Lesson video

Hello, my name is Dr.

Rowlandson and I'm excited to be guiding you through today's lesson.

Let's get started.

Welcome to today's lesson from the unit of graphical representations of data with scatter graphs and time series.

This lesson is called Constructing Time Series Graphs.

And by the end of today's lesson, we'll be able to construct time series graphs.

This lesson will introduce a new keyword, which is time series graphs.

Time series graphs show data over a period of time, the time period, it's always shown on the X-axis and data points are joined chronologically by line segments.

We'll see plenty of examples of that during today's lesson.

The lesson will contain two learn cycles.

In the first learn cycle, we're going to focus on plotting time series graphs, but in the second learn cycle, we're gonna look at a bit more detail at some of the decisions you need to make when you are plotting these graphs.

Let's start off with plotting time series graphs.

Here we have a table that contains part of a dataset from the Office of National Statistics, the ONS.

The data is about the percentage of households in great Britain with internet access.

In the left hand column, we have the years, and in the right hand column we have percentages, and that is the percentage of households in the UK with internet access on each of those years.

Now, this table only contains rows with 2005 up to 2010, but the entire dataset contains all years from 2005 to 2020.

Jacob looks at this and he says, this looks like bivariate data, so I'll plot a scatter graph with years as the independent variable.

So he does that and it looks a bit like this.

What do you notice about the points in this scatter graph? Pause the video while you think about this and press play when you're ready to continue.

Well, both Jacob and Laura are gonna help us with this.

Laura says, with scatter graphs, I often find that there are some points that are directly above other points, but that's not happened with this data.

That's because one data point has been recorded for each year.

And Jacob notes that also the points are equally spaced across the horizontal axis on this.

That doesn't usually happen with scatter graphs either.

Well, that's because this data has been recorded at regular time intervals.

So while this data may have looked like it would've been suitable for a scatter graph because it was two columns of numbers, the year is not really a measurement in the same way that percentages of households with internet access is a measurement.

It happens at regular time intervals, and we take one recording each time.

So rather than a scatter graph, a time series graph may be more appropriate.

Time series graphs are line graphs or line segment graphs with the time on the horizontal axis.

The vertical axis contains some sort of measure such as frequency or percentage or whatever it is you are measuring.

This measure is plotted against time at regular time intervals, which is why these points are equally spaced out across the horizontal axis and the points are joined chronologically by line segments from one point to the next.

Let's take a look at an example of this together now.

Here we have a table that is part of a dataset from the ONS about domestic internet access in Great Britain.

By domestic, it means internet access at home.

This data focuses on a particular sample within the population.

It is households with one adult that is age 65 or over, and we can see we've got the years across the top row and we have the percentage of households from this sample which have internet access.

This data could be presented as a time series graph because the measurements are taken at regular time intervals.

Let's do that together.

So if we wanna plot this on a time series graph, we first need to label and scale the axes with time on the horizontal axis like so.

And then we need to plot each data point on the graph.

So let's do that together.

In 2012, 36% of the households in this sample had internet access, and then in 2013, it was 40%.

And then we can plot the rest of the points in the same way.

Once we've done that, we need to join up the data points with line segments like so.

Now the data can be plotted as points like you can see here, but when plotting by hand, you may find it easier to use crosses instead.

And sometimes at times series graphs are presented with a point size, it's minimalized, so you can't actually see the individual points.

Now a time series graph doesn't just have to be used for one set of data.

When you have the same data for multiple samples of the population, they can be plotted together on the same time series graph like we can see here.

But the problem of what you can see right now is you don't necessarily know what each of these two sets of data are about.

So in these cases, a key is required to indicate which sample each line represents.

So in this case, the black line with crosses represents households with one adult age 16 to 64, and the purple line segments which have spots on, they represent households with one adult age 65 or over.

And by doing that, we can make comparisons between the two samples.

So let's check what we've learned.

The time series graph here shows the percentage of households in Great Britain with the internet access for two samples of the population.

