Crude Rate and Rates of Change
A crude rate is a simple measure that shows how often an event happens in a population, calculated by dividing the number of events by the total population size, usually multiplied by a constant such as 1000 or 100,000 to give a rate per head. A rate of change describes how a quantity increases or decreases over a period of time, often expressed as a percentage. In GCSE Statistics, crude rates are commonly used for things like birth rates, death rates or crime rates, so populations of different sizes can be compared fairly.
Before you start
No specific prerequisites - this is a good place to start.
Method
- Identify the number of events (for example deaths, births or crimes) and the total population size for the same time period and area.
- Divide the number of events by the total population to get the basic rate.
- Multiply this rate by a standard base, such as 1000 or 100,000 as stated in the question, to give the crude rate 'per 1000' or 'per 100,000' people.
- To find a rate of change between two time periods, find the difference between the new and old values.
- Divide this difference by the original (old) value, then multiply by 100 to get a percentage rate of change.
- State whether the rate of change is an increase or a decrease, and give your answer to an appropriate degree of accuracy.
Worked example
In a town with a population of 25,000, there were 50 deaths recorded last year. (a) Calculate the crude death rate per 1000 people. (b) The population the previous year was 24,000. Find the percentage rate of change in population.
- Crude rate = number of events divided by total population = 50 divided by 25000.
- Multiply by 1000 to express the rate per 1000 people: (50 divided by 25000) x 1000 = 2.
- So the crude death rate is 2 per 1000 people.
- Rate of change in population = (new minus old) divided by old, x 100 = (25000 - 24000) divided by 24000, x 100.
- Calculate: (1000 divided by 24000) x 100 = 4.166... = 4.17% (2 dp).
- Final answer: the crude death rate is 2 per 1000 people; the population increased by 4.17% (2 dp) from the previous year.
Practice questions
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Q1A town of population 10,000 records 20 births in a year. Find the crude birth rate per 1000 people.Show answer
Answer: 2 per 1000 (20/10000 x 1000 = 2).
Q2A city's population grows from 50,000 to 52,000 in one year. Find the percentage rate of change.Show answer
Answer: 4% increase ((52000-50000)/50000 x 100 = 4).
Q3A region records 90 crimes in a population of 45,000. Find the crude crime rate per 1000 people.Show answer
Answer: 2 per 1000 (90/45000 x 1000 = 2).
Q4A population falls from 8,000 to 7,600. Find the percentage rate of change, stating whether it is an increase or decrease.Show answer
Answer: 5% decrease ((7600-8000)/8000 x 100 = -5).
Q5A country of population 2,000,000 records 3,000 deaths in a year. Find the crude death rate per 100,000 people.Show answer
Answer: 150 per 100,000 (3000/2000000 x 100000 = 150).
Q6Explain why a crude rate is more useful than a raw total, such as the total number of deaths, when comparing two towns of different sizes.Show answer
Answer: A crude rate adjusts for population size, so it allows a fair comparison between places with different numbers of people, whereas raw totals would naturally be higher in a bigger population.
Exam-style questions
Written in the style of a GCSE Statistics exam paper, with a full mark scheme.
A hospital records 45 births in a population catchment of 15,000 people. Calculate the crude birth rate per 1000 people.
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The population of a village was 3,200 in 2020 and 3,360 in 2023. (a) Find the percentage rate of change in population from 2020 to 2023. (b) State whether this is an increase or a decrease.
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In Region X, there were 240 deaths in a population of 80,000. In Region Y, there were 150 deaths in a population of 60,000. (a) Calculate the crude death rate per 1000 people for each region. (b) State which region has the higher crude death rate.
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Free printable worksheet
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This topic is chapter 22 of GCSE Statistics Foundation Workbook 2, the whole course as one free printable PDF.
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