Video Transcript
High school students were surveyed about the colleges they would like to join. The population size was 40,000, and it was divided into categories according to student grades. A random sample was selected so that the number of students in each grade in the sample were in the same proportion as the number of students in each grade in the population. Is this considered to be a stratified sample?
We’re given a description of a method of sampling and asked if it’s considered stratified sampling. So let’s look at how we define stratified sampling and compare our definition with the given sampling method. Stratified sampling is used when a population can be subdivided into nonoverlapping groups, or strata. A random sample is taken from each group, or stratum, where the size of each sample reflects the proportion of the population represented by that group, or stratum. In our case, we’re told that the population was divided into categories according to student grades, so the first part of our definition for stratified sampling does apply. Our population is indeed subdivided into nonoverlapping groups, or strata, and these are defined by the grades.
We’re also told that a random sample was selected from each grade and that the number of students in each sample were in the same proportion as the number of students in each grade in the population. This matches with the second part of our definition for stratified sampling. The proportion of each group in the sample, that is, the size of each sample within the overall sample, reflects the proportion of the population represented by that group, or stratum.
Since the given sample matches with our definition of stratified sampling, the samples selected from the population of high school students is considered to be a stratified sample. So the answer is yes.