My question to you is, what is missing from this graph? Pause the video while you write it down and press play when you're ready for an answer.

A key is missing from this time series graph.

Otherwise, we don't know what these two samples represent.

What does the horizontal axis on a time series graph show? Is it A, the categories; B, the frequency; C, the percentages, or D, the time? Pause the video while you choose and then press play when you're ready for an answer.

The answer is D, time.

Here we have an axis from a time series graph.

A point on the vertical axis has been marked with P.

What is the value of P? Pause the video while you write it down and press play when you're ready for an answer.

The answer is 16.

Each of those small intervals represent two because there are five of them between zero and 10, and the P is positioned at three of those intervals above the 10, so it must be 16.

Okay, it's over to you now for task A.

This task contains two questions and here is question one.

The table shows data taken from the office of national statistics about the percentage of households with internet access focusing on households with two adults age 65 or over.

And what I'd like you to do please, is plot a time series for this data.

Pause the video while you do that and press play when you're ready for question two.

And here is question two.

Here we have another table that shows data from the ONS, but this one is about how often adults use the internet.

The data shows a number of adults in the millions who use the internet either daily or weekly each year.

And when it says weekly, it doesn't include daily within that figure.

So if we look for example at the number 29 in that table, that represents 29 million people.

And what you need to do is plot these two sets of data on a time series graph and you'll need to draw a key so you can show what each line represents.

Pause the video while you do that and press play when you're ready for some answers.

Let's see how we got on with that.

Then in question one, we need to plot a time series graph for this data and hopefully it looked a bit like this.

And then question two, when we plot our time series graph here, we should have something looking a bit like this.

Now in this one, you can see that one set of data has spots and if one has crosses, you may have done something different to that or use different colours, but you definitely need a key and here's the key for this data.

Well done so far.

Now let's move on to the second learning cycle of today's lesson, which focuses on the all important decisions we need to make when we are plotting time series graphs.

Here is a data cycle that is often used when conducting investigations that handle data.

And decisions we make about our time series graphs may affect different parts of this data cycle.

For example, when preparing a time series graph, you may need to decide what time intervals to use whether that is yearly, monthly, weekly, daily, and so on.

And this will depend on what question your data investigation intends to address.

And once the question has been decided, data needs to be collected and the time interval you intend to use may affect what data needs to be collected for that.

Once we have our data, we then move on to organising it and presenting it.

Well, the horizontal axis of a time series graph represents time.

Therefore the time interval that was used to collect the data will affect how the horizontal axis is scaled and how the data appears.

And the next part of this data cycle is about analysis and interpretation of that data.

The wave at the time series graph appears may affect what you are able to observe and interpret from that data, and this will affect the outcomes and action stage of a data cycle.

Ultimately, these decisions we make may affect what conclusions are made and what is reported from the data investigation and any potential actions that are taken as a result.

So there are some decisions that need to be made of a time series graph relatively early in this data cycle and the effect each and every stage of that cycle as well.

Let's take a look at an example together.

Aisha wants to collect data and plot a time series graph to show temperatures in Sheffield between 2012 and 2019.

And we've got the template for our time series graph here.

But what different time intervals could Aisha use on her horizontal axis? Pause video while you think about this and press play when you are ready to continue.

Let's look at some options together.

The data could be plotted for every month of each year, like we can see here.

We've got the years and for each year, there are 12 data points or data could be plotted for every quarter or season.

That means every three months and that'll look a bit like this.

Or another option is to plot a single data point for each year.

And if you do that, you may need to decide what each data point represents.

Does each data point represent a particular day of the year and preferably the same day every year, or does it represent the average for the whole year? These decisions about time intervals may depend on what you want to be able to observe from your graph.

For example, when plotting a time series graph about temperatures, by plotting a data point for each month, it can be helpful to observe how temperatures fluctuate throughout the year if that's what you want to focus on.

On the other hand, plotting a data point for each year can be helpful to observe how temperatures compare from one year to the next.

