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Cat has taught a variety of subjects, including communications, mathematics, and technology. Cat has a master's degree in education and is currently working on her Ph.D.
Stacy owns a cupcake shop. She is working on inventing new flavors that will encourage children to eat more vegetables. She is excited about unveiling her newest cupcake flavor: broccoli cupcakes. Stacy wants to taste test the cupcakes to see how children like the broccoli cupcakes. However, Stacy doesn't have the resources to give every child in the town a taste test. She can best learn how the children like her cupcakes by using random samples.
In this lesson, you will learn about random samples and how they are used in statistics.
Before using a random sample, Stacy needs to understand the definition of a random sample and the types of random samples that exist.
First, let's talk about populations. Populations are all members of a specified group. For example, if you wanted to learn about the average age of a person living in New Jersey, then everyone living in New Jersey would be your population for your experiment. When you conduct an experiment or gather data, you are trying to find out information on that population.
Second, you are probably collecting information from a sample. A sample is a part of a population used to describe the whole group. Since you often can't collect data on the entire population, you usually use a sample. This brings us to random samples, which are a sequence of equally distributed variables. Much of mathematics, especially statistics, is based on random sampling.
Some of the types of random sampling are:
You will learn more about each of these types of sampling in other lessons.
Now that Stacy understands the definition and types of random samples, she needs to understand when to use random samples, how to select them, and the benefits and risks of random samples.
Random samples are best used to gather data about large populations. This is because you aren't likely to get an entire population to participate in a study.
Many times, there aren't enough resources to do this, or it is simply physically impossible to collect that much data. For example, Stacy probably doesn't have enough cupcakes for every child in the town, which is why she will use random samples instead. We can use random sampling to make observations about the entire population.
When you use random sampling, you want to make sure that you are giving all subsets, or all possible outcomes, equal probability. For example, rolling one 6-sided die is a random sample of what would happen if you rolled all of the 6-sided dies in the entire world. Since there are only six options, rolling one die gives all the outcomes equal probability.
In Stacy's case, there are many different possible outcomes in her population. She will want to include children in her sample that are of different ages, genders, and ethnicities to cover the population of her town. If she gave a taste test to just 10-year-old boys, then her sample would not give equal probability to all of the children in the town.
Selecting random samples has a lot to do with what type of random sample you are using. For example, Stacy may ask children to sign up to participate in the taste test. She can then assign each student that signs up a number and only select the even numbers to participate in the taste test. She could also use a random number generator to select the children for the taste test.
Accessibility is a benefit to using random samples. They allow researchers to gather information without using the entire population. Think of how many experiments that wouldn't happen if we had to test every member of a population! We gather much of our information from random sampling!
Randomness is actually a risk that is involved in collecting data from random samples. Sometimes, collecting data randomly will result in data that doesn't represent the entire population. For example, if Stacy randomly selected children for her taste test and happened to get several children that were allergic to an ingredient in her cupcakes, then the sample would not accurately reflect the population of children as a whole.
Random sampling is a common method of data collection and observation used by many researchers. Random samples are a sequence of equally distributed variables. Remember, Stacy may ask children to sign up to participate in the taste test. She can then assign each student that signs up a number and only select the even numbers to participate in the taste test. This would be an example of random sampling. Random sampling is based on population, which is all members of a specified group.
Remember, random samples are used to gather data about large populations. When using random samples, make sure you give all possible outcomes equal probability. You can select random samples in a variety of ways; we will talk more about this in future lessons when we discuss different types of random samples. When a sample does not accurately reflect the population, it can be caused by the randomness of the sample. However, using random sampling gives researchers greater accessibility when conducting experiments and gathering data.
Upon completing this lesson, you will be able to:
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Statistics 101: Principles of Statistics11 chapters | 144 lessons | 9 flashcard sets
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