Friday, May 28, 2010

The confusion of average vs. normal

Normal gas station sign


I wanted to do a short little (we'll see, won't we?) informative post today about the difference between the terms "average" and "normal," because I think they're confused a lot in our culture, even by those who theoretically should understand them due to their training (i.e., health professionals, who I believe take science and math classes to graduate, whereas I was an English major), as well as by parents who are either unjustifiably concerned about not meeting averages or unsuitably (but understandably) proud at beating them.

This article —

"Average age versus normal range," by Michael K. Meyerhoff

— originally published at Pediatrics for Parents, is what really helped me understand the differences between these two concepts, during those developmental phases that we as parents get antsiest.

An average (in terms of "mean") is a mathematical construct that takes data, (often) filters out the extreme outliers, adds up all the numbers that are left, and then divides the total by the number of items. We all know this, right? It's just when it gets put into practice that it gets murky.

bell curve graph of standard deviation and normal range
Bell curve showing normal distribution of data.
The average is the "mean score" in the middle.
Normal, on the other hand, is always a range, when referring to "normal distribution," the bell curve shape you would expect to find within a group of data. For instance, it might be normal for a baby to crawl (or scoot, as in Mikko's case!) between six months and ten months. The average time for a baby to crawl, then, might be eight months, but it is still normal for a baby to crawl starting at six months or not until ten months. Six months might be at the far left of the bell curve and ten months at the far right, but both are still within the expected range for crawling.

When I talked about "extreme outliers" in defining average, that's where you get abnormal. I don't really like the term "abnormal," because it sounds pejorative, but I hope you know that I mean by it simply outside the normal, expected distribution. As in, a baby who crawls at four months would be outside the norm and would be an early crawler. A baby who didn't crawl (or scoot or walk) until fourteen months would be a late crawler. Their age of crawling would not be normal and would fall outside the expected bell curve distribution. The babies themselves might still be perfectly healthy (more on that in a minute), or they might not, but it's only at that point that it bears looking into. Up until the end of the "normal" range (barring any other signs pointing toward developmental delays), it's perfectly reasonable for a parent to wait patiently for a child to "catch up" to the children who took a developmental step earlier (note I said "earlier," and not "early").

What I find frustrating is medical professionals and other experts who don't understand the difference between average and normal when it comes to diagnosing problems. For instance, the average length of a pregnancy (or so someone decided) is 40 weeks. The normal length of a pregnancy is 38 to 42 weeks. If a woman is a day past 40 weeks, she is not "overdue" or "late." She is normal. If she is two weeks past her "due date" (a term I wish outlawed), she is still not late! (Again, barring any indications of a problem. Being past the due date is not in itself a problem.)

You also see this with weight gain recommendations, both for pregnant women and for babies. A pregnant woman will gain five pounds one month and be warned off eating fat for the next month. She'll gain only two ounces the next month and be told to increase her fat intake. It's ludicrous. Averages don't work that way! An average is over time, over a large set of data. It doesn't mean that every month is going to exactly match the average. But health professionals (and those trusting them) get it into their heads that the "average" monthly weight gain of a healthy pregnant woman is also the magic number that must be met every month, and it simply isn't true.

There's another fallacy inherent in looking toward an average weight gain and applying that to every woman (or baby or child). No woman is average. I cannot emphasize this enough. An average is a mathematical construct, a calculated midpoint within a set of data. It is not a human being. No individual woman or man is average; no pregnancy weight gain is average; no baby's growth chart is average; no child's development is average. No one meets the average!

Let's take some real numbers as an example.

1 6 7 8 10 11 12 27

Play along with me and assume that we determine that 1 and 27 are outside of normal distribution, so we discard them. Now we're left with 6 7 8 10 11 12. We add them up: 54. We divide them by the number of numbers (6) and are left with our average (mean): 9.

Is 6 abnormal because it is not 9? No. It's true that 6 is lower than 9, but it is still within the range of normal. Is 12 too big because it is not 9? No, because it is still normal. Note, too, that 9 doesn't even exist! It is only a theoretical, mathematical construct. It is an average but not an item in itself. (Yes, I chose the numbers this way on purpose to make a point.)

Now, is 27 or 1 outside of normal? In this exercise, perhaps so. Maybe if 1 and 27 represent people with some potential health issue, they should get that looked at. But maybe they're fine, too, and if we had more data to go on it would help determine what the normal, expected distribution might be. Maybe 6-12 are simply occupying that widest part of the bell curve, but 1 and 27 are still within the narrow ends on either side.

