Lesson video

Hello, my name is Dr.

Rowlandson, and I'm thrilled that you're joining me in 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 Interpreting Time series Graphs.

And by the end of today's lesson, we'll be able to interpret time series graphs, including commenting on trends.

This lesson will use the term time series graphs quite often throughout.

Time series graphs show data over a time period.

The time period is always shown on the X axis, and data points are joined chronologically by line segments.

The lesson contains two learning cycles.

In the first part of the lesson, we're going to be identifying trends in time series graphs.

And then the second part of the lesson, we're going to be identifying narratives in time series graphs.

Let's start off with identifying trends.

Here we have a time series graph that shows data from the Office of National Statistics, the ONS.

The data is about the average cost to rent a residential property in the UK.

So the horizontal axes shows the months with January every two years marked out as a reference, and the vertical axes shows the UK average monthly rent, which is in pounds.

Now Laura and Sam are taking a look at this graph, and Laura notes something.

She says, "I thought the points was supposed to be joined "by straight line segments.

"So why does this line look so squiggly?" Sam comments that, "The data is plotted monthly, "which means there are 12 points for each year.

"So even though the points "are joined by straight line segments, "the overall line appears squiggly "because the points are so close together." So now we've got that cleared up, time series graphs can be used to observe any trends in the data over time.

What observations can be made from this data? Pause the video while you take a look at this time series graph, and see what you observe about any trends in this data, and then press play when you are ready to continue.

Well, let's hear from Laura and Sam.

Laura says, "The average monthly rent "seems to increase slightly most months, "doesn't really go down at any point, "but it does seem to keep going up and up and up." And Sam says, "It has increased more "during some years than others," and we can see that at points where it appears steeper.

A trend in a time series graph can be used to predict data for the future.

However, this only be an estimate, as unknown future events may affect the data.

So how can we go about doing that? Well, if the data appears to be changing at a constant rate, then one method could be to model this with a straight line, a bit similar to a line of best fit on a scatter graph.

Let's try that now with this time series graph, I could draw a straight line here, and then I could use this line to make some predictions for dates that are beyond the range of my data, for example, January, 2025, I could use this line to predict that the UK average monthly rent in January, 2025 would be 1,200 pounds.

Now you might note that that value is pretty much the same as the last data point we have in this time series graph, which is just before January, 2024.

But we've previously noted that the UK average monthly rent is increasing slightly each year, so it wouldn't have increased from our last data point to this one.

So why has that happened? Well, one reason could be because we've based our trend analysis on all the data from January, 2015.

However, the data for UK average monthly rent seems to increase more sharply from January, 2022 onwards.

The data that you choose to use for your trend analysis may affect the grading of the line.

For example, if this trend was just based on data since January, 2022, instead it might look a bit like this.

And if we use this to make a prediction for January, 2025, we'll get a value of 1,300 pounds, and that is more but our last data point just before January, 2024.

However, the further a trend is extrapolated into the future, the less reliable our predictions about the data may become.

So for example, we could continue this trend and make a prediction for January, 2027.

However, there is more than three years of unknown data between our last recorded data point and January, 2027, and a lot can happen in three years.

Some sort of event might happen that might cause rent to increase more sharply again, or some sort of event might happen that might cause rent to stop increasing.

We don't really know, so we've gotta be really careful when we are extrapolating into the future, because the further into the future we go, the less reliable our predictions may be.

Sometimes a time series graph may show data that increases and decreases periodically.

For example, here we have a time series graph that is based on data from the ONS, the Office of National Statistics, about the amount of money spent each week on retail in the UK.

Now, the horizontal axes shows us time with the January of each year marked out as a reference, and the vertical axes shows the average weekly retail value, which is in billions of pounds.

So when you look at this graph, what observations can be made from this data? Pause the video while you think about this and press play when you're ready to continue.

One thing you might notice is that the amount of money spent on retail tends to increase and decrease during each year, and this seems to happen at regular intervals.

For example, retail value is at its highest towards the end of each year.

That's probably because we are leading into the holiday season there.

And retail value is usually at its lowest in January, and then tends to increase steadily until around September.

Pretty much each year it's at its lowest in January, it increases till the middle of the year, and then sort of levels off a little bit, dips down a bit, and then shoots up for December.

However, you may have noticed that January, 2020 was a bit different.

This was an unusual year because retails at its lowest at the end of the first quarter in April.

And the reason why the data for 2020 looks a bit different for this year could be because this was the year that the UK locked down in response to a pandemic, and lots of shops close their doors for a temporary period of time, and that happened at the end of March, so it would've affected the retail in April.

Determining whether a measure is generally increasing or decreasing can be more difficult for data that fluctuates periodically like below.

