EDEXCEL GCSE FOUNDATION MATHS - What are Samples

Edexcel GCSE Foundation Maths: What are Samples?

Understanding Samples

In statistics, we often work with data collected from a population. A population is the entire group of individuals, objects, or events that we are interested in studying. For example, if we want to study the heights of all students in a school, the population would be all the students in that school.

However, it is often impractical or impossible to collect data from the entire population. Instead, we take a sample, which is a smaller group of individuals selected from the population. The sample should be representative of the population so that we can make inferences about the population based on the sample data.

Types of Samples

There are several types of samples, but two common ones are:

• Random Sample: Each member of the population has an equal chance of being selected for the sample. This helps ensure that the sample is representative of the population.
• Stratified Sample: The population is divided into subgroups (strata) based on a characteristic (e.g., age, gender). Then, a random sample is taken from each stratum, ensuring representation of all subgroups.

Why Use Samples?

There are several reasons why we use samples:

• Cost-Effectiveness: It is often cheaper and faster to collect data from a sample than from the entire population.
• Time Efficiency: Collecting data from a sample can be done more quickly than from the entire population.
• Practicality: In some cases, it may be impossible to collect data from the entire population (e.g., studying the population of the world).

Example:

Let's say we want to study the average height of students in a school. The population is all the students in the school. To collect data, we could take a random sample of 50 students from the school. We would then measure the height of each student in the sample and use this data to estimate the average height of all students in the school.

Key Points:

• A sample is a smaller group selected from a larger population.
• Samples are used to make inferences about the population.
• Samples should be representative of the population.
• Random sampling and stratified sampling are common methods for selecting samples.

Remember:

• The larger the sample size, the more likely it is that the sample will be representative of the population.
• We can use statistical methods to estimate the confidence level of our results based on the sample size.