Lesson video

Good day everyone, and welcome to another numerical summaries lesson with me, Mr. Grason.

Thank you so much for joining me in this lesson where we will construct and interpret different types of bar chart and pictogram.

Pause here to check the definitions of bar chart and pictogram.

First up, let's have a look at features that make for constructing a great bar chart or pictogram.

When following the statistical inquiry cycle, stage three is all about the processing and presenting of data that has been collected.

Within this stage, correct choice of visual representation is absolutely important to avoid the data or any conclusions from the data being misleading.

Visual representations include bar charts, pie charts, and pictograms, but what is a pictogram? Well, pictograms are one of the most visual ways of representing data.

Pictograms use simple icons that represent the data in some way.

If the data was about a group of people, the icon might be a person's silhouette.

If the data was about an animal, the icon might be a dog's paw.

Furthermore, if the data was about some leaves, the icon might be a leaf.

Notice how each icon is pretty simple and not too complicated.

This allows people to understand the icon easily as well as for flexible use of the icons or part of the icons when constructing a pictogram.

Pause here to think about or discuss what icon would you use for data about countries visited? To represent frequencies or data values, we assign the icon a value.

The value the icon takes is written in a key so the reader can interpret the pictogram clearly.

For example, in this pictogram, we have leaves that represent different plants.

Each icon is worth two leaves as we can see in the key at the bottom of the pictogram.

We use this information to conclude that plant one had 4 times 2 equals 8 leaves.

Notice how plant two has a 1/2 leaf icon.

We can then say that there are 1.

5 leaf icons.

Therefore plant two has 1.

5 times 2 equals 3 leaves.

In total, how many leaves did plant three have? It had 4 leaves, 2 times 2 equals 4.

This different pictogram now suggests that each icon represents five leaves, not the two from before.

Pause here to think about or discuss.

Does this value make sense in the context for this pictogram? Actually, no, this doesn't quite make sense for plant two, which has 1.

5 icons, this implies that plant two has 7.

5 leaves.

Choosing an appropriate value is important when constructing a pictogram to avoid any decimals in contexts where decimals do not make sense.

Pause again here to think about or discuss this new pictogram.

Does the value of 10 work for this icon? This time, the answer is yes.

Plant two would have the 10 leaves for the whole icon plus the 5 leaves for the 1/2 icon equaling a total of 15 leaves.

This works as the answer is now an integer number of leaves.

However, what if another plant is added but this time it has 17 leaves? Pause here to consider how you would represent this plant on the current pictogram whose key says one icon equals 10 leaves.

For this plant, you would need one icon that was split into tenths, 7/10.

In fact, this would be very challenging with an icon like this leaf, and even if it was possible to split this leaf up into exactly 7/10 of an icon, would it be easy for someone to identify that that icon represented 7/10 of a full leaf? Pause here.

Can you think of a better icon or key that could better represent the data for a plant with 17 leaves? As you can see, sometimes it can be very difficult to find a good icon and value to fit the data.

This is a massive limitation of pictograms. Izzy says, however, you can always choose a symmetrical icon and a value of two for a key.

Then you can always represent that data as a pictogram.

Do you agree with Izzy? Well, I do.

It's always possible to draw a pictogram in this way, but let's have a look at some examples to see if it's always sensible.

In example one, we can see that the frequencies of 10, 7, and 8 are represented in a pictogram with 5, 3.

5, and 4 icons respectively.

Each icon represents two votes and each 1/2 icon represents one vote.

In example two, we have frequencies of 28, 29, and 33.

I know for certain that there are 14, 14.

5, and 16.

5 icons on that pictogram, but I only know this because I halved the frequencies.

I certainly did not count all of those icons.

Pause here to think about or discuss which pictogram is harder to read.

For pictograms to be effective as a visual representation, the number of icons needed for each row should be kept fairly low.

This can be done by being mindful of the value of the icon, and increasing the value will reduce the number of icons needed.

However, this has to be done carefully.

In this example, data has been collected about the number of merits earned by Andeep each week and then represented as a pictogram.

Pause here to identify the key elements of this pictogram.

