I'm Business Insider's maths reporter, and these 10 everyday things drive me insane

Maths, statistics, empirical analysis, and data visualisation are all incredibly powerful tools for understanding the world.

Unfortunately, there are many ways in which these tools are misused and abused that, to greater or lesser degrees, lead to confusion rather than clarification, and make the world just a slightly worse place.

Here are ten such things that personally aggravate me.

1. Misleading vertical axes

There are a few ways in which graphs can have badly misleading y-axes. Column or bar charts are a great way to compare values, since the lengths of the columns or bars should be proportional to the values being displayed.

But things can go horribly wrong if the base of the vertical axis is not set at zero. A classic example was a chart shown on Fox News last year comparing Obamacare enrollment numbers just before the enrollment deadline to the administration’s goal:

As Media Matters pointed out in their post on the chart, the actual enrollment figure of 6 million was about 85% of the goal of a little over 7 million, while the column representing the current enrollment is about a third the height of the column representing the goal.

This is a deeply misleading way to represent these figures. Fortunately, Fox News later presented a corrected and more responsible version of the chart:

The “start at zero” rule mostly applies to column and bar charts. For line charts, it’s fine to use whatever axis boundaries you need in order to show the trend you’re interested in. This chart from FRED shows the decline in the labour force participation rate, or the percentage of adults either employed or looking for work, since 2007. It has an axis ranging only from 62.5% to 66.5%:

That roughly 3% drop in labour force participation, however, represents millions of Americans who have stopped working or looking for work, and is one of the biggest mysteries of our current economic situation. The downward trend is the main story here, and so it’s fine to choose axis bounds that clearly tell that story.

2. Multiple vertical axis scales

Another unfortunately common abuse of axes is putting multiple scales on a graph. This is usually done to show some kind of relationship or correlation between two time series. Unfortunately, because one can basically choose any scale one wants for the two axes, it’s very easy to insinuate relationships that may or may not actually exist or matter.

Further, even if there is a valid relationship between the two series, the dual y-axis design can still be visually confusing, making it difficult to see the nuances of that relationship. Scatter plots are usually a better option for showing the relationship between two sets of values.

One of the most egregious examples of a misleading multiple scale graph is this chart combining the Dow Jones Industrial Average in the runup to the 1929 stock market crash with more recent stock market movements:

The implication is that the vague similarities between the two time periods means that a 1929-like stock crash is imminent. This, of course, makes no sense, since this apparent pattern only emerges with a very selective choice of vertical axis scales, and because two lines looking somewhat alike tells us nothing about the similarities and differences between the underlying market and economic situations — the things that actually matter when trying to figure out the likelihood of a crash — during the two time periods.

3. Horizontal axis disasters

Things can go wrong with the horizontal axis as well. One of the biggest problems is a missing horizontal axis on a time series chart. Showing how a quantity changes over time is a lot less useful if the actual time period being analysed is unclear:

Just having an x-axis for a time series graph doesn’t necessarily mean you’re in the clear however. Business Insider Deputy Editor Sam Ro tweeted out this intriguing chart from a Bank of America research note, ostensibly showing technological development and population growth over time:

The time scale is uneven, and appears to have no actual relationship with the data being presented. Apparently Greece and Rome peaked around 1000 AD, and the industrial revolution, moon landing, and invention of railroads all occurred within the last fifteen years.

When big events happen, Twitter will frequently visualise activity on the social network related to those events. Unfortunately, their charts usually lack both an x-axis and a y-axis, making it rather difficult to get any insight at all:

4. The lottery

Taking a break from aggravating things in charts, I am not a huge fan of playing the lottery. Buying a lottery ticket is almost always a losing proposition: Even in the case of immensely large jackpots, the probability of winning is so low that the expected value of a lottery ticket will almost certainly be negative.

Of course, this is a matter of personal taste. I’d rather not waste a dollar, but other people can certainly enjoy buying a ticket for non-monetary reasons like fear of missing out on a jackpot, or the simple rush of taking the gamble.

