The Average Person Hates Math
The "Average Person" is one of 3.13 People in Their Family
Math can be misleading. Or, at least the interpretation of numbers and statistics by some people is often confused, or confusing. Mark Twain said, “Figures Don’t Lie, but Liars do Figure.”
Oftentimes, for instance, an average is quoted and is promoted as meaning that a certain event or outcome is common. That is not always the case. Here are three examples:
1) Average Length of a Day
What is the average length of a day? You might say 24 hours, but that’s just one type of day; there’s also a longer, indefinite period of time called a day, such as “grandpa’s day” (perhaps lasting from 1902-1979, for example) or “in the days of the dinosaurs” (a good while ago, and lasting a pretty long stretch of time).
What I’m talking about here, though, is the length of the sunny portion of a 24-hour day; in other words, when the sun is “up,” as in daytime vs. nighttime. The average length of that sort of day is twelve hours: twelve hours of sunlight, along with twelve hours of darkness. And yet, although that is the average length of day (and night, too), it only happens twice a year. So although it’s the average, that exact day (and night) length only occurs twice in 365 (sometimes 366) days, or 0.55 % of the time. Those two times are the spring equinox (on or around March 20th) and the fall equinox (on or around September 22nd). Three months after the spring equinox is the longest day (and shortest night) of the year, and three months after the fall equinox is the shortest day (and longest night) of the year.
Note, though, that these dates are reversed in the southern hemisphere, where the fall equinox occurs in March and the spring Equinox takes place in September; Complicating matters further, the sunrise and sunset times differ based on latitude — hence the super-long summer days (and super-short winter days) experienced way up north in Alaska, Greenland, Finland and suchlike places as well as way down south in places such as Chile and Australia. Also, I notice that here in Monterey, California (a fair distance north of the equator while also being more than just a few hops, skips, and jumps south of Alaska) it seems that we will perhaps hit the "Singularity" (12 hours of sunlight/darkness) as early as tomorrow (March 17th). I make that prediction based on today's sunrise being slated for 7:17 am, and tonight's sunset being prophesied to occur at 7:15 pm; Since the sun is “rising” a little earlier each day, as well as setting later each day (until the start of summer, when things will start moving in the opposite directions), I would think that both tomorrow's sunrise and -set will be at 7:16.For Mokelumne Hill, though, just 192 miles to the northeast of us (as the highway unfurls, and where I “mostly” grew up [in both senses of the word], and where my parents and younger brother live — and my sister a few miles away), sunrise is set for 7:12 and sunset for 7:10 (five minutes ahead of us).UPDATE 3/17/23
It turns out that Monterey is probably as close as it’s going to get to the Daytime/Nighttime “Singularity” today, with sunrise slated for 7:15 am and sunset for 7:16 pm. But those figures are obviously rounded, so maybe more precisely sunrise will be at 7:15:29 am (rounded down to 7:15) and sunset will occur at 7:15:30 pm (rounded up to 7:16). I don’t know. Mokelumne Hill, OTOH, has both a sunrise and -set of 7:11 today. I just added Pontianak (which, according to the interwebs, is the only city in the world directly on the equator) to my iPhone’s weather app, and I will compare its sunrise/set times on March 20th as well as the day before and after. I’m guessing they will match (or be opposites, so to speak) on the official spring equinox date.
On March 21, Monterey had a sunrise of 7:09 am and sunset of 7:20 pm.
Pontianak, West Kalimantan, Indonesia
March 19th: Sunrise 5:47 am, Sunset 5:53 pm
March 20th: Sunrise TBD am, Sunset TBD pm (forgot to check, but must have been either 5:46 or 5:47 for sunrise, and 5:53 for sunset based on interpolation)
March 21st: Sunrise 5:46 am, Sunset 5:53 pmRegardless of all that, what I intend to emphasize is that what is average is not always a common occurrence. In fact, sometimes the average of something never happens. More on that anon.
