Every writer has an "idiolect," or a personal vocabulary of distinguishing words that they use a lot, or common words they use hardly at all. For example, Shakespeare rarely used the word "also" for some reason. In all of his writing the word appears a total of less than 40 times. His contemporaries used it as much as we use it today, which is to say: constantly. Shakespeare, for reasons known only to him, just did not use the word much. Maybe he didn't like it, or maybe it reflects some extreme hyper-local dialect of English he learned.
One of the things that stands out about my own writing is how often I use the word "accordingly." Another thing I say a lot – intentionally – is "modal."
I apologize in advance if this is information you already know, but I've had the experience several times in the last year of very intelligent people – editors, journalists, people in the publishing industry – send me edits on things I've written indicating that they are not clear what modal means. It is possible that in an academic field in which everyone is used to dealing with data sets I encounter that term regularly enough to assume it is common. But when people who know the language highlight it and say "This isn't clear, please explain" it obviously is less common elsewhere.
I say "modal" a lot because when people say "average," they almost always mean "modal." It's a pet peeve. Allow me very briefly to explain the most familiar measures of central tendency in data and explain why you see a certain kind of news story in political journalism that incorrectly substitutes average for modal.
Average (or mean) is widely understood. Add up the salaries of a group of 10, divide the sum by 10, and that is the average salary. Unfortunately average is also used in non-data contexts as an adjective meaning "ordinary" or "common." That is bad.
Why? Well here's a true story – of the 11 players on my high school football team's defense, our average net worth today is well over $5 million. Seriously. Ten of us make totally unremarkable incomes doing normal jobs, and the eleventh guy made over $50 million playing in the NFL. On average, we're all worth seven figures!
So, averages can be very misleading. Especially in smaller sets of data.
Median is the middle value that divides a set of observations in half. If the median household income in the US is $56,516. That means 50% of households earn less and 50% earn more. Imagine every observation in the data lined up in a row; the median is the one right in the middle.
While the median household income is $56,000, the average is $79,000. See? High values – people making billions of dollars – skew the average toward the right (on a simple graph).
That brings us, finally, to mode. The mode is the most commonly observed value in a data set. This generally is only useful – but then tends to be the most useful – when the data are categorized subjectively. For example, say we decided to categorize households as Rich, Middle Class, and Poor based on some subjective cutoff points. Count up the total number in each category; the one with the most is your mode.
Another great example of when mode is useful is academic: grades. Say the Dean wants to know how my students did in a course. There are 20 students. I calculate everyone's grade as a percentage of all possible points. I say, "The average grade was 80%." But what does that mean? There are almost infinite combinations of 20 percentages that will average to 80%. Maybe 16 students got 100% (A+) and 4 got 0% (F). Maybe all 20 got exactly 80% (B-). A better way to reflect the performance of the class would probably be to say, 16 students got an A+. But 4 students enrolled and never showed up, so they got an F.
That brings me to the reason I think about this daily: news stories about the "average" voter in the United States.
There is no "average" voter because several of the important variables for "measuring" voters are categories like race, gender, educational attainment, and so on are not continuous values. You cannot "average" race or the attainment of degrees in the American electorate. What you could do, just as one example, is to say that 44% of the electorate falls into the category of "White, no college degree." Therefore, the "Cletus Safari / Diner Enthusiast" guy constantly being interviewed in the media is not average; he cannot be. He is the modal American voter, as long as the criteria of interest are race and education.
It's a petty hill to die on, and most people understand fine what is meant in common usage when a journalist refers to the "average voter." But it is incorrect as well as silly – because we have a perfectly good term for what he or she actually means.