How to make statistics understandable

On July 10th the Slideshop blog had a post titled How to Present Statistics that Make Sense. Headings were:

Frame it from the perspective of your audience
Use a tangible and concrete point of reference
Plot statistics on a graph or chart

One of their examples placed the height of the tallest wind turbine (220 meters) between the tallest giraffe (6.1 meters) and the tallest tower (634 meters). Lengths are pretty easy. What about weights or volumes?

The 1938 image shown above says U. S. bituminous coal production was about 10 million tons per week. People can relate to coal being transported in the usual container, which back then was a railroad hopper car holding 100 tons. So, that’s also 100,000 cars per week.

100,000 cars per week converts to 14,285.71 cars per day, or 595.24 cars per hour, or 9.92 cars per minute. Ten cars a minute is easy to imagine.

How else can we express this in human terms? A car is roughly 50 feet long, so we can imagine a single coal train going by at a speed of 500 feet per minute or 5.7 miles per hour for that whole week. According to Wikipedia an average walking speed is 3.1 miles per hour, so you’d have to jog instead of walk in order to keep up with it.  

What should you avoid? In a blog post July 15, 2011 titled What can we say about a really big hole in the ground? I discussed the Bingham Canyon open pit mine near Salt Lake City. Kennecott Utah Copper said that each day they mine 500,000 tons of ore, which was described as being 10,000 50-ton humpback whales. Most of us don’t see humpback whales in everyday life, so that’s not a useful point of reference.

What about volumes? In another blog post on August 17, 2011 I discussed How to make a large number incomprehensible - or comprehensible. A July 22, 2011 article in The Week described how:

“....For Americans at home, flushing the toilet is the main way we use water. We use more water flushing toilets than bathing or cooking or washing our dishes or our clothes. The typical American flushes the toilet five times a day at home, and uses 18.5 gallons of water, just for that. What that means is that every day, Americans flush 5.7 billion gallons of clean drinking water down the toilet. And that’s just at home.”

It’s impossible to get your brain around that number, of course—5.7 billion gallons of water a day. But here’s a way of thinking about it. It’s more water than all the homes in the United Kingdom and Canada use each day for all their needs—we flush more water down the toilet than 95 million Brits and Canadians use.”

5.7 billion gallons a day is hard to comprehend. But it can be compared with something huge - it is about 9% of the flow over Niagara Falls. When you multiply anything by 308 million people, you will get a huge number. I discussed that problem in a September 23, 2012 blog post titled Is 540 million minutes per day a large number or a small number?

Bleach and milk both come in gallon bottles. Think about picking up and pouring 18 of them into a toilet, one at a time. So 18 gallons per person per day is easy to imagine and visualize.
Another statistic in that Slideshop blog post was: 

“Here’s an example of how a teacher could use statistics to promote motor vehicle safety to students.
 
Good: Don’t drink and drive. According to Centers for Disease Control and Prevention, in 2014 there were 9,967 people killed in alcohol-impaired auto accidents in the US. (Possible reaction: Wow! That’s a huge number!)

Better: Don’t drink and drive. According to Centers for Disease Control and Prevention, in 2014 an average of 27 people died every day from alcohol-impaired auto accidents in the US alone.  (Possible reaction: I could have been one of the victims!)”

27 people per day is a small enough number to visualize easily. (Imagine 27 coffins in three rows of nine). But, how does that number compare with the Top Ten list shown on the CDC FastStats web page for Leading Causes of Death?

As shown above in a bar chart, it’s about 4 times smaller than the 117 a day for #10 (suicide) and about 14 times smaller than the 372 for #4 (accidents of all kinds), and 62 times smaller than the 1682 for #1 (heart disease). Students who get curious and check that page will say that you are unjustifiably trying to scare them. 

Very small numbers are harder to express. I discussed small thicknesses in a January 13, 2010 blog post titled How thin is “extremely thin”?

If you are using the Google Chrome web browser, then you can install an extension called the Dictionary of Numbers (Quantity in human terms). It will automatically look up comparisons. I talked about it in a September 22, 2013 blog post titled Putting numbers into context with a browser tool - The Dictionary of Numbers.

UPDATE July 13, 2016

For another recent viewpoint, see Ashish Arora's June 29th blog post at SketchBubble titled Statistics don't need to be sleep-inducing in your presentation.