5. The concept of wind chill

Wind chill combines temperature and wind speed into a single index value, represented as an adjusted temperature. The goal is to capture the interaction between wind and cold: Wind blowing over exposed skin will pull heat away more quickly than still air of the same temperature.

This measure, however, is flawed. First, there are several other factors that go into a person’s experience of weather: Is it raining? Is it sunny or overcast? What time of day is it? Wind chill, while bringing together two important parts of weather, ignores these others.

Second, representing the combination of temperature and wind as another temperature is odd. A 35° F (1.7° C) day with 25 mile per hour (40 km per hour) winds doesn’t really “feel like” a 23° F (-5° C) day. Most immediately, a glass of water left outside on a windy 35° F day will never freeze, as the actual temperature is still above the freezing point, while a glass left outside on a still 23° F day will eventually freeze. Temperature is temperature, and wind speed is wind speed.

That said, wind speed (and other factors) are still very important! In conditions of extreme cold, exposed skin will suffer from frostbite faster in windy situations than in still situations, all other things being equal. I just find the representation of a combined temperature and wind speed as a new “temperature” somewhat odd. I’m perfectly happy looking up all the relevant forecasted weather conditions for a day when I wake up in the morning, and can decide on my own what type of clothing I should wear on that day.

6. Pie charts

Pie charts are intended to show how some whole is broken into component parts. In most cases, they completely fail at that goal. When we’re breaking a big circle into many pieces, it can be hard to directly compare the sizes of those pieces and thus the proportions of interest.

Here’s a chart breaking down the popularity of various pizza toppings. Note that each pie wedge needs to be labelled with its percentage, since otherwise it would be hard to tell, say, whether sausage or mushrooms are more popular, given the similar size of the two wedges:

Bar or column charts tend to do a better job of representing these kinds of breakdowns for a large number of subcategories.

On the flip side, pie charts can be somewhat clearer when looking at just a small number of categories with large differences between the percentages:

Of course, given that the relevant information from this pie chart is directly printed as text, and we’re basically just looking at a single number — the proportion of climate scientists who reject human-caused global warming — one might wonder why we’d bother with the chart at all.

7. Bad map colouring schemes

Maps can be an incredibly useful way to display geographically varying information. However, they must be designed carefully in order to clearly convey their data.

One somewhat frequent problem in creating maps is using arbitrarily chosen colours to display data. This map, from Imgur via @BeautifulMaps on Twitter, uses a very unintuitive colour scheme to show speed limits around the world:

There isn’t a natural flow in the colour scheme to go along with the naturally increasing scale of speed limits. I have no idea, at a glance, whether Texas’ blue speed limit is higher or lower than neighbouring Mexico’s light green speed limit. I have to reference the key every time I look at a different country to have any idea what that country’s colour means.

A better option is to stick with one colour, but vary the saturation, brightness, or intensity of that colour. This map from the Census Bureau showing the minority proportion of each state’s population in 2000 has a scale from light blue to dark blue, making regional patterns immediately apparent:

We can clearly see, even without looking at the key, that minorities tend to be a larger percentage of the population in the South and in more urban states, while the less densely populated states of the Midwest and Great Plains tend to have smaller proportions.

Two colours, varying by intensity, can be helpful in situations where there is a natural midpoint. Comparing Democratic to Republican votes in an election, seeing where incomes are above the national average or below the national average, or seeing where populations increased and declined in a given year are all cases where a two-colour scheme can work well.

As an example of the last case, here’s a map we made using Census data showing which US counties had population growth or loss between 2013 and 2014. Growing counties are in blue, with darker shades indicating faster growth; shrinking counties are in red, with darker shades indicating faster loss:

8. Questionable psychological measures

The human mind is an incredibly complex thing, and we know very little about how it works. This does not stop us from making often clumsy attempts to measure and compare people based on intelligence or personality.

