Lesson video

Hello there and thank you for joining me.

My name is Dr.

Rawlinson and I'll be guiding you through today's lesson.

Let's get started.

Welcome to today's lesson from the unit of comparisons of numerical summaries of data.

This lesson is called Problem Solving with Comparisons of Numerical Data.

And by the end of today's lesson, we'll be able to use our understanding of graphs and summary statistics to solve more complex problems. Here are some previous keywords that we're going to use again during today's lesson.

So you may want to pause the video if you want to remind yourself what any of these words mean before pressing Play to continue.

This lesson will contain two learning cycles.

In the first learning cycle, we're going to be using the multiple representations of data to make some interpretations.

And then in the second learning cycle, we're going to be fact checking with data.

But it starts off with multiple representations of data.

During mathematics lessons, we often find ourselves looking at a single visual representation of data at a time.

This is usually while we are first learning how to use these things.

And there are many situations outside the classroom where you may be presented with an individual graph or some summary statistics for a single dataset.

For example, this could be in the workplace, in reports in the media, or when dealing with your own personal finances and so on.

However, sometimes a single graph just isn't enough to give a full picture of a situation.

In some situations, different datasets are presented together in what is sometimes called a data dashboard.

These datasets are usually related to each other, but they may be presented using different representations.

These tend to be used by businesses, analysts, researchers, and many other people to analyse, track and interpret multiple aspects of a single subject because presenting multiple datasets can provide a detailed picture of a subject, but it can also be overwhelming to the viewer.

So let's take a look at some now.

Here we have a data dashboard which shows data from the Office of National Statistics, the ONS.

The data is about jobs in administration or secretarial occupations.

Let's take a look at what we've got.

We have three graphs.

On the left we have a scatter graph where each point represents a different occupation.

The horizontal axes shows the mean number of hours worked per week in each occupation.

And the vertical axes shows the mean weekly pay in pounds for each occupation.

And while these points are all for different occupations, one point has been highlighted and that is for administration and secretarial occupations.

In the middle we have a time-series graph, and this shows the number of vacancies in administration secretarial jobs each year where the vacancies are in the thousands.

And then on the right-hand side we have a pie chart.

This pie chart shows the employment status of workers in administration and secretarial occupations where the key at the bottom helps us interpret what each sector means.

The key is broken into two parts.

We have an E and an S, that shows whether a worker is employed or self-employed.

And we have an F and a P.

This shows whether a worker works full-time or part-time.

For example, the purple sector is labelled EF.

This represents workers who work, E, employed and F, full-time.

So those are employed full-time.

The pink sector, which is labelled SP, this represents workers who are self-employed and are part-time.

These three graphs together give quite a detailed picture of the workforce in administration and secretarial occupations.

And by referring to a combination of datasets and representations, we can provide a detailed picture of the data surrounding this occupation.

Let's consider what we can interpret from different parts of this data dashboard, starting with the scatter graph.

So what could we interpret from this about administration and secretarial occupations? Well, on average, people working in administration or secretarial occupations work approximately blank hours per week.

What would go in that blank there? Pause the video while you think about that and press Play when you're ready to continue.

Well, the mean hours worked per week is on the horizontal axes and this point is in line with 31.

So, on average, people working in administration or secretarial occupations work approximately 31 hours per week.

So what else can we interpret from this graph? Well, on average, they earn approximately so many pounds per week.

How many pounds per week do they earn? Pause the video while you work that out and press Play when you're ready to continue.

Well, the mean weekly pay is showed on the vertical axes and the scale makes it a bit difficult to get an exact figure, but we can get a good approximation.

On average, they earn approximately 480 pounds per week.

So here are two examples of what we could interpret about this occupation from a scatter graph, but there may be some other things you might be able to interpret as well.

Let's take a look now at the time-series graph which shows the number of vacancies each year in administration and secretarial positions.

And the numbers are in the thousands.

There are a lot of different things we can interpret from this particular graph.

For example, the number of vacancies in administrative and secretarial positions did what each year from 2009 to 2015.

What do you think would go in that blank? Pause the video while you think about it and press Play when you're ready to continue.

Well, if we look at the part of the line which is between those two years, it looks like the number of vacancies increased each year from 2009 to 2015.

