Describe stratified sampling.

Stratified sampling is a sampling technique where the population is divided into subgroups or strata, and a random sample is taken from each stratum.

Stratified sampling is a method of sampling that involves dividing the population into subgroups or strata based on certain characteristics. These characteristics could be age, gender, income, education level, or any other relevant factor. Once the population has been divided into strata, a random sample is taken from each stratum. The size of each sample is proportional to the size of the stratum in the population.

The main advantage of stratified sampling is that it ensures that each subgroup or stratum is represented in the sample. This is important because it allows for more accurate estimates of population parameters. For example, if we were conducting a survey on the average income of a city, we would want to ensure that we have a representative sample from each income bracket. Stratified sampling allows us to achieve this.

To calculate the sample size for each stratum, we use the following formula:

n_h = (N_h / N) * n

Where:
n_h = sample size for stratum h
N_h = population size for stratum h
N = total population size
n = total sample size

Once we have calculated the sample size for each stratum, we can select a random sample from each stratum using any appropriate sampling technique, such as simple random sampling or systematic sampling.

In conclusion, stratified sampling is a useful technique for ensuring that each subgroup or stratum in a population is represented in a sample. This can lead to more accurate estimates of population parameters and is particularly useful when dealing with populations that have significant differences between subgroups.