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Question
From the following table which relates to the number of animals of a certain
species at age x. complete the life table :
| x | 0 | 1 | 2 | 3 | 4 | 5 |
| lx | 1000 | 850 | 760 | 360 | 25 | 0 |
Solution 1
| 1 | 2 | 3 | 4 | 5 | 6 | 7 |
| Age | lx | dx | qx | Lx | Tx | `e_x^0` |
| 0 | 1000 | 150 | 0.15 | 925 | 2495 | 2.495 |
| 1 | 850 | 90 | 0.1059 | 805 | 1570 | 1.847 |
| 2 | 760 | 400 | 0.5263 | 560 | 765 | 1.0065 |
| 3 | 360 | 335 | 0.9305 | 192.5 | 205 | 0.5694 |
| 4 | 25 | 25 | 1 | 12.5 | 12.5 | 0.5 |
| 5 | 0 | - | - | - | - | - |
Where, dx = lx - lx+1
qx = `d_x/l_x`
`Lx = 1/2 ( l_x + l_(x+1))`
`T_x = L_x + T_( x + 1)`
`e_x^0 = T_x/l_x`
Solution 2
We have
dx = lx - lx+ 1
qx = `"d"_"x"/"l"_"x" = ("l"_"x" - "l"_("x + 1"))/"l"_"x"`
px = 1 - qx
`"e"_x^0 = "T"_"x"/"l"_"x"`
If x = 0 , x + 1 = 1
d0 = l0 - l1
q0 = `"d"_0/"l"_0 "p"_0 = 1 - "q"_0`
`"L"_0 = ("l"_0 + "l"_1)/2`
`"e"_0^0 = "T"_0/"l"_0`
| 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
| Age | lx | dx = lx - lx + 1 | qx = `"d"_"x"/"l"_"x"` | px = 1 - qx | Lx = `("l"_"x" + "l"_("x"+ 1))/2` | Tx | `e_"x"^0 = "T"_"x"/"l"_x` |
| 0 | 1000 | 150 | 0.150 | 0.850 | 925 | 2495.0 | 2.495 |
| 1 | 850 | 90 | 0.1059 | 0.8941 | 805 | 1570.0 | 1.8471 |
| 2 | 760 | 400 | 0.5263 | 0.4737 | 560 | 765.0 | 1.0066 |
| 3 | 360 | 335 | 0.9306 | 0.0694 | 192.5 | 205.0 | 0.5694 |
| 4 | 25 | 25 | 1.00 | 0 | 12.5 | 12.5 | 0.5000 |
| 5 | 0 | - | - | - | - | - | - |
RELATED QUESTIONS
Find the age standard death rate (S. D. R.) for the following data:
|
Age groups (in years) |
Population (in '000) |
No. of deaths |
|
0-10 |
11 |
240 |
|
10-20 |
12 |
150 |
|
20-60 |
9 |
125 |
|
60 and above |
2 |
90 |
Given the following table which relates to the number of parrots at age x, complete the life table for parrots.
|
X |
0 |
1 |
2 |
3 |
4 |
5 |
|
lx |
1000 |
940 |
780 |
590 |
25 |
0 |
Find the Age-Specific Death Rate (Age SDR) for the following data.
| Age groups (In year) |
Population (in '000) |
Number of Dearths |
| 0 - 10 | 11 | 275 |
| 10 - 20 | 12 | 180 |
| 20 - 60 | 9 | 81 |
| 60 and above | 2 | 32 |
From the following table find q0 :
| x | 0 | 1 | 2 | 3 | 4 | 5 |
| lx | 1000 | 940 | 780 | 590 | 25 | 0 |
Calculate CDR for district A and B.
| Age group (in years) | District A | District B | ||
| Population | No.of.Deaths | Population | No.of.Deaths | |
| 0 - 10 | 1000 | 18 | 3000 | 70 |
| 10 - 55 | 3000 | 32 | 7000 | 50 |
| Above 55 | 2000 | 41 | 1000 | 24 |
Compute Age - Specific Death rate tor the following data
| Age group (in years) | Population (in thousands | No. of deaths |
| Below 5 | 15 | 360 |
| 5 - 30 | 20 | 400 |
| Above 30 | 10 | 280 |
Fill in the blanks which are marked with a question mark in the following marked from the life table :
| x | lx | dx | qx | px | Lx | Tx |
| 20 | 88230 | ? | ? | ? | ? | ? |
| 21 | 79473 | 320552 |
Complete the following life table :
| x | lx | dx | qx | px |
Lx |
| 4 | 9100 | 60 | ? | ? | ? |
| 5 | ? | 45 | ? | ? |
Calculate age specific death (A-SDR) rates for the following data :
| Age group ( in years ) | Population (in '000) | Number of Deaths |
| Below 10 | 25 | 50 |
| 10 - 30 | 30 | 90 |
| 30 - 45 | 40 | 160 |
| 45 - 70 | 20 | 100 |
Draw scatter diagram for the following data and interpret it :
| x | 10 | 20 | 30 | 40 | 50 | 60 | 70 |
| y | 32 | 20 | 24 | 36 | 40 | 28 | 38 |
Calculate quantities indicated by'?' for the following part of a life table :
| x | lx | dx | qx | Lx | Tx | `e_x^0` |
| 4 | 9100 | 60 | ? | . ? | 510000 | ? |
| 5 | ? | 45 |