In this pictogram, we have a simple icon that can be easily spit up into halves or quarters.

We have icons that are all the same size and evenly spaced to reduce ambiguity, and we have a key with a well chosen value of four merits.

Four is sensible because we can have two merits as 1/2 an icon or one merit as a 1/4 of an icon.

For this check, this pictogram shows the amount of each material recycled every week by a local council.

Pause here to identify what important feature of a pictogram is missing.

The key is missing.

Without the key, I do not know how much of each material each icon represents.

For example, do three icons for paper mean three pieces of paper, three kilogrammes of paper? It is not clear at all.

Bar charts are super similar to pictograms except bar charts have a scale rather than a key and bars rather than icons.

However, both can be used to represent the same data.

There are features of a bar chart that are important to consider when constructing one accurately.

These are scales that increase equally such as this one that goes up in 10s with each interval.

Furthermore, we need gaps between each bar where each gap is the same length.

Furthermore, we need bars that themselves are the same width, so definitely no bars that are super narrow right next to a bar that is much wider.

This is definitely not sensible to have.

And lastly, make sure to label the axes so we know what the bar chart is even showing.

Pause here to fill in the missing label on this bar chart.

The missing label is frequency.

Make sure both axes are always labelled.

When constructing a bar chart, it is important to consider the increments of the scale.

For example, how much the scale you are using increases for every one unit taller a bar on the bar chart is.

This is similar to choosing the value of the icon on a pictogram.

For this frequency table, Jacob, Sam, Alex, and Andeep have all drawn a bar chart to represent the data shown in that frequency table.

They have all chosen different scales.

Pause here to think about or discuss who has chosen the most sensible scale.

Let's have a look at everyone's bar chart starting with Jacob's.

Jacob's takes up a lot of space since his scale goes up in twos.

However, Sam's scale seems a little bit more reasonable than Jacobs.

It is still a big enough bar chart that you can see the frequencies and the variation in the data easily without taking up as much space as Jacob's.

We can read all of the actual frequencies rather than finding estimates of them.

Alex's bar chart looks quite different from the others.

Alex is the only pupil who chose not to start their scale at zero.

Notice how this one starts at 34 instead.

Alex's chart is of a reasonable size as increments of two are used.

Because of this, it can be read easily and accurately.

However, Alex's bar chart is misleading.

At a glance, one could misinterpret that box C has twice the frequency as box B.

This is not true.

Furthermore, by only looking at the lengths of the bars, one might assume that box C has over five times the frequency of box D.

The reality is, however, that box C doesn't even have a frequency that's double that of D.

The fact that this bar chart is misleading is down to the frequency scale not starting at zero.

And lastly, (sighs) Andeep.

Andeep's scale makes the chart look far too small.

The bar chart loses any sort of accuracy or purpose.

Interpreting Andeep's bar chart requires estimation of its frequencies and isn't really that helpful at showing the variation between each box.

For this check, pause here to suggest a sensible scale for a bar chart to represent this data.

There are many suitable answers such as fours or tens.

Great stuff.

Onto the practise.

For question one, pause here to complete the pictogram using this frequency table For this question, we have a partially completed bar chart.

Before drawing on the bars for iris and dahlia, we first have to use the height of the current bars for tulip and rose to figure out the scale on the Y axis, the scale that represents the frequencies of each datum.

Pause here to find the correct scale of the y axis and then complete the bar chart.

For question three, pause here to identify the errors in both the bar chart and pictogram.

And finally, question four, both the bar chart and pictogram represent the same dataset, but both are incomplete.

Pause here to complete them both.

Great work.

Here are the answers.

Pause here to compare your pictogram in question one to the one on screen.

And for question two, well done if you identified that each square on the Y axis represents a frequency of three.

This was most easily identified by spotting that the bar for tulip was six squares tall, meaning each square needed to represent a frequency of three for the total frequency of that bar to be 18.

The height of iris is eight squares and dahlia seven squares.

For question three, the bar chart had no vertical axis label.

Does the height of each bar represent frequencies or not? Furthermore, it uses uneven increments.

10 to 15 to 30 is certainly not a linear scale.

