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Age table interpretation problem

  1. Jun 3, 2016 #1
    1. The problem statement, all variables and given/known data
    age table.png

    calculate for men and women each, the probability at which...
    the lifespan left, of a forty-year-old is 20-40 years.

    2. Relevant equations
    3. The attempt at a solution

    That's a mouthful of a sentence.
    It looks like if the lifespan is exactly 20 years... there could be many middle-aged men, who live exactly 20 years onwards from exactly 40 years age... Where do those men fit in the table though... There might be men who die exactly on their 60th birthday. What lifespan have they lived? 19.9999 years or 20 years?

    It looks like we have to calculate as the base, the forty- year-olds

    951 men are alive at exactly 40 years age. We must start from here.
    It looks like 20 years afterwards, there are 150 dead male forty-year olds...

    • For basic facts it looks like the probability we are interested in, is as follows.
    P( forty-year older dies in a timeframe in the future of 20-40 years)
    So he lives either 20 years minimum in the future, or maximum of 40 years in the future.

    • I suppose the only sensible way to estimate this probability is to look at the number of dead men, between ages 60 - 80. The final two rows. The dead people between ages 40-60 would have contained too young dead people, who should not have been counted into the 20 year lifespan. (because many of their lifespans would have been shorter than 20 years required, I think this is the gist of the thing.).

    • In other words, if a man dies at the age of 55, he dies between 40-60 years age. His lifespan would have been too short to be counted, because it would have been only 15 years.

    • common sense dictates that only those persons who are alive, can later die. So, at the minimum lifespan 20, there are 801 alive. At the maximum lifespan there are 294 alive. Therefore the number of dead men is the difference between.

    for men
    $$P(man ~~~~lifespan ~~between 20-40)= \frac {801-294} {951}~= 0,5331$$

    for women
    $$P(~woman ~~~~lifespan ~~between 20-40)= \frac {922-551} {979}= 0,3789$$
  2. jcsd
  3. Jun 3, 2016 #2

    Ray Vickson

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    The question can be better re-worded, to ask: calculate the probability that a 40-year old man has a remaining lifetime of 20-40 years. Do the same calculation for women.
  4. Jun 3, 2016 #3
    Hi late:

    You seem to have understood the problem OK. Did you have a question?

  5. Jun 3, 2016 #4
    I got confused initially because of the exact age boundaries of the mortality age table. 20, 40, 60, 80

    Although I suppose the wording makes it more clear. (age means the person is alive at the "roll call" at the age of 40 etc...)

    Projected lifespans in the future (without pre-knowledge) will always be estimations.
    But back-calculated lifespan which has some known boundary (range between birthdate and the time-of-death ) it could be exact.
    A person who survived until the 40th birthday, would have probably been called on the phone or been interviewed by the data-collecting people who made the mortality study. If he answers, it could be said that he survived until exactly 40 years. Then if he dies after that phonecall, then he would have died between the age range of 40-60.

    You can see readily, that the mortality will tend to increase quite rapidly as people get older into their 60-70s especially with men.

    age 0 babies are between 0 and 1 (not including 1 year)
    age 1 old boy is between 1 (including one) and 2 years old (not-including two)
    age 2 old boy is between 2(including two) and 3 years old (not-including three)
    This is the real-life interpretation of age of a person. If you ask a person on the street (myself)
  6. Jun 3, 2016 #5
    Hi late:

    I am not an expert, but I don't think mortality tables are generated by phone interviews. The following may be of some interest to you.

  7. Jun 3, 2016 #6

    Ray Vickson

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    Mortality tables were being constructed before the invention of the telephone, and certainly before anybody but the very, very rich had phones.

    Anyway, I think you are investing way too much time thinking about the data; the data is fake, invented just to give you some numbers to work with.
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