Here's another example of an observation we can make from this graph.

There was a dramatic decrease in the number of vacancies in the years what and what.

In which years could you see a sudden dramatic decrease in the number of vacancies? Pause the video while you think about this and press Play when you're ready to continue.

We can see this in parts of the time-series graph where it suddenly drops down.

These were in the years 2009 and 2020.

Both of these years correspond with events that happened at the time.

In 2009, this may have been in response to a global financial crisis, which did seem to lead to an increase in an unemployment.

While in 2020, this may have been in response to a global pandemic.

And one more example.

The highest number of vacancies was recorded in the year blank.

Which year would that be? Pause the video while you think about it and press Play when you're ready to continue.

This is the point on the time-series graph where the line is at its highest, and this was in the year 2022.

So here are three examples of interpretations that can be taken from this time-series graph, but there are other interpretations that can be taken from it as well.

Let's now take a look at what we can learn from the pie chart.

This pie chart shows the employment status of workers in administrative and secretarial positions, where those employment statuses can be split into either employed or self-employed or full-time and part-time.

For example, if we want to determine whether the vast majority of people working administrative or secretarial occupations are either employed or self-employed, we can do that by looking at the pie chart and comparing sectors that start with an E for employed, with sectors that start with S for self-employed.

we can see that the sectors that start with E are much bigger than the sectors that start with S, and they are definitely bigger altogether, so they are employed.

We could also think about whether the largest proportion of these workers are either full-time or part-time.

And we do that by looking at either the F or the P in each sector.

And what we can see is if we combine the sectors that say EF and SF, they would be larger than the sectors that say SP and EP.

Therefore, they are full-time.

So now we've gathered lots of different pieces of information from each of the graphs, we can combine it together to produce a narrative report about the occupation as a whole.

For example, a narrative report might look something a bit like this.

It says, "On average, people working in administrative or secretarial occupations work 31 hours and earn 480 pounds per week.

The vast majority are employed and the largest proportion of these work full-time.

The number of vacancies in this occupation has varied over the years.

There was a sudden drop in 2009 and 2020, possibly in response to the financial crisis and the pandemic, with a gradual increase during the years that are in between.

The highest number of vacancies on record was in the year 2022." So as you can see, this report is highly detailed and highly informative and pulls together lots of different interpretations that we took from that data dashboard.

And it could be helpful for somebody who is looking to get a job in this occupation or for employers themselves.

So let's check what we've learned.

Here we have a scatter graph where each point represents a different occupation.

The horizontal axes shows the mean hours worked per week in each occupation.

And the vertical axes shows the mean weekly pay for each occupation.

And one point is highlighted.

The highlighted data point represents jobs in caring, leisure and other service occupations.

On average, how many hours per week do people work in this occupation? Give your answer to the nearest hour.

Pause the video while you write it down and press Play when you're ready for an answer.

Given to the nearest hour, they work 29 hours per week.

It looks slightly more than 29, but it rounds down to 29.

On average, how much money do they earn per week? Give your answer to the nearest 100 pounds.

Pause the video while you do that and press Play when you're ready for an answer.

To the nearest 100 pounds, they earn 400 pounds per week.

It looks like it's slightly under 400 pounds, but it's closer to 400 than it is to 300.

And here's a pie chart for the same occupation.

The largest proportion of people in this occupation are.

Is it A, employed full-time, B, employed part-time, C, self-employed full-time, or D, self-employed part-time? Pause the video while you choose and press Play when you're ready for an answer.

The answer is A.

The largest proportion of people in this occupation are employed full-time.

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

You are presented with data from the Office of National Statistics about the weekly pay, hours and employment status of four jobs.

You've got some pie charts, a scatter graph and a table.

And you should note that these refer to the same four jobs.

For example, pie chart A corresponds with point A in the scatter graph and that corresponds with one of those four jobs in the table.

You need to use this data to answer five questions.

And here is question one.

"In which job do people tend to earn the most money?" Pause the video while you work this out and then press Play when you're ready for some more questions.

Here are questions two and three.