For the pictogram, it has no key and an over complicated icon.

I'm not sure if those partial rabbits are 1/2 rabbits or, I don't know, 13/30th of a rabbit.

It is just too unclear.

And finally, for question four, pause here to compare your diagrams to the ones on screen.

Now that we know how to construct a bar chart and pictogram, let's try interpreting ones that we might see when collecting secondary data.

Pictograms are very easy to understand and interpret due to their simplistic design, assuming, that is of course, suitable icons and values are chosen.

The pictogram shows the amount of sales on one day for three different shops.

Pause here to think about or discuss.

What information can you gain from this pictogram? Give as many details as possible.

Your interpretations could include that shop one sold the most items on this particular day, whilst shop two sold the least number of items. Shop three sold 20 fewer items than shop one due to that 1/2 an icon less.

For this check, pause here to identify which week yielded the least number of apples.

Week two yielded the least at only 80 apples.

Bar charts are useful visual representations of data as well and don't have some of the limitations of pictograms, such as needing representative icons that can clearly be spit up into 1/4 or 1/10.

For example, let's have a quick look at interpretations of this bar chart.

The weekend days had more visits than the weekdays as the weekend's two bars are higher than all five of the weekdays.

Tuesday was the busiest day out of all of the weekdays whilst Sunday was the busiest day out of the whole week.

Furthermore, I could say that the weekend represents a total of 47 visitors as I add the frequencies of Saturday and Sunday together by considering the heights of both bars.

Pause here to consider which colour was the most popular.

Purple was the most popular with the tallest bar at a frequency of 10.

This check will require a little bit more time to do.

Pause here to answer how many pupils in total were asked their favourite colour? I take the heights of each bar, 6, 8, 7, 9, 10, 6, and 8, and add them all together to get 54 pupils.

Does it matter that the bars in this bar chart are not ordered in terms of shoe size smallest to largest? Well, I mean we can still do some interpretation of this data.

We can still see that six is the most common shoe size, but is that really it? By putting the shoe sizes in order, can we gain any more insight into the data? Well, we can.

The ordering of the data allows us to see the distribution of all of the shoe sizes more easily.

Often the data collected is about non-numerical data, qualitative data, for example, colours, animals, food, et cetera.

Should the bars for those examples be in some sort of order? Well, in this context, no.

This type of data often does not have a helpful order.

However, contexts such as months are also qualitative and will have an obvious order.

And so it's best to put those bars in that sensible order.

For this check, is the following sentence true or false? The bars of a bar chart always need to be in a particular order.

Pause now to choose true or false.

That statement is false.

Pause now to choose the correct justification for your answer.

Some data have a known and relevant order, but not all things do.

Brilliant.

Onto the second practise task, pause here to identify which location had the most hours of sunshine and identify how many fewer hours of sunshine Stornoaway got compared to Valley.

And pause here to interpret this bar chart showing the number of cars parked on driveways.

And finally, question three, the editor of the Daily Oak newspaper has received this bar chart and extract from one of their journalists.

Pause here to explain in as much detail as you can whether the article matches the data given.

Brilliant.

The answers are Valley had the most sunshine and Stornoway got 800 hours less sunshine than Valley.

For question two, three driveways each had two cars and 12 driveways in total had at least one car on them.

12 is the sum of eight, three, and one, the heights of the three bars showing at least one car.

And this data was most likely collected during the daytime as most driveways were empty, meaning people were either at work or visiting somewhere.

And for question three, the bar chart doesn't make any timeframe clear.

The editor would need to check the original data or remove this claim.

Furthermore, this scale is highly misleading.

Company B did not have double the amount of company A, because the scale on the Y axis did not start at zero.

However, company D was the least wasteful out of the four companies as the bar for D was the shortest.

Thank you so much for your effort in a lesson where we have looked at bar charts and pictograms as visual representations of data.

We've seen that pictograms use icons to represent quantities of data whilst bar charts use bars and scales to represent that same data.

We've seen that technology can be used to construct bar charts for larger data sets.

Thank you all so much for joining me for this lesson.

So until next time, take care.

Have an amazing rest of your day and goodbye.