Rates of Change (Edexcel GCSE Statistics)

Revision Note

Written by: Roger B

Reviewed by: Dan Finlay

Crude Rates of Change

How do I calculate a crude rate of change?

Understanding rates of change in a population is important for planning purposes
- For example, a town with a high birth rate may need to think about building more schools for the increasing number of children
A crude rate is a way to understand how things are changing in a population
- It is often used to track births or deaths
  - But it can also be used to track other things, like marriages, unemployment, etc.
- A crude rate normally tells you the number of births (or deaths, etc.) per 1000 people
To calculate the crude birth rate (for example) use the formula
- $crude birth rate = \frac{number of births \times 1000}{total population}$
  - This formula is will be given to you in a question on the exam if you need it
    - So you don't need to remember the formula, you just need to know how to use it
- To calculate a crude rate for other things, replace 'number of births' in the formula with 'number of deaths', 'number of marriages', 'number of people unemployed', etc.
You may be given the crude birth rate (or death rate, etc.), and asked to work out one of the other values in the formula
- If you know any two things from the formula you can find the third one
- Substitute in the values you know
  - and solve to find the one you want to know
You can also calculate a crude rate per 100 people (instead of per 1000)
- Replace ' $\times 1000$ ' in the formula with ' $\times 100$ '
- Only do this if a question tells you to

Worked Example

Last year a particular town had a population of 75 992.

(a) Given that there were 783 deaths during the year, find the crude death rate for the town. Give your answer correct to 3 decimal places.

Use $crude death rate = \frac{number of deaths \times 1000}{total population}$

$\frac{783 \times 1000}{75992} = 10.303716 . . .$

Round to 3 decimal places

10.304

You could also answer '10.304 deaths per 1000 of population', but it's not necessary to get full marks

The crude birth rate for that same town last year was 11.317.

(b) Find the number of births that occurred in the town during the year.

Substitute the values you know into $crude birth rate = \frac{number of births \times 1000}{total population}$
It will be easier to replace 'number of births' with a letter like $b$

$11.317 = \frac{b \times 1000}{75992} = \frac{1000 b}{75992}$

Multiply the '75992' across

$\begin{array}{rcl} 11.317 \times 75992 & = & 1000 b \\ 860001.464 & = & 1000 b \end{array}$

Divide both sides by 1000

$\begin{array}{rcl} \frac{860001.464}{1000} & = & b \\ 860.001464 & = & b \end{array}$

Round to the nearest whole number
(Number of births has to be a whole number!)

860

Last updated: 7 May 2024

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