Misuse of Numbers

Statistics are criminally misused for personal gain. They are a powerful tool for strengthening one’s opinion or argument because they are often misunderstood by the audience. A statistic can be a headline or the central feature of a piece of prose designed to convey a message, and often provide the oomph required to influence a reader’s particular stance.

We are currently living in the age of #FakeNews where the media, and other professional bodies of note, but mainly the media, are culpable of failure to model good practice. As an educator, it particularly bothers me that young people are exposed to the deceitful and often crass misuse of numbers and graphs in influential publications. There are two main themes I want to discuss on this, and the first is around the use of graphical data.

I would like to begin with the caveat that I am aware that there has been a vast amount already written on the misuse of graphs and charts. Still, I have fervent desire to impart my thoughts on the matter. Although it has not (to my knowledge) even been a distinct part of the national curriculum or Maths GCSE, it is often taught at some point in a scheme of learning to help students reflect on how they create and use their own graphs – deepen their understanding if you will. But it seems that some working professionals have clearly not taken these learnings through to adulthood. Let’s look at some examples.

There might be nothing that grates on me more than the use of a 3D pie chart. The lack of integrity in their design is cringe worthy. Yes, they look pretty, but that is about it. They tell an inaccurate picture due to the perspective you view them from.

 

 

 

The chart on the left is distorted by an unhelpful perspective so that you cannot see the true size of the areas of each sector like you can in the chart on the right. Yet 3D pie charts are still published either because of their eye-catching charm, or unfortunately for the more malicious purpose of distorting the facts. What worries me is that spread sheet software that students use – such as Excel and Numbers- allows the creation of these monstrosities.

facebook graph

The bar chart above has so much wrong with it that it makes my head hurt. Should you feel uneasy that a professionally produced chart could be used as a discussion piece on bad practice in a classroom? Without delving into the specifics of bad design, the untrained eye may not notice that the vertical axis does not begin at zero. This gives the illusion that “company valuation” in January 2011 was more than twice that in December 2010, whereas close inspection of the numbers reveals that is in fact barely 10% bigger.

If manipulated accordingly, charts and graphs can provide a visually dishonest depiction of any statistic, that in turn can be used to convey a message. As educators, I believe we have a responsibility to encourage learners to scrutinise statistical diagrams, and not take them for granted. However, the misuse of numbers is more difficult to recognise, and they can carry more clout in their utilisation.

The cost to the NHS of visitors from the EU in 2016 was £340million. This type of statistic formed the part of the arsenal for political campaigns in the summer of 2016 which saw the highest public engagement in a national vote since 1992. Now 340,000,000 sounds like a large number to most people, probably because in their everyday lives they never encounter 340 million of anything, let alone 340 million pounds sterling. Yet, it is a meaningless number without proportional context. The total NHS expenditure for the previous year was £113.3billion. So, the drain on the NHS from EU visitors was close to 0.3%. Not the figure that the far-right press might have decided to go with on their front pages. Only when contextualised as a proportion do you then get a true representation of the statistic. My point is that numerical statistics, more often than not, need to be stated as proportions to allow a meaningful interpretation. And these proportions need to be handled carefully too. As an example, a tabloid article last year ran a headline stating that the chances of dying in a terrorist attack had gone up by a SHOCKING amount. It quotes facts such as deaths from terrorism increasing 9-fold in the past 15 years and up 80% on the previous year. It omits the fact that the actual probability of dying in a terrorist incident is about 0.00005%, or to put it another way, a 1 in 2.2million chance.

Students have difficultly visualising large numbers. In a popular Afl activity, students are asked to draw an arrow where one million would be on an empty number line. Said number line starts at zero and finishes at one billion. Many opt to go for around the half way point (which is 500 million, unknown to them) rather than the more accurate answer of virtually next to zero. To many of these students, a billion is perceived as a bit more than a million, rather than realising it is a thousand times larger. Once put into a context such as “someone that has £1000 is to a millionaire, what a millionaire is to a billionaire” gives them better understanding of the proportions. Even better is to clarify that 1 one million is a meagre 0.1% of one billion.

Obviously, we do not aim to deceive, but as educators, I think it is useful to reflect on how we use numbers to convey meaning in our various different subject areas. Thinking how numerical information could be interpreted is something to contemplate in the planning process for a teaching topic. Should the use of a statistic even be open to interpretation?

Many students are often submerged in a constant sea of social media that leaves them drenched in information and extraneous opinion: misuse of numbers and statistics is prevalent here. What we can offer students is a model of good practice, because they are unlikely to get it from looking at their phones.

Gareth Dudding, Maths

References:

http://www.businessinsider.com/pie-charts-are-the-worst-2013-6?IR=T

https://www.forbes.com/sites/naomirobbins/2011/11/17/whats-wrong-with-this-graph/#1b377412a336

http://www.bbc.co.uk/news/uk-politics-eu-referendum-36058513

https://www.forbes.com/sites/robinandrews/2017/05/24/how-simple-math-shows-us-that-manchester-style-terror-attacks-shouldnt-be-feared/#75fe7d7164ac

 

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