P
Pratik
Member
Hi can some one please explain this question....Totally stumped here...
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M
Mark Mitchell
Member
You'll need to be a bit more specific about your problem before anyone else can help you out here. What solutions are you looking at? Which steps are the problem?
It might help if you had a look at other similar questions - some of those might be easier, help you to develop your understanding, and then you'll be better at approaching this one.
It might help if you had a look at other similar questions - some of those might be easier, help you to develop your understanding, and then you'll be better at approaching this one.
P
Pratik
Member
Hi Mark,
Thanks for the suggestion. Have reworked on my grasp but this final question is still not falling through.
1. For Country A we have [x,x+1] and we need to get it to [x-1,x]...Therefore for the count of lives as on 01/02/2011 I have taken 44 years as on 2011, for 01/02/2012 I have taken 44 years for 2012 and for 01/02/2013 I have taken 44 years as on 2013. Based on this I have constructed the trapezium and evaluated the area under the same starting from 01/1/2012 till 31/12/2012.
2. For Country B we have [x-0.5,x+0.5] and we need to get it to [x-1,x]...Therefore for the count of lives as on 01/08/2011 I have taken 0.5*(44 years as on 2011 + 45 years as on 2011), for 01/08/2012 I have 0.5*(44 years as on 2012 + 45 years as on 2012)and for 01/02/2013 I have taken 0.5*(44 years as on 2013 + 45 years as on 2013). Based on this I have constructed the trapezium and evaluated the area under the same starting from 01/1/2012 till 31/12/2012.
As per my calculation,
Country A - for the calendar year is 396263.89
Country B - for the calendar year is 386361.11
Death Rate is 0.00575
Unfortunately this is not matching. My guess is that I am going wrong in the selection of the lives from the table.
Kindly guide,
Thanks and regards,
Pratik
Thanks for the suggestion. Have reworked on my grasp but this final question is still not falling through.
1. For Country A we have [x,x+1] and we need to get it to [x-1,x]...Therefore for the count of lives as on 01/02/2011 I have taken 44 years as on 2011, for 01/02/2012 I have taken 44 years for 2012 and for 01/02/2013 I have taken 44 years as on 2013. Based on this I have constructed the trapezium and evaluated the area under the same starting from 01/1/2012 till 31/12/2012.
2. For Country B we have [x-0.5,x+0.5] and we need to get it to [x-1,x]...Therefore for the count of lives as on 01/08/2011 I have taken 0.5*(44 years as on 2011 + 45 years as on 2011), for 01/08/2012 I have 0.5*(44 years as on 2012 + 45 years as on 2012)and for 01/02/2013 I have taken 0.5*(44 years as on 2013 + 45 years as on 2013). Based on this I have constructed the trapezium and evaluated the area under the same starting from 01/1/2012 till 31/12/2012.
As per my calculation,
Country A - for the calendar year is 396263.89
Country B - for the calendar year is 386361.11
Death Rate is 0.00575
Unfortunately this is not matching. My guess is that I am going wrong in the selection of the lives from the table.
Kindly guide,
Thanks and regards,
Pratik
P
Pratik
Member
Hi Mark,
Please confirm... The twist is that the countries record the deaths basis age next birthday. In which case the exposed to risk is matching...The deaths are also provided for age next birthday... so therefore correspondence is matching...Great...
But the question has asked for deaths age 45 last birthday... So what the solution has looked into is to shift everything down by ONE year... If that is the logic it makes sense...
Kindly guide and confirm..
Thanks and regards,
Pratik
PS: This question is really twisted.. I just hope these twists and turn strike under exam pressure..
Please confirm... The twist is that the countries record the deaths basis age next birthday. In which case the exposed to risk is matching...The deaths are also provided for age next birthday... so therefore correspondence is matching...Great...
But the question has asked for deaths age 45 last birthday... So what the solution has looked into is to shift everything down by ONE year... If that is the logic it makes sense...
Kindly guide and confirm..
Thanks and regards,
Pratik
PS: This question is really twisted.. I just hope these twists and turn strike under exam pressure..
M
Mark Mitchell
Member
First of all, the question asks us to estimate the death rate at age 45 last birthday. This gives us the age definition "last birthday" that we need to use in our calculation. So, we will need to take the total number of deaths aged 45 last birthday and divide by the total central exposed to risk at age 45 last birthday.
The total number of deaths aged 45 last birthday is the same as the total number of deaths aged 46 next birthday, which we are told is 4,800 for calendar year 2012.
For Country A, we are provided with the population using the definition "age last birthday", which is exactly what we need to calculate the exposed to risk at age 45 last birthday. That is, here we have correspondence automatically, and we can just use the population data from the table for age 45.
For Country B, we are provided with the population using the definition "age nearest birthday". This is not what we need, so we do not have correspondence. We need to adjust the population data in the table, so that it applies at "age last birthday". Since a person aged 45 last birthday must be either 45 nearest birthday (if they are in the range (45, 45½)) or 46 nearest birthday (if they are in the range (45½, 46)), we average the rows for 45 and 46 to get the required approximate populations for age 45 last birthday. (In your work, it looks like you've gone the wrong way (ie down in age, not up in age)).
Finally, it's a little unclear how you've calculated the exposed to risk using the trapezium rule. So, for each country, when calculating the exposed to risk for 2012, you will need two trapeziums to cover the whole year:
- for A, the first trapezium runs from 1/1/12 to 1/2/12 and the second from 1/2/12 to 1/1/13
- for B, the first trapezium runs from 1/1/12 to 1/8/12 and the second from 1/8/12 to 1/1/13.
The population counts on 1/1/12 and 1/1/13 are obtained by linear interpolation.
The total number of deaths aged 45 last birthday is the same as the total number of deaths aged 46 next birthday, which we are told is 4,800 for calendar year 2012.
For Country A, we are provided with the population using the definition "age last birthday", which is exactly what we need to calculate the exposed to risk at age 45 last birthday. That is, here we have correspondence automatically, and we can just use the population data from the table for age 45.
For Country B, we are provided with the population using the definition "age nearest birthday". This is not what we need, so we do not have correspondence. We need to adjust the population data in the table, so that it applies at "age last birthday". Since a person aged 45 last birthday must be either 45 nearest birthday (if they are in the range (45, 45½)) or 46 nearest birthday (if they are in the range (45½, 46)), we average the rows for 45 and 46 to get the required approximate populations for age 45 last birthday. (In your work, it looks like you've gone the wrong way (ie down in age, not up in age)).
Finally, it's a little unclear how you've calculated the exposed to risk using the trapezium rule. So, for each country, when calculating the exposed to risk for 2012, you will need two trapeziums to cover the whole year:
- for A, the first trapezium runs from 1/1/12 to 1/2/12 and the second from 1/2/12 to 1/1/13
- for B, the first trapezium runs from 1/1/12 to 1/8/12 and the second from 1/8/12 to 1/1/13.
The population counts on 1/1/12 and 1/1/13 are obtained by linear interpolation.