Tag: median

  • I am below average

    It’s one of those facts that gets brought up to illustrate how people don’t think rationally: way more than 50% of the population believes they are above average drivers. I think it is something like 90%. (Don’t quote me on that.)

    Now, you could argue terms. What do we mean by average? Are we referring to the median, which in this scenario would be found by lining up all the drivers in order of worst to best driving ability and picking the person who is exactly in the middle? Or, are we referring to the mean, which would be found by somehow adding up the driving ability “scores” of all drivers, dividing it by the total number of drivers and designating everyone above that number as “above average”?

    It matters, because when you use the median as your average, by definition half of the population will be below the median and half will be above it. That’s how the first paragraph builds its case. When you use the mean as your average, however, it would actually be possible for more than 50% of the population to be above average, if the below average drivers were just really bad. As an example, say there are ten students taking a test. Nine get 100% on the exam and one unlucky bloke slept through it and gets 0%. The mean grade would be 90% (add up all the scores, 100 + 100 + 100 + 100 + 100 + 100 + 100 + 100 + 100 + 0 = 900, and then divide the total number by the number of students, 900 / 9 = 90), so nine of the students would be “above average” and just one would be “below average” if by average we are referring to “mean.” The median would be 100% so ironically no one would be above average using that definition, although one student would be below average.

    Using the median definition of average, I feel quite confident in saying I am a below average driver, and half of the people reading this (zero?) should feel comfortable admitting to the same. Anecdotally this makes sense to me. Considering the drivers in my family, I am definitely in the bottom half of skill level. To be clear, I don’t think I’m a bad driver, per se, although that could be argued. (The fender bender I got into this morning was not a confidence booster.) But wouldn’t you hope that more than 50% of our drivers are good ones?

    On the other hand, if we use the mean definition of average, I’d be a little more uncertain about where I fall. There are some seriously bad drivers out there that would skew the mean downward, and I think it would be hard to be so outstanding at driving that you would meaningfully pull the mean upward. Perhaps I’d be able to squeak in “above average,” but if so more than half of all drivers would be with me.

    SDG