Lesson video

Hello and welcome everyone to another numerical summaries lesson with me, Mr. Gratton, thank you for joining me in a lesson where we will construct and interpret different types of bar chart composite bar charts and bar-line charts.

A bar chart is a graph consisting of bars that represent the frequency of objects or groups.

First up, let's construct some bar charts.

Basic bar charts can look slightly different.

There are a variety of different ways a bar chart can be represented, but each variation is essentially the same and can represent the same types of data.

A bar chart may have column bars or horizontal bars, or they may have lines instead of bars.

Each type is perfectly fine, as long as one bar chart only has one type of bar or line.

However, you can still compare two different bar charts with each one having a different type of bar.

Sometimes data that are collected can be split into groups known as strata.

Each group of data can then be represented by one bar on a bar chart.

For example, both Laura and Alex have recorded how long they watched TV for every day for one week.

Pause here to think about or discuss how this information could be represented on either one or two bar charts.

Here we have two bar-line graphs, each one showing the data for one pupil.

Each graph is perfectly correct with all the features that make for an accurate bar chart, such as the axes being labelled, gaps between each bar line and a Y-axis that is consistent in scale.

Because both graphs are fully accurate.

A comparison between Laura's and Alex's TV habits is possible using these two bar line graphs.

However, it may be easier if we put all this information into just one graph, but how? How could we turn all of this information into just one graph? Well, let's see.

Notice how each person's data is now presented on just one bar chart.

This is called a comparison bar chart because, well, it allows for easy comparison between two different data sets.

In this case, a comparison between the time Laura and Alex spend watching TV each day.

Whilst a key is necessary to know which colour of bar belongs to who, it is also important to ensure that there is consistency by having the same person on the left and the right of each pair of bars.

In this comparison, Laura's data is always on the left of each pair, whilst Alex's is always on the right of each pair.

For example, on Monday, we can see that Laura spent about two-and-a-half hours watching TV, whilst Alex spent three.

Laura's data was on the left and Alex's data was on the right.

Furthermore, the thickness of each bar must be consistent across both people so that there is no ambiguity over the importance or frequency of each person.

It is possible to have comparison bar charts that show many people's data.

For example, we could modify this bar chart so it shows the TV habits of Laura, Alex, Izzy, and Lucas.

Pause here to think about or discuss what this comparison bar chart could look like when showing the data of four people and what the possible limitations could be when having multiple data sets on one graph.

An alternative to a comparison bar chart that also allows for comparison between different data sets is a composite bar chart.

This is also known as a stacked bar chart.

As this type of bar chart stacks different groups of data on top of each other, rather than displaying them next to each other, here's how we can make a stacked bar chart for Laura's data.

So Monday goes at the bottom, then Tuesday above it, then Wednesday, Thursday, Friday, Saturday, Sunday, taking all of the same data that was in the individual bar chart for Laura and stacking those frequencies or results above each other.

As you can see on the right bar chart, all of Laura's data has been stacked into one tall bar, still separated into individual groups.

Each group representing one day of the week.

We can also have multiple different composite bars next to each other so we can compare different data sets.

Here's Alex's composite bar chart.

Again, Monday, then Tuesday, Wednesday, Thursday, Friday, Saturday, and Sunday.

Pause here to think about or discuss what is the biggest benefit of representing the data this way compared to a comparison bar chart.

Whilst comparisons between individual days may be a little bit more tricky, comparison bar charts are absolutely amazing for comparing the totals of different data sets.

For example, here we can see that Alex's total TV time during the week was greater than Laura's.

However, it is still possible to identify the TV time of each individual day.

We can do this by calculating the individual heights of each part of a bar.

To calculate only the hours for Saturday, on Alex's composite bar, we can identify the top height of the Saturday bar at 22 and the bottom height of the Saturday bar at 15.

And subtract these two values to get seven.

Seven represents the number of hours Alex watched TV on Saturday.

This is consistent with the height of the bar on the comparison bar chart.

In conclusion, the frequency or measurement associated with a single group of data on a composite bar chart can be found through a subtraction of two values.

For this check, we have a part of a composite bar chart.

Pause here to calculate approximately how much data is represented by the bar marked A.

Approximately 350 from the calculation of 1000, takeaway approximately 650.

There are two types of composite bar chart.

They can have either a vertical scale showing frequencies or proportions.

Each one is useful for different reasons.

Pause now to think about possible benefits of both.

To construct the composite bar chart with a percentage scale, the proportion for each group needs to be calculated.

This can be done by a few different methods where method one is to take a frequency, write it as a fraction, and then convert that fraction into a percentage.

For example, 126 out of the 250 total vehicles are car and 126 over 250 can be converted into the percentage 50.

4%.

We can then follow this exact same method for all other frequencies to get the percentage for that data.

Method two is to scale the total frequency of a dataset to 100 by using the proportionality of the total frequency of the dataset and the fact that the total percentage is always 100.

In this example, we have as a multiplier 0.

4, and so we can multiply each datum by 0.

4 to get its associated percentage, like so.

