Where are you flying?
Where do people fly to from London? What is good and bad about these representations?
Problem
Where do people fly to from London?
We collected data on the number of planes that flew to each continent from London airports in 2017.
Here are four representations of this data:
Figure 1
Figure 2: Popularity of destinations (by continent) in 2017
Figure 3: Destinations of flights from London in 2017
Figure 4: Number of flights from London airports in 2017
- What information can you deduce from each representation?
- What is good about each representation (including its caption)?
- What is bad about each representation?
- Who might create each of these representations and for what purpose?
- Could you create a better representation?
To see the original data used to create these representations, click on "Show".
| Continent | Total flights | Proportion |
|---|---|---|
| Europe | 374496 | 67.8% |
| Domestic | 57866 | 10.5% |
| Asia | 52336 | 9.5% |
| North America | 52259 | 9.5% |
| Africa | 11925 | 2.2% |
| South America | 2059 | 0.4% |
| Oceania | 1442 | 0.3% |
- Is there anything you might ask about this data?
To find out how this data was collected, take a look at the article Challenging Data Tasks: The Making of "Where Are You Flying?"
This resource is part of the collection Statistics - Maths of Real Life
Student Solutions
Some observations about these four representations:
- Pie charts are generally quite poor representations, as it is hard to compare angles, and there is no indication of absolute sizes. (There may have just been 100 flights, or maybe 10 million, for example.)
3D pie charts worse still, as segments near the back appear smaller than segments near the front, which is misleading.
Exploded 3D pie charts are even worse, since the sizes of the segments become even harder to compare, and segments moved towards the viewer appear even bigger. And one segment is almost completely obscured.
The colour choices are misleading, as dark colours attract attention and can make the segment seem larger than it is, while pale colours become less obvious.
The colour choices also make it hard to distinguish between some of the sectors: which one is Europe and which is North America, for example? And what about Africa and Oceania?
In the content of the article, the headline talks about "tourist destinations", while we only know about flight destinations, not people's reasons for travelling. Also, people visiting New Zealand do not fly directly there, so it is likely that their flights will be recorded as going to Asia (where they will then change for a connecting flight).
- It is very difficult to compare the sizes of these aeroplanes, and the ones in South America and Oceania are almost invisible.
It is unclear whether the areas or lengths of the planes are to be compared.
There is also no indication of absolute size.
The caption talks about popularity of destinations, but we don't know how many people flew to these destinations, only the number of flights.
It is not quite clear why there is a plane over the UK, but we could probably make a reasonable guess.
- It is clear what each disc refers to.
All of the discs have the same colour, which makes it easy to compare them.
It is clear that the number of flights to Europe is the greatest by some margin, while Domestic, Asia and North America have approximately equal numbers of flights.
The caption is meaningful and accurate; that the discs show the number of flights to each destination is implicit.
However, there is no scale indicated, so we do not know whether the discs are to be compared according to their radius or area, and there is no indication of absolute size.
The discs for Souther America and Oceania are almost invisible, which is somewhat unhelpful.
- The graph has a scale, which means that numbers can be read from the graph.
The caption is accurate.
Each bar has the same colouring making them easy to compare.
The graph starts at 1, so the graph is not misleading through use of a strange starting point.
However, the graph is on a "log scale" which makes it seem at a first glance that there is not that much difference between the different destinations, even though Europe has over 100 times more flights than Oceania.
It is also somewhat difficult to read an actual number from the scale; for example, it looks as though there were about 600 000 flights to Europe, whereas there were actually less than 400 000 flights.
For the data itself, we might ask a variety of questions, for example:
- How reliable are these figures?
- How do the number of passengers relate to the number of flights? Would it have been more useful to have passenger numbers instead?
- Very few people fly directly to Oceania, and direct flights only started very recently. So what are these 1442 flights?
- Related to the previous point, if people fly to somewhere far away and they take a connecting flight, what is the destination recorded as? So what does the data actually tell us?
- If we want to know where people fly, wouldn't it be simpler just to ask them (thinking about representation 1)?
Teachers' Resources
Why do this problem?
We are frequently presented information in the form of graphs and infographics, in newspapers and online. This problem offers some data along with a variety of interpretations and representations. It should help students to develop their critical faculties in relation to data: there are many issues with the way the data is presented here.
This problem would be particularly useful for students studying for GCSE or A-level Statistics, and for various modules/units in Core Mathematics, as it focuses on data literacy.
Possible approach
There are three printable worksheets containing the representations which may be useful:
- Where-are-you-flying-1.pdf The four representations on one A4 page
- Where-are-you-flying-2.pdf The four representations and the data table on one A4 page
- Where-are-you-flying-3.pdf The four representations laid out for easy cutting into separate representations (total of two A4 pages)
This could be used with students at any point in their studies, and could also be revisited at later stages.
Start by introducing the problem with the very brief introduction on the problem page. Then give each student a different representation of the data (using the third printable worksheet). Ask the students to individually work out what they can deduce from their representation. Then as groups of four, students can compare their different representations, and see how much more they can deduce from the combined representations.
Once they have done this, the groups can be asked the general question: "If I want to know about the destination of flights from the UK, how do these representations help me?"
Finally, students can be shown the original data table and asked: "Do these figures effectively represent the data?"
As an alternative approach, the class could be asked where people fly most from the UK before presenting the table of data. Questions might include "I want to present the data. If we simply list every individual location that people travel, there will be thousands or millions of them. How could we group them to make it simpler to see patterns?" (This does direct students away from the possibility of informative geographical maps; this is a point which could be returned to later.) There will probably be a variety of interesting responses, which could be discussed or collected for returning to later in the lesson.
Then present the given data, explaining that it counts the number of flights from London airports (rather than the whole of the UK), and has been broken up by continents, using data from the Civil Aviation Authority (CAA). Questions such as "What does this data tell us?", "What does this data not tell us?" and "What questions could you ask about this data?" might stimulate students to think critically about the meaning of this data.
With this in mind, ask students to critique the four presentations of the data. They could work on one presentation at a time, sharing their thoughts with the class before continuing to the next one. You may find it helpful to use one of the above worksheets for this purpose, together with displaying it on a projector to see the colours.
A final question on these representations could be "What would a really good presentation of this data look like?" Or perhaps, if the data itself has been critiqued, "What would be a better data set to present? And how would you present it?"
Key questions
- What does the actual data tell us?
- What do the various representations claim that the data tells us?
- What (if anything) is wrong or misleading about the data representations?
Possible extension
There are further questions at the end of the associated article Challenging Data Tasks: The Making of "Where Are You Flying?" such as "What other interesting questions could you ask about the data available? How might you go about answering them?" That article itself provides a significant extension to this problem.
Possible support
Thousands of People might be a suitable activity to begin the discussion about different representations.
Students might find it helpful to construct their own representations before looking at the given ones, so that they have something good to compare them to.