# Question Video: Determining the Appropriate Sampling Method in a Real-Life Context Mathematics

Which type of random sample should be used to determine the subject preferences of a group of 400 students given the ratio of males to females is 3 : 2? [A] Simple random sample [B] Stratified random sample

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### Video Transcript

What type of random sample should be used to determine the subject preferences of a group of 400 students given the ratio of males to females is three to two. Is it A) a simple random sample or B) a stratified random sample?

Let’s begin by recalling the definition of these two types of sampling methods. A simple random sample is a subset of a population, and remember the population is everyone, in which every single member of this subset has an equal probability of being chosen. It’s meant to be an unbiased representation of a group.

For example, we could choose a simple random sample of 30 students in a school of 400 by assigning a number to every student and using a random number generator to generate 30 numbers. It’s considered a fair way to select a sample though it doesn’t guarantee that the sample itself will be representative of the whole population.

A stratified random sample involves dividing the population into smaller groups, which are known as strata. These groups are based on specific shared attributes, for example, age or gender. Each member of the subgroups then have an equal probability of being chosen. But these probabilities might be different from subgroup to subgroup. And this method can be beneficial as it ensures a representative sample though strata must be carefully defined to ensure that there’s no overlap.

Now, let’s consider the population we’ve been given. We’re told that the population is 400 students. We’re also told that the ratio of males to females is three to two. This indicates to us that our sample needs to be truly representative of this breakdown. To ensure that this is the case, we’re going to use stratified random sampling. And as a little aside, we can use proportion to work out how many students would be in a sample.

Since the ratio of males to females is three to two, we can add three and two. And we can see that our population is broken down into five parts. Three of these parts represent the proportion of male students. So three-fifths of the population must be male. And two-fifths must be female. So we would need to ensure that three-fifths of a sample are males and two-fifths of that same sample are females.