Mortality Rate
Probability that a life aged x dies within the year.
Formula
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Example
d_x=200, l_x=100000: q_x = 0.002
How it works
This formula measures the share of people alive at age x who die before reaching age x+1, so it is a one-year death probability. It works because the number who die during the year, d_x, is compared to the number exposed to risk at the start of that age, l_x; dividing deaths by lives gives the proportion of that group that does not survive the year. In life tables and insurance calculations, this proportion is used to estimate risk at each age.
When to use it
Use this when analyzing life tables, pricing life insurance, or estimating survival and death probabilities for a specific age group. It is also useful in actuarial models that track how mortality changes from one age to the next.
Worked example, step by step
Suppose a life table shows that at age 50 there are l_x = 80,000 lives alive at the start of the year and d_x = 640 deaths during the year. Step 1: Write the formula: q_x = d_x / l_x Step 2: Substitute the values: q_50 = 640 / 80,000 Step 3: Calculate: q_50 = 0.008 Step 4: Convert to a percentage: 0.008 = 0.8% Final answer: The mortality rate at age 50 is 0.008, or 0.8% per year.
Common mistakes to avoid
- Using the number of deaths in the numerator but dividing by the wrong age group instead of l_x
- Confusing q_x with the number of deaths, when q_x is a probability or rate, not a count
- Forgetting to express the result as a proportion of those alive at age x, not of the whole population
Did You Know?
Human mortality roughly doubles every eight years of adult age — the Gompertz law.
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