Question two says, "In which job do people tend to work the greatest number of hours per week?" And question three says, "Which of these jobs has the largest proportion of part-time workers?" Pause the video while you work these out and press Play when you're ready for the final two questions.

Here are questions four and five.

Question four says, "Which of these jobs has the largest proportion of self-employed workers?" And question five says, "Which two jobs have similar proportions of workers with each employment status?" Pause the video while you work these out and press Play when you're ready to go through some answers.

Okay, let's now go through some answers to these questions.

Question one said, "In which job do people tend to earn the most money?" We can get this information from the table, and from this we can see that management jobs tend to earn the most money.

Question two said, "In which job do people tend to work the greatest number of hours per week?" We can get this information from the scatter graph and see that point D shows a job which works the greatest number of hours per week, but we'll then need to use a table to work out which job that one is.

And we can do that by looking at the mean weekly pay from the scatter graph and compare it to the table.

We can see that out of those four points highlighted, point D has the second highest mean weekly pay, which means it represents machine operators.

Question three, "Which of these jobs has the largest proportion of part-time workers?" For this, we'll need to refer to the pie charts.

And in this section of the data dashboard, we can see that the pie chart for job A has the largest proportion of part-time workers.

But what job does that represent? To work that out, you would need to refer to the scatter graph and look at point A in that.

That shows the job with the lowest pay and lowest mean worked hours.

So then we can refer to the table and see which job that is, which is sales workers.

And question four, "Which of these jobs has the largest proportion of self-employed workers?" Once again, we'll need to refer to the pie charts and take a look at the sectors that have an S in them.

If we do that, we'll notice that job C has the largest proportion of self-employed workers.

So then we need to work out which job that represents.

To do that, look at the scatter graph.

Look at point C.

That job has the third highest mean weekly pay.

So looking at the table, we can see that it represents skilled trades.

And then question five, "Which two jobs have similar proportions of workers with each employment status?" Well, if we look at the pie charts again, 'cause we're looking at employment status, we can see that the pie charts for job B and job D look pretty similar.

Overall, each of those sectors are pretty much a similar size to each other.

So which jobs do they represent? Once again, refer to the scatter graph and then refer to the table and you'll see that they represent management and machine operatives.

Great work so far.

Now let's move on to the second learning cycle for today's lesson, which is all about fact checking with data.

People are often presented with facts or claims that are seemingly supported by data.

Now this might be informal settings such as the workplace or research, but people are also presented with lots of claims in their day-to-day lives.

This could be in the news or in TV programmes.

It could be in printed media such as books, newspapers, or magazines.

It could be in adverts or flyers or pamphlets that are posted through doors, or it could be on the internet such as social media, blogs and videos.

Now, a lot of time, these claims may be perfectly valid and supported by the data that it refers to, but not always.

So if a claim is supported by data, why might it be invalid? Well, there are lots of possible reasons for this and here is one example.

Sometimes a claim might be invalid because it only focuses on a particular selection of data.

For example, here we have a time-series graph that shows real data taken from the ONS, that's the Office of National Statistics.

The data is about rental costs, the average monthly rent in pounds, and it shows the data for two regions.

We have the East Midlands with this bold line in purple and we have Yorkshire with this dashed line in green.

Now, looking at this data, Alex makes a claim.

Alex says, "It has always been more expensive to rent a home in the East Midlands than in Yorkshire." Now this time-series graph seems to support Alex's claim, but why might Alex be wrong? Pause the video while you think about this and press Play when you're ready to continue.

It certainly seems like this time-series graph does support what Alex is saying because all the way along it you can see the line for East Midlands, the bold line, is always higher than the line for Yorkshire.

So this claim appears true based on the data that is presented.

But this graph only shows four years of data.

So the reason why Alex's claim appears true, or at least is convincing, could be due to the data that has not been presented.

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

Here we now have a time-series graph for the same data, but includes more years worth of data.

And what we can see now is that the line for East Midlands is not always above the line for Yorkshire.

So Aisha makes a counter-argument to Alex's claim by looking at the wider selection of data.

She says, "Renting in Yorkshire was more expensive than in East Midlands during some of the years before 2017." Doesn't necessarily matter how many years, what Aisha has done here is proven that Alex's claim is not strictly true.

This scenario gives an example of one way to be critical about claims that are based on data.

