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  #1  
Old 01-17-2011, 10:01 AM
Machine Elf Machine Elf is offline
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Life expectancy histogram?

Life expectancy in the US is approaching 80 years. This is of course an average; some people die shortly after being born, while others live for well over a century, and everyone else dies at some in-between age.

Anyone know where I can view something like a life expectancy histogram, for the US and/or the world? This might be a complicated thing, since life expectancy is often calculated differently depending on one's current age. How about something simpler: is there a histogram showing the age, at death, for all people who died in the past year or decade?

I'm curious to see the shape of such a histogram. For example:
-If life expectancy is (for example) 75, do the vast majority of people die within +- 5 years of that age, or is the spread much greater?
-Is there a very large infant mortality spike at the low end of the histogram? What about teen years, when kids are old enough to do dangerous things but not yet smart enough to do them safely?
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  #2  
Old 01-17-2011, 10:37 AM
JWT Kottekoe JWT Kottekoe is offline
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Not an answer to your question, but there is a fascinating visualization of the history of changes in life expectancy available here:

http://freakonomics.blogs.nytimes.co...ality-history/
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  #3  
Old 01-17-2011, 10:41 AM
guizot guizot is offline
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I think Gapminder is close to what you want, maybe not with all that detail.

Last edited by guizot; 01-17-2011 at 10:42 AM..
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  #4  
Old 01-17-2011, 10:55 AM
JWT Kottekoe JWT Kottekoe is offline
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Originally Posted by guizot View Post
I think Gapminder is close to what you want.
Thanks for the Gapminder link. This is the same animated visualization as the NYTimes link above, but without the commentary, which is also worth hearing.
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  #5  
Old 01-17-2011, 11:33 AM
Shmendrik Shmendrik is online now
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Quote:
Originally Posted by Machine Elf View Post
Life expectancy in the US is approaching 80 years. This is of course an average; some people die shortly after being born, while others live for well over a century, and everyone else dies at some in-between age.

Anyone know where I can view something like a life expectancy histogram, for the US and/or the world? This might be a complicated thing, since life expectancy is often calculated differently depending on one's current age. How about something simpler: is there a histogram showing the age, at death, for all people who died in the past year or decade?

I'm curious to see the shape of such a histogram. For example:
-If life expectancy is (for example) 75, do the vast majority of people die within +- 5 years of that age, or is the spread much greater?
-Is there a very large infant mortality spike at the low end of the histogram? What about teen years, when kids are old enough to do dangerous things but not yet smart enough to do them safely?
This seems to fit the bill. Note that it's a logarithmic graph.
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  #6  
Old 01-17-2011, 12:10 PM
Wendell Wagner Wendell Wagner is offline
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Notice that, according to the graph given in Shmendrik's post, it is not true that "the vast majority of people die within +- 5 years of that age." The average age at death in 2000 (which is what the graph in Smendrik's post is for) was somewhere between 76 and 77. The most likely ages for death at that point were between about 80 and 85. The next most likely ages for death are between about 75 and 80 and the next most likely after that are between about 85 and 90.

This is because, as in many distributions, the median is not the mode. That is, the number that you get by looking at the median age of death is not the same as the most common age at death. Look at what happens for deaths (using the U.S. in 2000 in the graph as an example). The number of deaths per year for people born in a given year rises slowly up till the age of about 80. At this point somewhat more than half of the people born in that year are already dead. Then the number dying stays high for the next forty years until everyone is dead. This means that the age with the most deaths is about 83, while the average age at death is just under 77.

(Yes, I know that "the number of deaths per year rises slowly till 80" is not quite right. There's also the big bump at birth which decreases till the age of 10, when it rises again. It would still be true that the median is not the mode if this didn't happen.)
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Old 01-17-2011, 12:59 PM
Uncertain Uncertain is offline
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Quote:
Originally Posted by Shmendrik View Post
This seems to fit the bill. Note that it's a logarithmic graph.
Note that this sort of graph is influenced by differences in the number of people born in various years. For example, the number of deaths of 60 year-olds is about 1/3 of that of 80 year-olds. I imagine that there were more people born 60 years ago than 80 years ago, so the relevant number is smaller than 1/3.
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  #8  
Old 01-17-2011, 01:43 PM
TriPolar TriPolar is online now
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Anybody know how infant mortality figures in these graphs?
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  #9  
Old 01-17-2011, 02:50 PM
Galileo Galileo is offline
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Here's a table (in pdf format) from the National Vital Statistics System: Deaths by Single Years of Age, Race, and Sex: United States, 2007.

