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Statistics 101: Principles of Statistics11 chapters | 141 lessons | 9 flashcard sets

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Lesson Transcript

Instructor:
*Cathryn Jackson*

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.

Random sampling isn't always simple! There are many different types of sampling. In this lesson, you will learn how to use stratified random sampling and when it is most appropriate to use it.

Jackie is the president of the party planning committee of her school. Right now, the party planning committee is planning a winter formal. She is researching the different DJs that are available to work at the winter formal. Each DJ has a different percentage of music that he or she is able to play.

Jackie needs to find the right DJ for the winter formal so that the students of her school are happy with the music choices. Jackie can't ask every member of the school his or her music preferences. How can she figure out which DJ to hire?

In this lesson, you will learn about stratified random sampling, what it is, and how to use it.

**Stratified random sampling** is a random sampling method where you divide members of a population into 'strata,' or homogeneous subgroups.

Take a look at this chart:

This is the percentage of each music genre that each DJ will play. DJ Thunder Cat will only play 60% rock, 20% pop, 15% hip hop, and 5% country. DJ XtremeMix will only play 75% hip hop, 20% pop, 5% rock, and no country. DJ Midnight will only play 50% pop, 35% country, 10% hip hop, and 5% rock. Each of these genres is an example of a strata, or a homogeneous subgroup. The group or population is music, while the strata is each kind of music.

Stratified random sampling works the same way. Jackie doesn't have the ability to question every student in the school. However, she can use stratified random sampling to get an understanding of the music tastes of the students in the school. Jackie can divide the student body into different strata, or subgroups, and then ask each of these subgroups what types of music they prefer.

Stratified random sampling is different from other types of sampling because you are separating the population into groups first. You must be very familiar with the demographics of your population if you intend on using stratified random sampling. Let's discuss how to use stratified sampling and the ways you can use this sampling in an experiment.

Jackie decides that a stratified random sample may be the best way to collect her information. When dividing the school into stratified random samples, she must keep two things in mind:

- Stratified random samples cannot have crossover.
- Stratified random samples must include all members of a population.

Stratified random samples cannot have crossover. In other words, each of the strata must be mutually exclusive. In Jackie's case, she must choose some type of group in which each student is a part of one group but not more than one. Jackie could use something like age or school classification, such as freshman, sophomore, junior, and senior. Jackie decides the simplest way to collect her data is to divide her subgroups by school classification, like this:

Stratified random samples must also include all members of a population. In Jackie's case, she has included all members of the population because all students must be under one of the four classifications.

Stratified random samples are best used when the researcher is familiar with the demographics of the population and the proportion of the demographics are important to the data being collected. With that said, it is important to have a small amount of strata when collecting data. No more than four to six strata is recommended, but you can theoretically have as many strata as you want. You want to keep the sample proportionate to the experiment.

Take a look at this chart:

Now that Jackie knows the percentages of the student population in each classification, she must choose samples that are proportionate to the student body. Therefore, if Jackie decides to use a sample of 100 people, then exactly 35% of her sample must be freshman, 35% of the students must be sophomores, 20% juniors, and 10% seniors. If she chooses the number of students listed on the bottom right of the image above for her sample, then her sample will be proportionate to the population.

Now that Jackie knows the percentage of each classification in her population, she can use either simple or systematic sampling to get her sample from each strata. For example, she can get a list of all of the freshman, then put the names of each freshman in a bag and randomly select 35 names from the bag. Jackie can do this for each of the strata to construct her sample. Once she collected her sample, Jackie gave each student a survey asking about their music preferences. After Jackie passed out her survey, she got the following information:

Which DJ best matches the interests of the students?

Remember, Jackie wanted to conduct a sample experiment to find the interests of the student population. To do this, Jackie decided to use **stratified random sampling**, which is a random sampling method where you divide members of a population into 'strata,' or homogeneous subgroups.

Jackie divided the student body into different strata, or subgroups, then asked each of those subgroups what types of music they prefer. She needed to select students from each strata in proportion to the student population, which is why she selected 35% of her sample from students that are freshman, 35% that are sophomores, 20% that are juniors, and 10% that are seniors. Stratified random sampling is different from other types of sampling because you are separating the population into groups first.

Once you separate the population into strata, you can use simple or systematic sampling to select your sample. So which DJ was hired? Well it looks like DJ Midnight was the best match for the students.

After this lesson, you'll be able to:

- Define stratified random sampling and strata
- Identify what sets stratified random sampling apart from other types of sampling
- Explain how to conduct stratified random sampling

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Statistics 101: Principles of Statistics11 chapters | 141 lessons | 9 flashcard sets

- Go to Probability

- Simple Random Samples: Definition & Examples 5:10
- What is Random Sampling? - Definition, Conditions & Measures 5:55
- Stratified Random Samples: Definition, Characteristics & Examples 6:25
- Systematic Random Samples: Definition, Formula & Advantages 8:37
- Understanding the Law of Large Numbers 5:14
- Sampling Distributions & the Central Limit Theorem: Definition, Formula & Examples 5:06
- Find the Mean & Standard Error of the Sampling Distribution 5:03
- Finding Probabilities About Means Using the Central Limit Theorem 4:24
- Go to Sampling

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