The average weekly retail value is going up and down, up and down all the way through this data, so how do we decide whether it is generally increasing or decreasing over the years? One method could be to compare data from the same point of time each year.

For example, if we try and draw a line as close as possible to all the data from December of each year, it might look a bit like this, and we could do the same thing for January of each year.

Both of these lines have a positive gradient, so that will suggest that the average weekly retail value is generally increasing.

So how do we use trends in this situation, to make predictions for their future? Well, when predicting future data, it may be more appropriate to based estimates on the same months from previous years rather than the overall data.

For example, this time series graph shows data up to January, 2024.

So if I wanted to use this data to estimate the average weekly retail value for December, 2024, I would need to use the trend line at the top because that one is in line with all the previous Decembers.

And if I did that, I would get 11 billion 250 million pounds.

But if I wanted to make an estimate for January, 2025, then I would use the bottom line because that is corresponding with previous January's, and that would predict 8 billion 250 million pounds.

And comparing these two figures, it makes sense.

We expect the figure for December to be higher than the figure for January, and we expect both of them to be a little bit higher than previous years, because generally the data is increasing over time.

However, these estimates are based on the assumption that the pattern we've observed so far in the data will continue to repeat in the future.

And as we've seen with 2020, that might not necessarily be the case.

Some sort of event might happen that might cause a change in the data in some way.

So let's check what we've learned.

Here we have part of a scale from a time series graph.

A value has been marked P on the vertical axis.

My question to you is 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 50.

We can see there are five small intervals between zero and 250.

So divide 250 by five, you get 50 for each interval.

So what is the value of Q then? Pause the video while you write it down and press play when you are ready for an answer.

The answer is 400.

That point is three small intervals above 250, so that's 250 plus three, lots of 50, which is 400.

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

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

We have a times series graph that shows data taken from the ONS, that's the Office of National Statistics.

It's about the average monthly rent for three regions in the UK, London, the Southwest, and the Northeast.

You need to use this graph to answer the three questions, A, B, and C.

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

And here is question two.

This time series graph shows data taken from the ONS about the total number of visits abroad from the UK each quarter, a quarter is three months.

You've got the visits abroad per quarter, and that's in the millions.

So use this graph to answer questions A to D.

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

Let's take a look at some answers now.

With question one, you may want to start by drawing a trend line on each of those three sets of data.

And then we can use that to make some predictions about the average monthly rent for each region in January, 2024.

And that would be 2,000 pound per month for London, 1,100 pound per month for the Southwest, and 650 pound per month for the Northeast.

Now your answers may vary slightly compared to these, depending on precisely what method you used, and how precisely you were able to make readings from the scale.

But hopefully you got some answers that are pretty close to these.

And then part B, you had to use the graph to predict the average monthly rent for each region in January, 2025.

Well, for London it is 2,125 pounds per month.

For the Southwest it is 1,150 pound per month.

And for the Northeast it is 675 pound per month.

And once again, your answers may vary slightly depending on how you did it.

And for part C, it said which set of predictions are likely to be more reliable, part A or part B? Well, it's the predictions from part A, and that's because the predictions for part B were further into the future.

And then question two.

In this time series graph, we had to first decide which quarter of the year tends to have the most visits abroad, that is the third quarter of the year, which is July to September, the summer.

And then which quarter of the year tends to have the least visits abroad? Well, that's the first quarter of the year, and that is January to March.

And part C, we need to user graph to predict the number of visits abroad for each of these quarters.

So the first quarter of 2018 would be approximately nine million visits.

For the third quarter of 2018, that'd be approximately 12,250,000.

And for the first quarter of 2019, that would be approximately nine million, 500 thousand.

And again, your answers may vary slightly depending on precisely how you drew those lines, and how accurately you were able to take the readings from the vertical axis.

And Part D, which prediction part C is likely to be the least reliable? That would be the first quarter of 2019 because it's the furthest into the future from where this data finishes.

Great job so far.

Now let's move on to the second part of this lesson, which is all about identifying narratives from time series graphs.

Sometimes the effect of national or global events can be observed in data presented in a time series graph.

For example, this time series graph shows data from the ONS about the number of visits abroad from the UK each year.

What observations can be made from this graph? Pause the video while you think about this and press play when you're ready to continue.

Alex notices that, "The number of visits abroad "decreases very suddenly in the year 2020, "and then it increases again." So something clearly happened there that affected the data quite dramatically.

Izzy explains that, "The UK went into a national lockdown "that year in response to a pandemic." This meant that there were lots of travel restrictions that prevented people from going abroad.