I think that it contains the info that the OP is requesting, but not summarized graphically. There's definitely a spike in mortality in the first year after birth, and the lowest mortality is around ages 8 and 9. There's also a bit of a spike around age 22 for males, but not for females. Afterwards, the mortality seems to increase smoothly and exponentially. No indication that "the vast majority of people die within +- 5 years" of average life expectancy.

And, here's a table from Social Security Online, Period Life Table, with some interesting info on mortality rates.
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  #10  
Old 01-18-2011, 10:16 AM
Half Man Half Wit Half Man Half Wit is offline
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Alpha is pretty good with such data (I feel like recently, all I'm doing in GQ is pimping Alpha, but for certain types of factual query, it actually is quite a useful resource); it doesn't give you a histogram directly, but tabulates survival probabilities by age, which contains the same data (if I haven't misunderstood the OP). Here's the data for the US.
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  #11  
Old 02-27-2014, 10:53 AM
Machine Elf Machine Elf is offline
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Originally Posted by Galileo View Post
Here's a table (in pdf format) from the National Vital Statistics System: Deaths by Single Years of Age, Race, and Sex: United States, 2007.
I'm reviving this thread because I finally crunched through the data that Galileo linked to, and I wanted to share my results here with anyone who is still vaguely interested. The data at that link includes deaths by age, which is what I had asked for in my OP. This was easy to plot by itself, but I also wanted to plot survival probabilities for defined periods, which was a bit more interesting.

The challenge in doing so is that over the past 100 years, very different numbers of babies were born each year. It's actually varied by a factor of two, and not in the direction you'd expect:

Plot of US Cohort Births by Age in 2007
(please excuse the typo: the left vertical axis caption should read "...Population/100", not "..."Population/100M")

Note that the horizontal axis is "age in 2007". So people who were 100 in 2007 were born in 1907. The birth [i]rate[/i ]was about twice as high then as it is now (30 vs. 14 live births per 1000 people), but the total population then was about 1/4 what it is now (70M vs. 300M). The net effect is that the total number of live births in 1907 was about half what it is now. So when you want to compute survival probabilities, you have to start by dividing the absolute number of fatalities in each cohort by the absolute number of live births in that cohort. Then you can run the numbers:

Plot of US Mortality and Conditional Survival Probability by Age in 2007

The blue trace is the raw number of fatalities in each 1-year cohort in 2007. So for example, if you were 83 in 2007, you saw 15X more of your friends die than your 20-year-old grandson did. When you correct these raw numbers for live births, you end up with the magenta trace, and it's those corrected values that I used for computing survival probabilities. Those traces answer the question: "given that I have reached the age of X, what is the probability that I will survive another one/five/ten years?"

Some notes and speculations about the features in the data:

-Sadly, infant mortality is very real. An uncomfortably large number of infants died in their first year of life. If you’ve got a healthy toddler, give him/her a hug; they’ve made it through the scariest part of their childhood.

-Fatalities are very low for pre-teens. Once kids get to their upper teen years, something happens to cause higher fatality rates. I'm guessing this is related to teens' poor judgment of risk and reduced parental supervision - car wrecks, drinking, violence, etc.

-Things calm down a bit in the late 20's: young adults are getting smarter about risk, and are still relatively healthy.

-After 35, the fatality rate starts climbing steadily, presumably corresponding with a gradual decline of physical health.

-The raw fatality numbers did some funny things for people in their early 60's. These are folks who were born during or shortly after WW2, when birth rates did correspondingly funny things. Normalizing for the number of live births squelched a lot of that zig-zag, though not quite all of it. I would assume deaths are well-documented these days, but maybe births were not as reliably documented in the 1940's, so maybe that accounts for the remainder of the jiggling there.

-One-year survival probabilities for centenarians becomes increasingly noisy because in 2007 the number of fatalities in each cohort is very low. For supercentenarians (those who have reached/exceeded 110), the numbers fall to virtually nothing: six 110-YO’s died in 2007, and one 112-YO. The noise for the five-year and ten-year survival probabilities is much lower because they are calculated by multiplying five or ten of the subsequent one-year probabilities, which smooths things out quite a bit.
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  #12  
Old 02-27-2014, 12:21 PM
Hermitian Hermitian is offline
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Quote:
Originally Posted by Machine Elf View Post
I'm reviving this thread because I finally crunched through the data that Galileo linked to, and I wanted to share my results here with anyone who is still vaguely interested.
Awesome graph. I like it.

The thing that caught me by surprise is how quiet the 1-13 age range is.
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