A “Yeah, But” Concerning 24-hour Days: Due to “Daylight Saving Time,” two days per year are not 24 hours long. The day we “spring forward” (last night, dadburn it!) is only 23 hours long, as the hour that we skip ahead is taken from us, a fact which is lamented with much gnashing of choppers each year by my wife. Vengefully, though, we steal back that pilfered hour when we “fall back” half an annum later, and enjoy the year’s only 25-hour day, sleeping one of those hours “all over again” as a sort of unconscious encore.2) Average Lifespan
You often hear (well, to be clearer, I have often heard this; but you probably have, too) that back in the “olden” days people usually only lived into their 40s or even 30s. For example, one website says:
At the time of America's founding in 1776, the average newly-minted American citizen could expect to live to the ripe old age of 35, giving them a few months to run for the presidency before they keeled over.By 1787, the average life expectancy had risen to 38, and by 1900 it had climbed to 47. Still low, though.
People spout these averages and seem to think that residents of those time periods suffered from Benjamin Button disease (technically Progeria, or Hutchinson-Gilford progeria syndrome (HGPS)), and assume that there were a lot of people dying at 35 in Revolutionary Times and at 47 around the Turn of the Century.
Obviously, some did die at those ages back then, just as some do even now. But that doesn’t mean that if you lived in those days you would have been bald, wrinkled, and shuffling along with a walking cane in one hand and an ear trumpet in the other when you reached your 30s or 40s, expecting to “pluck at the coverlet” any day. Rather, it was primarily the dangers of being a child that caused the average life expectancy to be so low in those times. There were people living into their 70s and 80s on a regular basis, and some even into their 90s and 100s during those times: Washington Irving lived to be 76, Benjamin Franklin lived into his mid-80s, John Adams lived to be 90, and his son John Quincy Adams lived to be 80. Even Mark Twain, who was a heavy smoker from his youth on, lived to be 74 (and-a-half).
So how was it that the average life expectancy was so low in those times? Again, there were many deaths from childhood diseases, as well as babies who died at birth — and mothers (who were obviously relatively young at the time) often died while giving birth. And then there were the poets sprinkled in here and there, who almost always die young. So with the following ten people with their ages at death:
Man 1, lived to be 80
Woman 1, lived to be 82
Man 2, died in a farming accident at 45
Woman 2, lived to be 90
Woman 3, died in childbirth at 20
Baby 1, died at birth
Male Child 1, died at 3 from childhood disease
Female Child 1, died at 2 from childhood disease
Man 3, a poet, lived to the “average” age of 38
Man 4, died at 20 in war or hunting accident
…you have an average life expectancy of 38, which was the average life expectancy in 1787.
And these examples are not at all far-fetched. It was common for families back then (most of whom were farmers who needed as many helping hands as possible) to have ten or twelve children, and to lose half of them either at birth or in the first few years of life. Many of a family like that could live into their 80s and beyond and yet the family still end up with an average lifespan of only 40-some years.
Even in those rough and primitive times, if you survived your childhood (and, in times of war, your young manhood), you had a pretty good chance of living to a “ripe old age” a la Rip Van Winkle.
You can see, then, that you can’t always take averages at face value. You have to consider the various factors, the outliers, and what is really going on with those numbers.
Now for a final example:
3) Average Football Score
Let’s briefly analyze the average score of a football game. It’s quite possible that it’s something like 22-21 or 22-20, yet very rarely does a team actually end up with a final score of 22 points. It’s possible, but it’s definitely not commonplace (the only impossible final score for a team in the NFL is 1 — you can score 1 point in a football game, true, but only after you’ve already scored 6, that one point being called an “extra point”). But 22-21 is a possible average score, and very well may have been the average score of a game at some time in the past (average scores keep going up, due mainly to rule changes that give offenses the advantage, so nowadays the average score is probably more like 24-23 or 27-24 or some such).
And if you wanted to get precise about it, the average score probably involves real numbers, such as 26.2-23.9, both of which are impossible.
Math (especially averages and statistics) can be fascinating, and if you take the time and make the effort to examine things closely, you may see that there is often more there than meets the eye at a passing glance.
Are you that average person, who hates math? Or are you an outlier?