It really depends on what it is you want to use the graph for.

When plotting a time series graph, you may need to make decisions about how to scale your axes as well.

The vertical axes on a time series graph represents the variable that is being measured, and one consideration is whether or not to start the scale at zero.

Let's take a look at some examples of that now.

This time series graph shows data taken from the ONS about the mean number of hours worked per week by full-time workers.

So the horizontal axis has time measured in years and the vertical axis has a measure which is the mean hours work per week for full-time workers each year.

And what you can notice here is that the vertical axis does not start at zero, and when this happens, sometimes it looks like you can see here and other times it might be highlighted, more explicitly with an axis break.

Now Sophia and Lucas are looking at this and Sophia says, it looks like the amount of time people work increased a lot from 2009 to 2014.

But Lucas says, I wonder what it would look like if the vertical axis began at zero.

Try and imagine that for yourself.

It would look a bit like this.

The same data is plotted again, but this time with the vertical axis starting at zero.

It looks quite different, doesn't it? Sophia says, it now looks like the time people spent working has been fairly consistent.

The changes between years are so small and Lucas says, but I wonder how important those small changes are in the context of this data.

Decisions about the scale on the vertical axis may depend on what amount of change would seem important in the context of that data.

For example, if we look at this particular part of each graph, it only looks like it changes a tiny bit on the left hand graph, but it looks like it changes quite a bit on the right hand graph.

That change is 30 minutes.

How significant would work in an extra 30 minutes per week seem to you? If it's not very significant, if it's only a tiny change, then the left hand graph shows that.

But if it seems like a big change, then the right hand graph shows that.

Let's check what we've learned then.

True or false: Time series graphs always use years as a time interval? Pause and choose either true or false and then press play when you're ready for some justifications.

The answer is false.

So what's our justification for that? Here are two options to choose from.

Pause video while you do so and press play when you're ready for an answer.

It's false because the time interval used in a time series graph depends on what the graph is intended to show.

Which time intervals are regular and quarterly? You've got four options to choose from, and it may be more than one.

Pause the video while you choose and press play when you're ready for an answer.

The answers are B and C, quarterly being every three months.

Okay, it's over to you now for task B.

This task contains two questions, and here is question one.

You have a table that shows data from the Met Office about rainfall in Sheffield.

You've got the year and you've got the average monthly rainfall for each year.

So please could you represent this data as a time series graph and this time, unlike in task A, you'll need to make decisions about how to scale your axes.

Pause the video while you work through this and then press play when you are ready for question two.

And here is question two.

This table shows data from the Met Office about rainfall in Sheffield, but this time, you can see it's quarterly.

Please could you represent this data in a time series graph? Pause the video while you do that and press play when you are ready for answers.

Let's take a look at how we got on with that then.

In question one, our time series graph will look something a bit like this.

We have years going across the horizontal axis and we have the average monthly rainfall going up the vertical axis.

Now, you may have used a different scale in your vertical axis or you may have not started at zero, but hopefully the overall shape of your time series should be the same.

The main thing that might differ is how pronounced or subtle those changes appear on your graph.

Pause the video while you check this graph against your own and then press play when you're ready to take a look at question two.

Let's now look at question two.

Our time series graph should look something a bit like this.

This time our horizontal axis shows each year in quarters, and then our vertical axis once again shows average monthly rainfall.

But if you scaled your vertical axis differently to this one, you should still have the same overall shape, but the changes between years may be more pronounced or it might be more subtle.

Pause the video while you check this graph against your own and then press play when you're ready for today's summary.

Fantastic work today! Now let's summarise what we've learned.

A times Series Graph is a visual representation of how data changes over time.

The horizontal axis of a time series graph represents the time and any time interval could be used so long as it's regular and also appropriate for the data.

The vertical axis on a time series graph represents a measurement, frequency, percentage or whichever variable is being used in the data.

And consecutive points on a time series graph are joined by straight line segments.

Thank you very much.

Have a great day.