A new survey by Pew Research Center found how over the course of the last 12 months, people went to libraries twice as often as they went to see movies in theaters (10.5 times vs 5.3 times). Does this strike you as odd? Me, too. The study also says things are the other way ’round – in the past year, the average person went to movie theaters more often than libraries (thrice to twice). Which finding generates the most attention? Which one makes for a better headline? The one where libraries come out ahead of movie theaters by a two-to-one margin, of course, because it goes against what most of us know, which is how reading has fallen by the wayside as we’ve become a society that prefers watching. The same thing happens when your information gatekeepers choose “facts” to make headlines that grab your attention, much like how tabloid editors use aliens, Elvis, and others.

The story about how people go to libraries more often than movie theaters used the mean, a term from statistics class, meaning the mathematical average. The story where movie theaters beat libraries used the median, the actual middle of the data set, balancing both sides like same-sized kids balance a playground seesaw.

What science and math types call the arithmetic mean, most of us call average.

Most also think typical and average are the same thing in spite of the fact numerical averages are usually anything but typical. Does the typical American family have 1.8 kids? Actually there are zero families with 1.8 kids. How’s that for not typical? Washington, DC gets an average of 40.8” of rain per year. Some days it will rain more and some days it will rain less, but here’s one thing we can count on –  it will not rain exactly .1117″ every day. Average and typical are two different things.

Let’s get back to our “average person” who went to a library 10.5 times (mean) or 2 times (median), depending on how you look at it. There is a third story, too, and we shouldn’t leave it out. The mode is the simplest average – it’s the number that shows up most often. Here is simple data display of the number of times respondents visited a library in the past year.

Our attention is grabbed by the big numbers at the ends and the heights of the vertical bars representing the % of people in the survey who answered in one of these six ways. We clearly see that most of the responses are on the two extremes, far apart from each other, with only a few in the middle. The tallest bar is the value that occurs most often, so this study’s mode is zero. The second largest group is on the right, where 26% of respondents went ten times or more, some weekly, some every day.

The average number of times people went to the library last year is 10.5 or 2 or zero, depending on the story someone wants to tell you.

When we are shown a number that claims to be the “average,” we should ask for the other two ways of calculating it, too. I like to look at the situation from three different angles because each tells me a different story. People who want to sell you something or prove their point are prone to showing you only statistics that support their argument, and not the information you need to make better decisions. Next time someone uses the words average or typical to describe people and things, ask them to talk a bit about where their conclusions came from.

Response ranges alter the facts, too.

Read the numbers in the circles above. The first three columns are single numbers (0 or 1 or 2). The column labeled 3-5 includes a range of three different values (3,4,5) and the column labeled 6-9 includes a range of four different values (6,7,8,9). When we see categories that include more than one value, we know the data are warped, but we don’t know where. When categories include an unknown number of values (in this example, the category of 10+ has a statistically practical upper limit of 365), the distortion is severe. So the chart above includes 1, 3, 4, and Jack and the Beanstalk-sized catchall ranges. We are not told if the six categories in the table were collected that way (back-end driven, user-unfriendly) or reported that way or why.

If so few read books, why are so many going to libraries?

It’s a good question. The answer is they’re not going there to read. Libraries have made profound changes this century. In the research that led to my writing I’d rather be tased than read a book, I found that 30 million adults in the U.S. can’t even read, so the explanation for why they’re going to libraries must be elsewhere.

Modern libraries loan things I never even thought of, like music, movies, and TVs.

Smithsonian says a library in Ann Arbor lends everything from telescopes to musical instruments and artworks, a library in Illinois lends out expensive digital equipment, and in Oakland, library patrons can borrow from thousands of tools. Try-before-you-buy is popular among would-be hobbyists who borrow fishing poles, knitting needles, and cake pans. Not your thing? How about test-driving iPads, Kindles and Nooks before you buy a tablet reader?

Three other things about modern libraries – they:

• Provide computers, printers, free interweb access, and training in all of them. 
• Offer free meeting spaces for community groups.
• Are learning centers where staff members help with filling out job applications, resumé writing, and dealing with government forms, including tax and health insurance paperwork, and all of it for free.

Now I understand why in a world that reads less, libraries are doing more.

And just to tidy up the averages thing, the following statement is completely true and my favorite example of the meaninglessness of “average.” The average person in Miami is born a Hispanic Catholic and dies a European Jew.