Mean, median, and mode

When someone uses the term “average”, it may indicate different things, depending on which specific way of determining the average is used. Most people use “average” like when a teacher figures a student’s grade — all of the grades are added up, and then the total is divided by the number of different grades. That’s the “mean”. There are two other ways of figuring the “average,” though, which may make a difference in research.

“Median” is, like the median between two sides of a divided highway, in the middle. You write all the numbers in order, and pick the one in dead center.

“Mode” is the most common number. My little “cheat” for remembering this is that when something is popular, it’s “modish”; and while “a la mode” means “with ice cream” when it’s on menus, just in general, it means “stylish” which also is “popular.” So, “mode” is the most popular number.

How does this play out in research? Well, let’s give a hyperbolic example to prove a point.

Let’s say you have five men in a room, and you want to find the “average” net worth of that group. Two people owe more than they’re worth — they’re both $10,000 in the hole. Man #3 has $1,000; man #4 has $5,000; while man #5 has $1,000,000.

In this scenario, the “mode” is negative $10,000, because that’s the most common number; the “median” $1,000, because it’s right in the middle; and the “mean” is $197,200, because that’s what all the numbers added up together, divided by 5 equals.

If you were to be given the “average” amount of money from this group, which would you receive? Quite a difference between what some people mean when they say “average” and what others mean, isn’t it!

It’s important when looking at research to be able to keep this kind of thing in mind, because sometimes the results may vary widely, depending on how researchers determined the “average.”

In the case of a medication or a procedure, it is possible for there to be a negative effect as well as a positive effect. Take Vioxx, for example. I’m picking on it because I worked at a pharmacy when it came out, and remember all the fanfare and hoopla about it, and how that just about every doctor switched every patient with any sort of arthritis or other pain over to that drug. When people came in for their refills, after having been on it for a month or so, we’d sometimes ask them how it worked — because all we really knew about it was what the drug reps had said (yes, the pharmacist read the information packet, but that doesn’t tell us how Mr. Jones is going to feel after taking it). We expected most people to rave about it, but the reaction was mostly bland. A few people said it was a lot better than what they had been taking (usually over-the-counter ibuprofen, sometimes other medications); a few people said it didn’t work nearly as well; and most people said it was neither better nor worse.

But most people kept taking it, even though it didn’t help their arthritis pain better than what they had been on, including cheap OTC medications. Then came troubling reports of potential heart attacks associated with taking Vioxx. Suddenly, the slight benefit didn’t seem worth the huge but rare risk. The “average” person got more benefit than harm from the drug, but it was still pulled. From my personal recollection of our customers who took Vioxx for the first few years (I got married and moved away before Vioxx was actually pulled, so I missed the hysterical furor that probably erupted from hundreds of patients who had taken it), a few had great relief from it (they were the “millionaires” in the above example); some had good relief from it (the guys with a couple grand in the bank); but most didn’t seem to do better or worse, as far as arthritis/pain relief went; and a few got worse relief. But, the “millionaires” skewed the statistics. Looking at the group as a uniform whole, you just can’t see that most people’s benefit is too small to justify any risk. And a greater risk of heart attack is quite a risk! For a few people — those who get great benefit — it may be worth it to them to run the slightly increased risk of a heart attack for full relief from arthritis pain. But for the overwhelming majority of the world, it simply is not.

Hopefully, most research will properly look at these things, and report the best way of looking at and determining “average”; and if not, then it is to be hoped that there is enough information provided so that people reading the study can look a bit behind the numbers and see for themselves. Otherwise, statistics can be skewed to make it appear that the benefit is greater than the risk, or conversely, that the risk is greater than the benefit.

One Response

  1. I gave birth to 3 wonderful children, all came in less than 15 minutes, and I experienced no pain at all.

    As a matter of fact it was quite joyful!

    I created the Zero Pain Child Birth Blueprint. You can read about it here:

    http://www.scottchopchop.com/zpb

    or here

    http://sites.google.com/site/zeropainchildbirth/

    Sophia Nelson

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