Life tables

Introducing the life table

A typical demographic life table is shown in Table 1. This is a mortality life table and describes the survival of women in the UK in 1985. It looks very complicated but this module is designed to demystify it. Notice that it is a series of columns of figures with some rather odd column headings - these are traditional. In this table the ages are grouped (except for the first year) and because of this it is called an abridged table. A complete table would deal with single year ages and would consequently be very long. Abridged tables are common: note that the groupings do not have to be equal.

interaction Place your mouse cursor over the columns to reveal the column headings underneath the table.

x
0
1
5
10
15
20
25
30
35
40
45
50
55
60
65
70
75
80
85
n
1
4
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
 
nqx
0.008252
0.001630
0.000905
0.000935
0.001409
0.001534
0.001818
0.002826
0.004410
0.007199
0.012348
0.020831
0.035455
0.058507
0.087310
0.139189
0.220993
0.352367
1.000000
npx
0.991748
0.998370
0.999095
0.999065
0.998591
0.998466
0.998182
0.997174
0.995590
0.992801
0.987652
0.979169
0.964545
0.941493
0.912690
0.860811
0.779007
0.647633
0.000000
lx
100 000
99 175
99 013
98 924
98 831
98 692
98 540
98 361
98 083
97 651
96 958
95 761
93 756
90 432
85 141
77 707
66 891
52 109
33 747
ndx
825
162
89
93
139
152
179
278
432
693
1 197
2 005
3 324
5 291
7 434
10 816
14 782
18 362
33 747
nLx
99 258
396 311
494 842
494 388
493 808
493 080
492 253
491 110
489 335
486 523
481 798
473 793
460 470
438 933
407 120
361 495
297 500
214 640
189 604
Tx
7 756 261
7 657 003
7 260 692
6 765 850
6 271 462
5 777 654
5 284 574
4 792 321
4 301 211
3 811 876
3 325 353
2 843 555
2 369 762
1 909 292
1 470 359
1 063 239
701 744
404 244
189 604
ex
77.563
77.207
73.331
68.394
63.456
58.542
53.629
48.722
43.853
39.036
34.297
29.694
25.276
21.113
17.270
13.683
10.492
7.758
5.618

Table 1: A typical mortality abridged life table.

Source: Office for National Statistics

 

x = Age

The age column x. All tables need either age or time since event. In this table we have age, which is time since birth. Note that the ages are the age at the beginning of the interval. Although each row represents an interval the x value is given as the start of the interval.

n = Interval width

nqx = Probability of dying

npx = Probability of surviving

lx = Number of survivors
(from the original radix e.g. 100 000)

The column headed lx is spoken exactly as it reads - "the l x column". Notice that the column is headed by the nice round number of 100,000. In every demographic life table there is such a figure, although it could just as well be 1,000 or 100 or even just 1. This is the anchor of the table and is known as the radix, from the Latin word meaning "root".

Looking down the lx column you see that as age increases the lx value decreases until at age 85 the number has decreased to 33,747. This column therefore shows survivors from the radix, by age. For this reason it is often called the survivors column or the survivorship column. This is a key column of any life table and summarises the table in that all other columns can be derived from this one column (with some minor exceptions).

ndx = Number of deaths
(that have occurred in the lx column)

nLx = Person-years lived in the interval

Tx = Total person-years
(nLx cumulated from bottom)

ex = Expectation of life

The column headed ex shows expectation of life from age x. The first line gives expectation of life from birth – a commonly quoted figure – but expectation of life can be read from any age.