Rates of change over time including percentage change, births, deaths, house prices and unemployment; calculating crude rates with a given formula; standardised rates at Higher tier; making predictions from rates.

What this dot point is asking

Edexcel code 2d.02 requires you to interpret and calculate rates of change over time, including percentage change and rates such as births, deaths, house prices and unemployment. You calculate crude rates using a formula that is given in the question, and (Higher tier) standardised rates, and you use rate formulae to make predictions. Reading rates from tables and graphs, and commenting on trends, are common tasks.

Percentage change

A positive result is an increase, a negative result a decrease. Percentage change lets you compare rises and falls across quantities of very different sizes, and it links directly to index numbers (an index of $125$ is a $25\%$ change). To apply a percentage rise repeatedly, multiply by the decimal multiplier (a $25\%$ rise multiplies by $1.25$).

Crude rates

Crude rates express how often an event happens per $1000$ of the population, so populations of different sizes can be compared.

The units are "per $1000$ of the population". Edexcel gives the formula in the question, so the marks are for substituting correctly, computing the value, and stating the units. Crude rates let you compare, for example, the birth rate of a small town with that of a city.

Standardised rates

A crude rate can be misleading when two populations have very different age structures (a town with many older people will have a higher crude death rate even if it is no less healthy). A standardised rate (Higher tier) adjusts the crude rate to a standard population, removing the effect of the differing structure so a fair comparison is possible. The relevant formula is given when needed; the key understanding is why standardisation is used: to compare like with like.

Interpreting and predicting from rates

Rates are often presented in tables or graphs, and you interpret the trend: a falling crude birth rate, a rising unemployment rate, and so on. To predict, you apply the rate formula forward (for example assuming a percentage change continues), but every such prediction assumes the past pattern holds. Edexcel rewards awareness that extrapolating a rate into the future is unreliable when conditions may change.

When comparing a rate between two populations or two years, make sure you compare the rate (per $1000$, or as a percentage) and not the raw counts. A town with more births than another may still have a lower birth rate if its population is much larger, so the rate, which accounts for population size, is the fair basis for comparison. This is the whole reason rates are used instead of raw frequencies.

Other context-specific rates

Beyond birth and death rates, Edexcel may give you the formula for other rates and ask you to apply it. Examples include rates of unemployment (as a percentage of the workforce), house price changes (as a percentage per year), and population growth rates. In every case the method is the same: read the formula carefully, substitute the given figures, compute the value, and state the units. Because the formula is supplied, the marks are for accurate substitution and interpretation, so always finish by saying what the rate means in the context of the question, for example "the unemployment rate rose from $4\%$ to $6\%$, so a higher proportion of the workforce is out of work".