One of the worst offenders is the Myers-Briggs Type Inventory, which attempts to assign a personality “type” to test-takers. The test sorts people into 16 categories, based on four binary personality trait variables: introverted vs. extroverted, intuitive vs. sensing, thinking vs. feeling, and judging vs. perceiving.

The test has numerous problems. First off is the dichotomous nature of the four trait scales: A person who takes the test and scores just slightly more extroverted than introverted is placed solidly in the “extrovert” bucket, despite having a mixture of traits.

Related to this problem is the reliability of the test: It’s not uncommon for people who take the test and then re-take it a few weeks later to end up assigned to a completely different personality type. Since the test is supposed to be measuring something fundamental about a person’s psyche, that variability is extremely problematic.

The MBTI also has somewhat questionable origins. It was developed by a mother-daughter team in the 1940s, neither of whom had any formal psychological training. The test also has come under strong criticism from social scientists for its lack of empirical validity or theoretical justification in the decades since its development.

9. General bad chart design

In addition to the sins of axes, pie charts, and map colours mentioned above, there are plenty of other ways charts and infographics can fail at their task of conveying data. In his seminal 1983 book “The Visual Display of Quantitative Information,” data visualisation pioneer Edward Tufte coined the word “chartjunk” to describe unnecessary and distracting elements of a graph that either add nothing to the reader’s understanding of the information being presented or even actively detract from that understanding.

Tufte worst graphic everEdward Tufte‘This may well be the worst graphic ever to find its way into print.’

Chartjunk can take on many forms. Some common forms include poorly chosen shading, background, or border options that draw the eye away from the information being presented, excessively distracting decorative elements, and the use of poorly scaled 3D and related design effects that distort the reader’s perception of the data.

Tufte includes the chart to the left of the age breakdown of college students in his book, writing, “This may well be the worst graphic ever to find its way into print.”

The chart essentially only displays five numbers: the proportions of college students 25 and older over a five year period. To do this, the chart has four brightly coloured regions, two of which are there just to provide an off-center 3D perspective effect that is both distracting and makes the graph harder to read. Like the misleading y-axis of the initial Fox News Obamacare chart above, the blue region draws the reader’s eye up, confusingly suggesting that the earlier years’ proportions are higher than they actually are.

Further, the top half of the chart, showing the proportions of college students under the age of 25, is entirely redundant: This is literally the mirror image of the lower half of the chart, since the percentage of students under the age of 25 is just 100% minus the percentage of students over the age of 25.

The chart and charts like it that have poor chartjunk-laden design decisions take very simple data sets and present them in an almost incomprehensibly over-complicated and ugly way. Former Business Insider reporter Walt Hickey found several examples of extremely poor chart design and compiled them here.

10. Big round numbers

On December 23, 2014, the Dow Jones Industrial Average crossed 18,000 for the first time in the index’s history, and the headline on that morning’s Business Insider market update post reflected this “milestone”.

Several of my friends will be turning 30 this year, which seems somewhat more momentous and important than my upcoming 29th birthday.

Dow jones milestone traderREUTERS/Brendan McDermidTrader Theodore Weisberg smiles as he wears a hat from March 1999, the first time the Dow rose above 10,000, on the floor of the New York Stock Exchange, October 14, 2009.

Privately held tech startups that raise money at a valuation of at least $US1 billion are labelled “unicorns”, while presumably an app developer worth only $US990 million on paper would just be a run of the mill horse.

There are 10 items on this list, rather than 9 or 11, either of which would have been certainly possible either by removing an item or finding more things that annoy me.

In each of these cases, and in several other everyday situations, multiples of powers of ten are favoured over other numbers as important cutoffs or milestones. But this is an essentially arbitrary thing: The big round numbers we view as important are only seen as such because the most common number system in the modern world is the base ten decimal system.

The most likely reason we use decimal rather than a different number system is because human beings generally tend to have ten fingers. This itself is an arbitrary side effect of human evolution.

This arbitrary nature of big round numbers, and of related decimal-biased numerical events, is a thing that annoys me.


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