_next/image?url=https%3A%2F%2Foaknationalacademy-res.cloudinary.com%2Fimage%2Fupload%2Fv1697783339%2Fcveht1g9kyieqrl4kiye.png&w=1080&q=75", "imageKey": "99fd7af1-047a-b185-0a4c-b78e655662d3/question/d3fdd1e6e32b609443b7e15e396793da.png" }, "questionType": "Short answer", "correct": [ { "text": "16" }, { "text": "sixteen" } ], "id": "b1cf987a-11b1-4611-47b4-772401144c51", "lessonId": "6f956a2d-4e50-d834-38b3-7b87114c117b" }, { "type": "Question", "question": { "text": "If a bar chart was to be constructed for data about favourite pizza toppings in a class, the bars would have a specific order. True or false?" }, "questionType": "Multiple choice", "correct": [ { "text": "False - there is no relevant order to pizza toppings so they can be in any order" } ], "choices": [ { "text": "True - order from the most favourite to the least favourite topping" }, { "text": "False - there is no relevant order to pizza toppings so they can be in any order" } ], "id": "545669b1-f0f7-13e4-93da-ff39936bfd95", "lessonId": "6f956a2d-4e50-d834-38b3-7b87114c117b" }, { "type": "Question", "question": { "text": "This is an example of a __________ bar chart.", "image": "https://www.thenational.academy/_next/image?url=https%3A%2F%2Foaknationalacademy-res.cloudinary.com%2Fimage%2Fupload%2Fv1697783334%2Fcldqucwoyr7h1jcqxgms.png&w=750&q=75", "imageKey": "99fd7af1-047a-b185-0a4c-b78e655662d3/question/52fada52cc5fa9ae7ca4c0d7d3afb88a.png" }, "questionType": "Multiple choice", "correct": [ { "text": "comparison" } ], "choices": [ { "text": "standard" }, { "text": "comparison" }, { "text": "stacked" } ], "id": "7f85fb3d-5f00-f7ba-d00a-29abf81c79cf", "lessonId": "6f956a2d-4e50-d834-38b3-7b87114c117b" }, { "type": "Question", "question": { "text": "The frequency axis needs to have a suitable scale for the data it is presenting. The scale will go up in ______ increments." }, "questionType": "Short answer", "correct": [ { "text": "equal" } ], "id": "a4c996f2-290d-7297-617a-70e0adbc2664", "lessonId": "6f956a2d-4e50-d834-38b3-7b87114c117b" }, { "type": "Question", "question": { "text": "Three pupils are discussing this bar chart. Who is correct with their observation?", "image": "https://www.thenational.academy/_next/image?url=https%3A%2F%2Foaknationalacademy-res.cloudinary.com%2Fimage%2Fupload%2Fv1697783335%2Fjgthfjlpb51oe63maed0.png&w=750&q=75", "imageKey": "99fd7af1-047a-b185-0a4c-b78e655662d3/question/ed222f122436b8060616f11a61611690.png" }, "questionType": "Multiple choice", "correct": [ { "image": "https://www.thenational.academy/_next/image?url=https%3A%2F%2Foaknationalacademy-res.cloudinary.com%2Fimage%2Fupload%2Fv1697783336%2Fiaapslxhehjcluultxbw.png&w=640&q=75", "imageKey": "99fd7af1-047a-b185-0a4c-b78e655662d3/question/5f156b19c58c8ce589f480923457eee3.png" } ], "choices": [ { "image": "https://www.thenational.academy/_next/image?url=https%3A%2F%2Foaknationalacademy-res.cloudinary.com%2Fimage%2Fupload%2Fv1697783332%2Fa4pkzov8c9ngdjfsaybd.png&w=640&q=75", "imageKey": "99fd7af1-047a-b185-0a4c-b78e655662d3/question/52c3d80d1fcfcbce399ef6f5a7c8e09b.png" }, { "image": "https://www.thenational.academy/_next/image?url=https%3A%2F%2Foaknationalacademy-res.cloudinary.com%2Fimage%2Fupload%2Fv1697783333%2Futa5vwaum3n4iifohzde.png&w=640&q=75", "imageKey": "99fd7af1-047a-b185-0a4c-b78e655662d3/question/911884ed8ed5419aeb5941c408710164.png" }, { "image": "https://www.thenational.academy/_next/image?url=https%3A%2F%2Foaknationalacademy-res.cloudinary.com%2Fimage%2Fupload%2Fv1697783336%2Fiaapslxhehjcluultxbw.png&w=640&q=75", "imageKey": "99fd7af1-047a-b185-0a4c-b78e655662d3/question/5f156b19c58c8ce589f480923457eee3.png" } ], "id": "8846255b-a365-7504-8aa7-122c3bacb6a9", "lessonId": "6f956a2d-4e50-d834-38b3-7b87114c117b" }, { "type": "Question", "question": { "text": "Which bar chart matches this data?", "image": "https://www.thenational.academy/_next/image?url=https%3A%2F%2Foaknationalacademy-res.cloudinary.com%2Fimage%2Fupload%2Fv1697783337%2Fcn59q41uiyavxl6jnd49.png&w=640&q=75", "imageKey": "99fd7af1-047a-b185-0a4c-b78e655662d3/question/61d60667d035de4325ec5209e8990478.png" }, "questionType": "Multiple choice", "correct": [ { "image": "https://www.thenational.academy/_next/image?url=https%3A%2F%2Foaknationalacademy-res.cloudinary.com%2Fimage%2Fupload%2Fv1697783336%2Fb2yy1hl0o6gg7yixbdjc.png&w=750&q=75", "imageKey": "99fd7af1-047a-b185-0a4c-b78e655662d3/question/81a903947e3cce22375ba3bed4bda006.png" } ], "choices": [ { "image": "https://www.thenational.academy/_next/image?url=https%3A%2F%2Foaknationalacademy-res.cloudinary.com%2Fimage%2Fupload%2Fv1697783336%2Fb2yy1hl0o6gg7yixbdjc.png&w=750&q=75", "imageKey": "99fd7af1-047a-b185-0a4c-b78e655662d3/question/81a903947e3cce22375ba3bed4bda006.png" }, { "image": "https://www.thenational.academy/_next/image?url=https%3A%2F%2Foaknationalacademy-res.cloudinary.com%2Fimage%2Fupload%2Fv1697783332%2Fcdr7a7khsnoy4pipygwa.png&w=750&q=75", "imageKey": "99fd7af1-047a-b185-0a4c-b78e655662d3/question/491a1b6a3adea198f94a3b80037818f7.png" }, { "image": "https://www.thenational.academy/_next/image?url=https%3A%2F%2Foaknationalacademy-res.cloudinary.com%2Fimage%2Fupload%2Fv1697783340%2Funpi4z4o4yy01ltztqyl.png&w=750&q=75", "imageKey": "99fd7af1-047a-b185-0a4c-b78e655662d3/question/ff5c566c42d5ec2f7ea41c03c3e562a8.png" } ], "id": "90b89b65-a31b-4163-9ea7-707d7665ee53", "lessonId": "6f956a2d-4e50-d834-38b3-7b87114c117b" } ], "lessonId": "6f956a2d-4e50-d834-38b3-7b87114c117b", "meta": { "gradeStageId": "ks3", "subject": "Maths", "grade": "Year 8", "topic": null, "unit": "Graphical representations of data", "lessonCount": "11", "age": [ 12, 13 ], "gradeId": "age_12_13", "gradeStage": "Key Stage 3", "lesson": "Securing constructing bar charts by hand" } } ] }