That figure is average life expectancy. IE 50% of US man are expected to reach 77.
I can’t access the full paper that this is in reference too, so I’m not sure how they calculate it… but isn’t life expectancy usually the mean age of death? I would expect the distribution to have a left skew from people who die young, which should mean that more than 50% of US men are expected to reach 77.
Take a life table, check the column that says lx, that means how many people of the model are alive with x years, normally l_0 = 10000. Then go down until you found lx = 5000 or lx = 1/2 l_0, that x is your life expectancy at birth. If you want to know the life expectancy at any age, look for the value of lx at that age, then look in how many years that value half, that’s the expectancy.
Source: I’m an actuarie and study that in college, but don’t ask me to go deeper because I don’t use that at my job.
That marks the median age of death, but I don’t think that’s the definition of life expectancy (though maybe the term is used loosely or imprecisely to mean the median age of death or the average (mean) age of death in different situations…). The definitions of life expectancy I found claim it’s the mean age of death, which would make sense because the expected value of a random variable is the arithmetic mean. That said, the median on the life tables that I have found seem to correlate much more closely to the age of 77 versus the life expectancy at birth which is much lower (78-79 for the median and 74 for the life expectancy at birth for 2020 data)… but the actual paper is behind a pay wall so I have no idea what they’re actually computing for 77 years of life expectancy… my guess is that it’s the median and not the mean, but maybe they’re considering people over a certain age or something… either way, the mean / median getting confused is an issue and I wish people were more clear about what metric is actually being communicated.
Okay, I couldn’t look at this table when I responded last night (I thought you were referring to the zip files, not the PDFs at the bottom). Got a chance to look at them on my computer today!
Would you call the point where I_x = 1/2 I_0 the life expectancy at birth? In the life tables you link to (direct link to the 2020 table) there’s an “expectation of life at age x” column which differs! My understanding is that in official metrics of “life expectancy” they usually mean the “life expectancy at birth”, which is calculated in the “expectation of life at age x” column in this data set, do actuaries use a different definition?
In this table “life expectancy at birth” is estimated at 74.2 for men in the USA in 2020. This is calculated in this table by computing T_0 / I_0, which is the arithmetic mean for the ages of death in this period. The estimate for the median age of death in this table is between the ages of 79 and 80. There’s about a 5 year difference between these two numbers, and furthermore only about 40% of the population of men has died by the ages of 74-75 in this table, which is quite different from 50% if we assume “life expectancy” is this arithmetic mean. These are pretty big differences, and I really wish people / articles would be more clear about how the number they’re quoting was actually calculated and what it means! The estimated median age of death from the point I_x = 1/2 I_0 is a useful measure too, but I have no idea what a random person or article intends when they say “life expectancy” :|. I’ve grown to deeply distrust any aggregate measure that people discuss informally or in news articles… It’s often very unclear how that number was derived, what that number actually means in a mathematical sense, and if it even means anything at all.
I think im going crazy because I was sure that the ex was the easily calculated as I told before, but I just checked a couple of different mortality tables and the math doesn’t check out. I have no worked with life tables since college, but I’m going to ask my boss, that used to work with life insurance, about it tomorrow and follow up with his answer.
I just talked to my boss and he didn’t knew where the fuck I learned that because it had no sense. Maybe I saw some wicked up life tables where for some reason it worked like that. The formula is sum(i=x,w) l_i /l_x, that means (l_x + l_x+1 + … + l_w) / l_x, where w is the maximum life of the table.
To me mean = average, so the two statements are the same.
Are you talking about median age of death?
When child mortality was very high (pre- 20 century) that was definitely the case. I am not so sure that it is now. I feel that average life expectancy will be a lot closer to 50% survival rate (median age of death) than it was in the past.
To me mean = average, so the two statements are the same.
Are you talking about median age of death?
The median is the midpoint of a sample, not the mean. So, the median point represents the age where 50% of people will live to, the mean does not represent that (it’s often relatively close to the median assuming the data doesn’t have too much skew, but it can be way off).
When child mortality was very high (pre- 20 century) that was definitely the case. I am not so sure that it is now. I feel that average life expectancy will be a lot closer to 50% survival rate (median age of death) than it was in the past.
There are still plenty of people who die young, even though child mortality is less of a factor in wealthy countries right now. Plenty of people die in car accidents at a relatively young age, for instance. I’m sure the median and mean aren’t like 10 years off of each other, but I wouldn’t be surprised if they’re 3 or even 5 years off, which could be pretty significant in this context.
Well, the definition of the mean and median of a sample doesn’t depend on the particular data set, and there’s plenty of non-age related causes of death in the world which would logically skew the distribution to the left! You can look at actuarial tables to see this in action:
Male life expectancy at birth in this table is 74.12, but you’ll notice that you don’t get to 50% of the population dying until somewhere between the ages of 78 and 79.