You can see this play out in everyday life. For instance, the "average" woman's menstrual cycle is 28 days. Well, fine, but that doesn't mean that my average cycle is 28 days. Mine happens to be 29 days. I am still normal. AND, furthermore, my cycle ranges from 27 days to 34 days. You know what? All those cycles: still normal. Possibly very few of them are 29 days. But the average emerges over time, given enough data. I know that if my period doesn't magically appear after 29 days, that doesn't mean I'm pregnant. I just give it a few more days. If my period comes "early," on day 28, I just shrug and put in my DivaCup. It's all fine. I also don't get bent out of shape that my cycle isn't an average 28 days, because — say it with me — no one is average.

Now, again, this is where outliers come into play. If my cycle average was 23 days, I might in fact have a fertility problem due to a short luteal phase. If my cycles varied wildly, really wildly, from 23 days one month to 38 days the next, that might suggest a hormonal imbalance (or miscarriage or menopause). That's where averages help — averages can assist in setting a range for what "normal" might be, but they don't by themselves define normal.

And just another word about outliers. I want to repost my son's growth chart from when he was 10 months old. Talk about unaverage!



He wasn't even, strictly speaking, normal. You can see he's actually breaking the weight chart. But he was fine. He was healthy, and is healthy, and his growth slowed way down after that point and has remained at almost a plateau (which, again, is totally fine). (You can see more pictures of his chubbiness in development here.)

Mikko also talked and walked later than the average, but still within normal range. We weren't worried. We knew some people who were. He caught on just fine once he started, and proved our lack of worry correct. Now, if he still wasn't talking now at 2.75 years old, I probably would have gotten his hearing checked again or looked into other physical problems that might exist. But, even then, there are children who for whatever reason choose not to speak for longer than is "normal" and end up fine. It's one of those things where, if it's really worrying you, it's probably best to check, because there might be an undiagnosed hearing problem or similar. But if everything seems fine otherwise — it probably is. And, on the flip side, if your baby starts talking or walking "early" but still within the normal range, go ahead and brag — why not? But just know that it doesn't indicate anything about meeting future developmental milestones (or your prowess as a parent — but you already knew that, didn't you?).

My point is this: If your child is within the range of normal (or your weight, or your cycles, or times your child breastfeeds per day, or hours your kids sleep, or length of your pregnancy, or progression of your labor, or whatever it is), and you don't see any reason to be worried — and even if you're outside the range of normal but you believe you have good reason to be (for instance, we factored in that both Sam and I are taller than average — but still normal! — to our interpretation of Mikko's large size) — then don't sweat it if you're not hitting the average in every respect. No one does.

We're all normal that way.

I want to include a tiny disclaimer that I am not a health professional, and please don't take the word of a blogger as reason not to have any health concerns checked out by someone who's qualified. Just don't let anyone bully you into thinking average is the same as normal, because it isn't. So there. I'm only trying to empower all those who are within norms to stand up for their right not to be average. And I love all those of you outside the norms, too, because I'm there as well in various ways.

When have you been confronted with the confusion between average and normal? Has anyone told you that you or your children weren't normal when you knew everything was fine, thankyouverymuch?

"Normal" gas station photo courtesy jendo on stock.xchng.
Bell curve distribution chart snagged from University of
Kansas Medical Center
, and I hope they don't mind,
because it was the bestest one I could find.

18 comments:

allison said...

Yeah, my kids didn't crawl until sixteen and seventeen months. Abnormal? Lazy? Surrounded by people who would bring them exactly what they wanted? My doctor made an appointment for Eve at the children's hospital. I was like, "dude, when you try to make her stand on her legs she jackknifes them up and holds them out straight. I'm pretty sure that takes more muscular control than actually standing." Being a perverse creature, she pulled up and stood the day before the appointment. Ha.

Maman A Droit said...

How about, on average American mommies only breastfeed for a few months, but it's normal to do so for much longer than that!

Dionna @ Code Name: Mama said...

Lauren - this is an EXCELLENT post!! You explained the difference in a way that I've never read in any textbook. Awesome :)
(And I love Maman A Droit's comment about bf'ing! :))
Hmm - Kieran's been on the later end of normal for holding his head up, scooting, crawling, & walking. But the boy has all kinds of athletic prowess now (wink wink), so I'm glad I didn't worry about it.

the grumbles said...

This stuff drives me CRAZY because we have several babies in the family all around the same ages. So it's like some kind of competition- who's the biggest? who's the tallest? who crawled first? Who can stand now?

They're all going to do everything at their own rate and that's 100% normal. Do we really need to compete over this? Family dynamics add an extra dimension to the "what is normal" debate. Ugh.

Olivia said...

Great post! For a long time I have tried to not use the word normal for many things because I don't want to label anybody "abnormal". Instead I use "typical", "common", or "average". However, after reading this I see I've been wrong to say "average range" when applied to baby development.

By the by, my daughter is 14 months, below average for weight and height, and is not walking or talking yet. And, I am not worried one bit. I think she is soaking it all in and will start talking in sentences in a few months. ;)

Cave Mother said...

Interesting to see a bit of maths in a parenting blog! I did maths at uni. Though I must take exception to your use of the word "average"; of course what you were referring to was the mean. There are three kinds of average: mean, median and mode.

Don't worry, I'm not being serious. This is a good explanation of something that a lot of people get confused about (how many times have you heard on the news "50% of children are below average in reading and writing!").

Amber, The Unlikely Mama said...

OOOH this makes the stats nerd in me happy (psych research major here!). People really don't get statistics, so when doctors (or other scientists) throw numbers out there...they can sound impressive or even scary, but they aren't the whole story.

I completely agree with you that we should be more concerned with making sure that our kids (or ourselves) are healthy...rather than hitting milestones at exactly the "right time".

With a baby that was a preemie, we have all sorts of experts checking in with us. It's almost infuriating. They tried to give me a hard time because Alexa wasn't crawling at 11 months (so 9 months adjusted). Hello, still normal! Not to mention, she was already cruising, and didn't really "need" to crawl to get to things. Of course, as soon as they tried to freak me out into going for early intervention therapy, she crawled like a week later!

Babies will do things at their own rate. The comparison is just another thing for us to get bent out of shape about. Hell, my mother likes to compare what I did as a baby to what my daughter does. Apparently I was "gifted" heh!

gyenyame said...

love love love this article.
Thank you so much for writing it!

Lauren @ Hobo Mama said...

Allison: I love your attitude — and your daughter's! :) My doctor really, really wanted Mikko to crawl because of some (somewhat disputed) links between crawling and learning disabilities, and he would only scoot on his bum. He was super fast, too! After he learned to walk (at 18 months), he then learned to crawl, and she was finally satisfied.

Maman A Droit: Good one! That's a great example, too, of how the average can be skewed so that the normal range seems much smaller than it is. Like, if it's average to wean at 3 months, then how bizarre is it that I'm still nursing at 35 months? Um, as it turns out — not bizarre at all! :)

Dionna: Thank you! Glad I'm not the only one with a non-superstar baby. ;) My niece, and I don't begrudge her this, was on the early end with everything, and according to my mother (ahem), so was I, so there was a little family expectation going in that Mikko would also be some developmental prodigy. So silly in retrospect!

the grumbles: Totally! Those dynamics are obnoxious. It's so funny (not the ha-ha kind), because I have a cousin who has a son who wasn't talking for a long time, and then for a long time after that rather garbled. And my mom was always on their case (behind their back) about it, saying they really should get that kid to speech therapy right away. Then, when Mikko went through the same thing: No talk of speech therapy anymore. (Well, at least, to my face!) It's funny, too, because sometimes she'll say I did something at such and such an age, and I'll check my baby book and she's skewed all her memories earlier. :)

Olivia: I could see "average range" meaning the same thing, since it has the word "range" in there. I mean, the "average" part I guess wouldn't be mathematically intended but just the common usage of the word. I like your point of "typical" and "common." I also dislike saying or implying "abnormal." Your baby sounds utterly sweet and typical. :)

Cave Mother: I knew I should have run it by a math whiz! I did think of clarifying between the types of averages but, um, didn't. See, English major here. :) I've added "mean" to the article so there's not as much confusion, though I do think the mean type of average is what most people mean when they say average. I thought about it, and I think that the average age children walk or whatever would have to be mean, because median doesn't really make sense. In some cases, mode might be an option, but I'm still guessing mean is the one.

Amber: I know I'm still learning lots about statistics. I find it fascinating, even though I'm still trying to absorb! Like what Cave Mother said about "50% are below average!" — plenty of things sound scary when there's a percent sign attached. :) I bet it's even harder with a preemie, because there's so much pressure to make sure they "catch up." Good thing Alexa showed them what's what! :) And glad I'm not the only one who has a mother comparing us to our own babies.

gyenyame: Thank you! See you soon. :)

Melodie said...