The person who is making the claim and is presenting the data has chosen which data to present.

So as well as think about the data they present, one way to be critical is also to consider what data has not been presented as well.

Let's check what we've learned.

Here we have a time-series graph that shows data from the ONS, that's the Office of National Statistics, about house prices.

Along the horizontal axes, we have the years and the vertical axes shows the average house price in the thousands.

And here we have Laura who makes a claim based on this data.

She says, "Average house prices were at an all time high in the middle of 2010." Why might Laura be wrong? Pause the video while you write down a reason why and then press Play when you're ready to see an answer.

Laura might be wrong because the graph only shows a few years of data, whereas Laura's claiming to be an all time high.

Here we have a time-series graph now for the same data, but includes more years.

Use this time-series graph to write a counter-argument to Laura's claim now.

Now write down a sentence and refer to something in the data that will support your counter-argument.

Pause the video while you do that and press Play when you're ready to see an answer.

An example of a counter-argument could be that the average house prices were higher in 2008 than in 2010.

So 2010 was not an all time high.

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

This task contains one question that is in four parts and the first two parts are available on the screen here.

This question refers to the data that's presented in two graphs.

The page shows census data from the ONS, that's your Office of National Statistics, about age, salaries and qualifications.

On the left we have a bar chart that shows census data about the highest level of qualification of people in the UK in the year 2011 and 2012.

On the right-hand side, we have a line graph that shows the average salary in the thousands for people of different ages depending on what the highest level of qualification is.

And you need to use these graphs to provide counter-arguments to the following claims. In other words, for each part A, B, C, and D, you'll see a claim and you've gotta try and explain why it's not necessarily correct.

So here are the first two claims. Part A, "People with degrees always earn more on average than people without." And part B, "People's salaries tend to stop increasing with age at around 35 years old." Pause the video while you write a counter-argument to each of those claims and press Play when you're ready for part C and D.

And here are parts C and D.

In part C the claim is, "There have always been more people whose highest qualification is A-level than those whose highest qualification is GCSE." And part D the claim says, "The number of people with GCSEs grade 4+, or equivalent, decreased from 2011 to 2021." Pause the video while you write a counter-argument to both of these claims and press Play when you're ready to see some answers.

Let's take a look at some example answers now.

So part A, "People with degrees always earn more on average than people without." A counterargument to this would be, "People with apprenticeships earn more or similar to people with degrees, on average from ages 21 to 24." Which you can see on the graph on the right-hand side.

In Part B the claim is, "People's salaries tend to stop increasing with age at around 35 years old." A possible counter-argument here could be, "For people with apprenticeships or degrees, people aged 40 to 50 tend to earn more than people aged 35." You can see that with the graph on the right-hand side again.

In part C the claim was, "There have always been more people whose highest qualification is A-level than those whose highest qualification is GCSE." A possible counter-argument here could be to say that in 2011 there were more people whose highest qualification was GCSE than those whose highest qualification was A-level.

And then part D the claim was, "The number of people with GCSEs grade 4+ decreased from 2011 to 2021." Now a counter-argument here can be a bit tricky 'cause it does look like that, looking at the bar chart.

When you look at GCSEs or grade 4+ on the left-hand side of it, you can see at the bar for 2011 is higher than the bar for 2021.

So what is wrong with this claim? Well, the bar chart is based on the highest qualification that people have, not the number of people altogether with that qualification.

And the number of people with apprenticeships, A-levels and degrees have all increased from 2011 to 2021.

And many of these are likely to also have GCSEs.

Fantastic work today.

Now let's summarise what we've learned during this lesson.

When presented with a large volume of data, valid interpretations can be difficult.

So we can understand why someone might make a mistake when they are interpreting from data because it can be tricky.

So it is really important that any conclusions that are made are supported by the data.

That assures people that the conclusion isn't just made up, but it also means that people can check the data and just make sure that a mistake hasn't been made.

Data can also be used to check the validity of claims made by others and support counter-arguments against those claims. And that's a critical skill that we worked on in the second part of today's lesson.

Because in the real world, data may be represented using multiple representations, so critiquing them is a vital skill.

Thank you very much.

Have a great day.