This website has a pretty good chart showing the skew for a 2019 dataset:
I can’t access the full paper that this is in reference too, so I’m not sure how they calculate it… but isn’t life expectancy usually the mean age of death? I would expect the distribution to have a left skew from people who die young, which should mean that more than 50% of US men are expected to reach 77.
Take a life table, check the column that says lx, that means how many people of the model are alive with x years, normally l_0 = 10000. Then go down until you found lx = 5000 or lx = 1/2 l_0, that x is your life expectancy at birth. If you want to know the life expectancy at any age, look for the value of lx at that age, then look in how many years that value half, that’s the expectancy. Source: I’m an actuarie and study that in college, but don’t ask me to go deeper because I don’t use that at my job.I was wrong.
That marks the median age of death, but I don’t think that’s the definition of life expectancy (though maybe the term is used loosely or imprecisely to mean the median age of death or the average (mean) age of death in different situations…). The definitions of life expectancy I found claim it’s the mean age of death, which would make sense because the expected value of a random variable is the arithmetic mean. That said, the median on the life tables that I have found seem to correlate much more closely to the age of 77 versus the life expectancy at birth which is much lower (78-79 for the median and 74 for the life expectancy at birth for 2020 data)… but the actual paper is behind a pay wall so I have no idea what they’re actually computing for 77 years of life expectancy… my guess is that it’s the median and not the mean, but maybe they’re considering people over a certain age or something… either way, the mean / median getting confused is an issue and I wish people were more clear about what metric is actually being communicated.
Okay, I couldn’t look at this table when I responded last night (I thought you were referring to the zip files, not the PDFs at the bottom). Got a chance to look at them on my computer today!
Would you call the point where I_x = 1/2 I_0 the life expectancy at birth? In the life tables you link to (direct link to the 2020 table) there’s an “expectation of life at age x” column which differs! My understanding is that in official metrics of “life expectancy” they usually mean the “life expectancy at birth”, which is calculated in the “expectation of life at age x” column in this data set, do actuaries use a different definition?
In this table “life expectancy at birth” is estimated at 74.2 for men in the USA in 2020. This is calculated in this table by computing T_0 / I_0, which is the arithmetic mean for the ages of death in this period. The estimate for the median age of death in this table is between the ages of 79 and 80. There’s about a 5 year difference between these two numbers, and furthermore only about 40% of the population of men has died by the ages of 74-75 in this table, which is quite different from 50% if we assume “life expectancy” is this arithmetic mean. These are pretty big differences, and I really wish people / articles would be more clear about how the number they’re quoting was actually calculated and what it means! The estimated median age of death from the point I_x = 1/2 I_0 is a useful measure too, but I have no idea what a random person or article intends when they say “life expectancy” :|. I’ve grown to deeply distrust any aggregate measure that people discuss informally or in news articles… It’s often very unclear how that number was derived, what that number actually means in a mathematical sense, and if it even means anything at all.
I think im going crazy because I was sure that the ex was the easily calculated as I told before, but I just checked a couple of different mortality tables and the math doesn’t check out. I have no worked with life tables since college, but I’m going to ask my boss, that used to work with life insurance, about it tomorrow and follow up with his answer.
I just talked to my boss and he didn’t knew where the fuck I learned that because it had no sense. Maybe I saw some wicked up life tables where for some reason it worked like that. The formula is sum(i=x,w) l_i /l_x, that means (l_x + l_x+1 + … + l_w) / l_x, where w is the maximum life of the table.
To me mean = average, so the two statements are the same.
Are you talking about median age of death?
When child mortality was very high (pre- 20 century) that was definitely the case. I am not so sure that it is now. I feel that average life expectancy will be a lot closer to 50% survival rate (median age of death) than it was in the past.
The median is the midpoint of a sample, not the mean. So, the median point represents the age where 50% of people will live to, the mean does not represent that (it’s often relatively close to the median assuming the data doesn’t have too much skew, but it can be way off).
There are still plenty of people who die young, even though child mortality is less of a factor in wealthy countries right now. Plenty of people die in car accidents at a relatively young age, for instance. I’m sure the median and mean aren’t like 10 years off of each other, but I wouldn’t be surprised if they’re 3 or even 5 years off, which could be pretty significant in this context.
Well, both of us are making assumptions without doing the research.
So. I respect your opinion but neither of us knows that we are actually correct.
Well, the definition of the mean and median of a sample doesn’t depend on the particular data set, and there’s plenty of non-age related causes of death in the world which would logically skew the distribution to the left! You can look at actuarial tables to see this in action:
https://www.ssa.gov/oact/STATS/table4c6.html
Male life expectancy at birth in this table is 74.12, but you’ll notice that you don’t get to 50% of the population dying until somewhere between the ages of 78 and 79.
This website has a pretty good chart showing the skew for a 2019 dataset: