Random Sampling

How many texts do middle school students send in one day? Statistical questions are used to gather data about a population.

That could take a long time…

By surveying a sample of the group, you can make a generalization about the entire group.

The population is the entire group being studied. A sample is part of the population being surveyed.

Example 1: What if we wanted to predict the winner of the upcoming presidential election? Adults walking to work All votersPopulation Sample

Identify the population and sample in the following survey: To gauge students’ preference for a new school mascot, the Student Council President surveys her soccer team. Population Sample You Try!

A Common Mistake How tall are 7 th graders? Not all samples will lead to good predictions about an entire population.

Representative sample Valid inference Accurat e Prediction based on data

It is not representative of the population. Example 1 Your principal is ordering t-shirts for all the students at your school. He surveys 30 members of the football team about their shirt sizes. Is this a representative sample?

Example 2 Your principal is ordering t-shirts for all the students at your school. He surveys every 4 th student that walks in the building. Is this a representative sample? It is representative of the population.

Sampling methods Unbiased Sample doesn’t favor a particular outcome. Biased Sample favors a particular outcome.

 100 fallen leaves collected from the ground  100 leaves on tree branches c) 50 fallen leaves and 50 leaves on branches d) 50 fallen oak leaves and 50 oak leaves on branches Example 1 Which is an example of an unbiased sampling method that could be used to predict the color of leaves in September?

Which is an unbiased sampling method for predicting the type of payment most frequently used at a grocery store? Record the type of payment used by…  Students at the local high school  Every 10 th customer entering the store c) Every 10 th customer in the cash-only line d) Visa card holders You Try!

1. Simple random sample 2. Systematic random sample 3. Stratified random sample Unbiased sampling methods

Simple random sample Chosen completely at random.

6 12 Systematic random sample Chosen randomly but there is some type of system to it.

25 Stratified random sample Breaks population into groups first, and then chooses a certain amount from each group at random.

Unbiased sampling methods are RANDOM. Simple random sample Stratified random sample Systematic random sample

GPS devices are put on one male and one female goose from each of 100 groups of geese throughout Canada. Example Researchers are studying the migration pattern of Canadian geese. Identify which type of random sample is used. Stratified random sample

An exit poll is meant to predict the results of an election before the votes are counted. Reporters outside a voting site ask every 20 th voter who they voted for. You Try! Identify which type of random sampling is used. Systematic random sample

Convenience sample Voluntary response sample Biased sampling methods

Convenience sample Whatever is “convenient” or “easy”.

Voluntary Response Sample Members of the population volunteer to participate.

GPS devices are attached to every goose on one lake in Canada. Example Researchers are studying the migration pattern of Canadian geese. Identify which type of sampling is used. Convenience sample

Students are asked to raise their hands at an assembly to share their opinions about changing the mascot. Example A school is deciding whether or not to change its mascot. Identify which type of sample is used. Voluntary Response sample

Practice: Random Sampling Worksheet

Random Sampling Activity You are buying ice cream for a party at your school, in which 700 students will attend. You need to design a random sample to figure out which types of flavors you should buy. Describe the sample you would survey. What type of unbiased random sampling would you use?