And now pause here to work out the proportion for oak using this frequency table using either of the two methods that we just saw.

And the answer is 15.

2%.

Great stuff onto the practise.

For question one, pause here to construct a bar-line graph.

Make sure that the graph is fully accurate and has all the features that make for a good bar chart.

For question two, here we have an incomplete composite bar chart.

The black bars correctly represent the data for Oakfield Academy and any white bars that are drawn or need to be drawn represent Acorn Park Academy.

Pause now to complete this composite bar chart.

For question three, both this composite bar chart and frequency table represent the same data, but both are incomplete, complete both representations including the key for the composite bar chart.

Brilliant effort so far.

Pause here to have a look at one example of this correct bar line graph.

Compare this one to your own and identify the common features between the two.

Do you disagree with any of the features showed in this example? And if so, why do you disagree? And pause here to compare your composite bar chart to this one.

Well done if you added a key.

And lastly, for question three, we have this composite bar chart.

You should have drawn on Laura's bars for Thursday and Friday, which have frequencies of four and two, which translate to two and one squares in height on the graph.

The total frequency of Laura's bars is therefore 25, which we can see is ever so slightly less than Jacob's total bar height of 26.

Also a very well done if you are able to label the key with all of the days of the week.

Pause here to check whether your completed composite bar chart fully matches this one on screen.

Now that we are familiar with these different types of bar chart, let's see if we can interpret bar charts that we see in the news or in statistical investigations.

For this bar-line graph, Lucas is playing a game that he can either win, draw or lose.

His last 50 results are displayed here.

Pause here to think about or discuss the answers to these three questions.

Lucas drew 18 games, Lucas didn't lose 30 games.

We can identify this information by adding the two bars that represent not lose, win at 12 and draw at 18.

We can then use this information and compare it to the 20 losses to conclude that the third statement is false.

Whilst his most common result was lose at 20, Lucas also did not lose 30, and therefore Lucas not losing is actually the majority.

For this check, pause here to consider which of the following statements are correct for Aisha's results.

There are 45 results displayed across the three bars.

Aisha won more than she lost and her modal result was draw, because the draw bar was taller than either the win bar or the lose bar.

We see composite and comparison bar charts a lot during real world investigations.

However, some of these graphs are more or less useful than others.

In this particular set of composite bar charts, we see the number of working adults in two different locations, Cambridge and Birmingham.

Due to the population difference of these two locations, this composite bar chart is incredibly unhelpful when trying to make any comparisons.

For example, of course more people in Birmingham work from home compared to Cambridge.

The population of Birmingham is well over five times larger.

We don't need this bar chart to assume this conclusion.

However, we've got this type of composite bar chart showing proportions rather than frequencies.

This allows us to see the distributions of different travel methods across both locations.

For example, whilst more people in Birmingham work from home, a higher percentage of people in Cambridge work from home.

A fact that we could not easily tell from the previous graph.

Furthermore, this is also true for adults who cycle to work.

In fact, we can see just how much higher a proportion of Cambridge adults cycle to work when compared to Birmingham adults.

For this check, complete the sentence by writing the correct location in the correct place.

A higher proportion of working adults in Birmingham drive compared to working adults in Cambridge.

Brilliant work for this practise task.

Pause here to interpret this bar-line chart to answer the following questions.

On this particular day, which flavour is the least popular? How many sales did the ice cream parlour make on this day? And complete the following sentence, strawberry was as popular as blank on this particular day.

On to question two, using the information from this comparison bar chart, draw from scratch yourself and then label a fully accurate composite bar chart.

Making sure to add a key as well.

Pause now to do this.

And lastly, for question three, evaluate which chart is most effective when being used to answer the following questions.

How many semi-skimmed milk bottles were sold in total.

Which size of bottle was the least sold across all three different types of milk.

And semi-skimmed and whole milk had a similar proportion of which sized bottles? Pause here to first investigate all three charts and identify what sort of information you can gain from each one, and then figure out which chart can be used to answer each question.

Your answer should include both an answer to the question and the chart that you used to find that answer.

Onto the answers.

For question one, the least favourite flavour of ice cream was chocolate.

The total sales was 95.

This is the sum of the heights of each of the four bar lines.

And vanilla was as popular as strawberry on this particular day.

For question two, pause here to compare your composite bar chart to the one on screen.

And lastly, for question 3A, chart B was helpful in informing us that there were 150 semi-skimmed bottles.

For part B, using chart A, the six pint bottle was the least sold.

And for part C using chart C, the one pint and two pint bottles had similar proportions in semi-skimmed and whole milk.

Great interpretation skills everyone, in a lesson where we have looked in detail at two different types of bar chart, the comparison bar chart and the composite bar chart, where some of them are also bar-line charts.

We've looked at them both in terms of how to draw them accurately and also when interpreting them.

We've also seen that technology can be used to construct these bar charts from much larger data sets, which allows for easier interpretation of that data.

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

I hope to see you soon for more statistics adventures.

But until then, take care and have an amazing rest of your day.