So that's why the visits abroad dropped down very suddenly in year 2020, but then started to increase again afterwards as the UK came out of its lockdown.

So this graph is an example of where you can see the effects of an event very very clearly within a dataset.

Here's another example.

The time series here shows data from the ONS about the average annual income per person each year.

The bottom line is the median annual income, and the top line is the mean annual income.

Pause the video while you think about any observations that you can make from this data and press play when you are ready to continue.

Well, let's hear from Jun and Lucas, Jun notices that the mean income is always greater than the median income, how come that is? I wonder if you can think about why the mean might be greater than the median? Well, one reason could be to do with outliers? Lucas says, "Outliers affect the mean "more than it affects the median." So if the mean is higher than the median, it could mean that there are outliers that are at the higher end of the data that are pulling the mean up higher than the median.

Now you might notice that the mean and median are relatively close for the first 20 years of this data, but from around about year 2000 onwards, they separate more apart.

Can you think about why that might be? Pause the video while you think about what might cause the mean to increase more than the median, and then press play when you're ready to continue.

Well, one explanation could be that average annual incomes in the top half of data might have increased, and that will pull the mean up but not necessarily the median, because all those data points were already above the median.

Alternatively, another explanation could be that the average annual incomes in the bottom half of data, they may have increased, and that will cause the mean to increase, but not necessarily the median so long as that middle point in the data doesn't change.

Now Lucas knows his economics history pretty well, and he notes that a national minimum wage was introduced in the year 1998.

So this means there are likely to be more outliers with a higher wages than lower wages.

In other words, the national minimum wage reduces the chance of any outliers at the bottom of the data range.

However, there isn't a national maximum wage, so there are still outliers at the top of the data range.

So let's check what we've learned, Here we have a time series graph that shows data from the Office of National Statistics about the number of adults who use the internet either daily or weekly, and the data for weekly does not include the data for daily.

So since 2010, the number of adults who use the internet daily has generally what is it, A decreased, B increased, or C stayed the same? Pause video while you make a choice and press play when you are ready for an answer.

The answer is B, increased.

In which year did the number of adults who use the internet daily decrease slightly, while the number of adults who use the internet weekly increase slightly? Pause the video while I write the year down, and press play when you are ready for an answer.

The answer is 2017.

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

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

You've got two time series graphs, one is about bus journeys.

It shows the number of bus journeys in the billions for each year.

And the other time series graph is about the average time spent working per week by full-time workers, and that's in hours.

In the year 2020, the UK went into a national lockdown in response to a pandemic.

And your job here is to circle this event on each graph and describe what it shows in the context of this data.

In other words, write a sentence to say what effect did that have on bus journeys and what effect did it have on the average time that people spent working per week? Pause the video while you do that and press play when you're ready for question two.

And here is question two.

You have two more time series graphs.

The top one shows the average house price for each year, and the vertical axis scale is in the thousands.

And on the bottom time series graph shows you the percentage of adults who are unemployed each year.

And here the vertical axis shows you the unemployment rate as a percentage.

And once again, both of these graphs are based on real data from the Office of National Statistics about the whole of the UK.

Now in the year 2008, there was a global financial crash.

And what I'd like you to do please is circle this event on each graph and once again, describe what it shows about the context of that data.

What effect did this event have on average house prices and the unemployment rates? Pause the video while you do that, and press play when you're ready for some answers.

So let's take a look at question one now.

So we have to circle the year 2020 on each graph and describe what effect that event had on the data in its context.

On the top time series, it's here.

And as we can see, the number of bus journeys decreased quite significantly during that year, before starting to increase again the year after.

And then in the bottom time series graph it's here.

And what we can see in this case is that the average amount of time that full-time workers spent working decreased during that year.

And then you might have commented by increased a year after.

And then question two, we have two more times series graphs, and the event we are focused on here was the global financial crash in the year 2008.

If we circle that event in the top time series graph, we can see it here.

And what we can observe from this data is that the house prices decreased quite sharply in that year before we started to increase again.

And then in the bottom time series graph, that event can be seen here.

And what you can observe from this data is that the unemployment rate increased during the financial crash.

Excellent work today.

Now let's summarise what we've learned.

Time series graphs can be used to estimate a frequency or a measure at a given point in time.

They can also be used to help us spot underlying trends or systematic patterns, by systematic patterns we're talking about how the data might increase and decrease periodically throughout the data, such as retail going up and down each year at the same points.

Trends can be used to make predictions about future events, although predictions may become less reliable the more we extrapolate into the future, so we should be cautious when we're doing that.

Trends can be interpreted in the context of data, and also context may explain patterns or unusual results are observed in the graph as well.

Thank you very much, have a great day.