This post is going to make a lot of moms feel better about their "abnormal" (pshaw!) kids. Nice work!

Emily said...

One of my favorite quotes: it would be very boring to be normal! :-)

Kathy said...

This is spot on and I wish more people understood this distinction. Having had one child who was an outlier on the high side (bit like Mikko's charts above) then two children who were light & short compared with the *average* (but still within the "normal" range!) I got really tired on having these conversations. Next time someone comments that my 15-month-old is "littler than average, huh?" I think I'll just reply, "Yep, she's totally normal!" and refer them here.

Lisa C said...

My son was a late crawler, and his teething is pretty abnormal, too. But he is healthy! The teeth thing worried me a little bit (thought he might be vitamin D deficient), and then my mom told me that I was a late teether, too. Genetic.

Of course the late crawling was blamed on my holding him so much, which I simply do not believe is true, and even if it was, so what? It's not like I was holding him captive.

Anyway, we're lucky to have a pediatrician who seems to have a good understanding of what is normal. I came in concerned about him being late on some things, and he told me that he would catch up. And of course he did.

♥ Fanged Faerie Girls ♥ said...

Hey, this was a good post and reminded me that I obsesses over the small things sometimes. It is almost like it becomes a reflection on your parenthood if your child is late/early/average.

_______________

When have you been confronted with the confusion between average and normal? Has anyone told you that you or your children weren't normal when you knew everything was fine, thankyouverymuch?
______________

My daughter just started walking yesterday, at a little over 13 months and it seems like all I heard before then was people telling me their child walked earlier than that or expecting all kids walked before a year.

The biggest thing is her petite-ness (about 19 lbs atm) which everyone has to comment on. She has been small since birth and her ped. says she is healthy and wait for it...normal.

It still upsets me though, I cannot really help it. The worst was a woman that said (in a sad voice) 'oh, she's so skinny' which made me so mad and also hurt my feelings. :(

She is not SO SKINNY, she is normal!

Amber said...

Earlier today, I actually said that I wish that they banned growth curves. I see so much anxiety surrounding those things. My own children grow in spurts, so their percentiles constantly fluctuate. And as soon as babies are dropping percentiles, people freak out. But for them, it's normal. They are healthy children following their own growth pattern. You can see that just by looking at them. The growth chart? So, so not helpful.

oursentiments said...

Oh, this post brought me back to the Ped. visits for DD's reflux. She was born "underweight" at 5 pounds 8 ounces. Now at 3 she is 24.5 pounds. Do you know she had to give blood and was advised to have extra butter, oils, decrease nursings and more solids to 'gain weight'! Her visits became more about weight than reflux!

Even though I agreed with my Dad, she is healthy and normal, I just could not get over that "Failure to Thrive" on a sheet of paper in her file. Oh, and how she will not grow a healthy brain....

It was our family doctor who stated "Maybe she is going to be a small person or a tall and very thin person." Which is what I was telling the Ped. all along.

BTW My Mother is short and so is my sister, My father tall, I am 5'4" at 105 pounds. DH is about 5'5" and his family is around his height but a bit on the larger side, but his brother is also tall and a bit built. Do you think that mattered at all to the Ped.?

Jami said...

I want to print this out and staple it to the bulletin board at our ped's office. Literally. lol I get so annoyed with doctors being so focused on percentages and what's "normal" (when that is not what they are interested in, they don't even understand the concept!!). Every appt. they remark how short both of my kids are, like they are some kind of pigmy aliens or something lmao I always point out that its genetics and get "Oh really??? What makes you think that???" Umm because I am 5'2" and my husband is 5'4"? Doesn't take a genius to see that it is pretty likely our children will be on the smaller side. But, appt after appt. I hear the same thing. Throw out the growth charts if you can't interpret them correctly. There is a whole RANGE OF NORMAL. And yes, even my pigmy alien children are well within it. haha ;)

MamaMeg said...

Hi Cave Mother!
Actually Lauren is totally correct. The average is the mean. They are two words for the same thing. Mode and median are often taught at the same time in school, but they are not different types of average. There are many different descriptive statistics that can be chosen as a measure of the central tendency of the data items, and in addition to the average or mean, one can use a mode or median to describe a data set.
Love your blog and the post! I'm a crunchy mama in training whose first ” child” was a PhD in biophysics!

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