Crude and Standardised Rates
Crude and standardised rates are two ways of measuring how often an event, such as death or birth, occurs within a population. A crude rate simply divides the number of events by the total population, usually multiplied by 1000, while a standardised rate adjusts for differences in population structure, such as age, so that populations with different structures can be compared fairly.
Before you start
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Method
- For a crude rate, divide the total number of events (for example deaths) in a population by the total population size, then multiply by 1000 (or the base stated in the question, such as per 100,000) to give a rate per head.
- Recognise that a crude rate does not account for the population's structure, so crude rates from two populations with very different age profiles (for example an area with many elderly people compared with one with mostly young people) can be misleading to compare directly.
- To find a standardised rate, apply the age-specific rate for each age band of the population being studied to the corresponding number of people in a given standard population.
- Sum the expected number of events across all age bands to find the total expected events for the standard population.
- Divide the total expected events by the total size of the standard population, then multiply by 1000 (or the stated base), to get the standardised rate.
- Compare standardised rates, rather than crude rates, between populations, since standardisation removes the effect of differing population structures.
Worked example
In a town, there were 240 deaths in a population of 60,000 during one year. Calculate the crude death rate per 1000 people.
- Crude rate = (number of deaths / population) x 1000.
- Crude rate = (240/60000) x 1000.
- Crude rate = 4.
- Final answer: 4 deaths per 1000 people.
Practice questions
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Q1A city had 350 births in a population of 70,000. Calculate the crude birth rate per 1000 people.Show answer
Answer: 5 per 1000 ((350/70000) x 1000)
Q2A region recorded 90 deaths in a population of 45,000. Calculate the crude death rate per 1000 people.Show answer
Answer: 2 per 1000 ((90/45000) x 1000)
Q3A town's crude death rate is 8 per 1000 and its population is 25,000. Calculate the number of deaths.Show answer
Answer: 200 deaths ((8/1000) x 25000)
Q4Explain why comparing the crude death rates of a seaside retirement town and a university town could be misleading.Show answer
Answer: The retirement town has a much older population structure, so it would naturally have a higher crude death rate regardless of how healthy the population is; a standardised rate should be used instead
Q5A standard population has 10,000 people aged 65 or over. The age-specific death rate for this age band in Town A is 30 per 1000. Calculate the expected number of deaths in this age band for the standard population.Show answer
Answer: 300 ((30/1000) x 10000)
Q6Using a standard population of 50,000, the total expected number of deaths, summed across all age bands, for Town B is 400. Calculate the standardised death rate per 1000.Show answer
Answer: 8 per 1000 ((400/50000) x 1000)
Exam-style questions
Written in the style of a GCSE Statistics exam paper, with a full mark scheme.
A hospital catchment area has a population of 80,000 and recorded 640 deaths in one year. Calculate the crude death rate per 1000 population, showing your working.
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The table shows a standard population split into two age bands, and the age-specific death rates for Village X: under 65 (standard population 8000, rate 2 per 1000); 65 or over (standard population 2000, rate 40 per 1000). (a) Calculate the expected number of deaths in each age band. (b) Hence calculate the standardised death rate per 1000 for Village X.
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State one reason why standardised rates are more useful than crude rates when comparing death rates between two towns with very different age structures.
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See real GCSE Statistics past-paper questions, with official mark schemes →
Free printable worksheet
Want more practice on paper? Download the crude and standardised rates worksheet pack - 16 pages of exam-style questions with a full mark scheme. One email opens every download in this browser for 14 days - no account, no card. Print it for personal and classroom use.
This topic is chapter 28 of GCSE Statistics Higher Workbook 2, the whole course as one free printable PDF.
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