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 tallare 7th

graders?

Not all samples will lead to good predictions about an entire population.

Representative sample

Valid inference

Accurate

Prediction based on

data

It is not representative of the

population.

Example 1Your 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 2Your principal is ordering t-shirts for all

the students at your school. He surveys every 4th 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.

BiasedSample favors

a particular outcome.

a) 100 fallen leaves collected from the ground

b) 100 leaves on tree branchesc) 50 fallen leaves and 50 leaves on branchesd) 50 fallen oak leaves and 50 oak leaves on branches

Example 1Which 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…

a) Students at the local high schoolb) Every 10th customer entering the storec) Every 10th customer in the cash-only lined) Visa card holders

You Try!

1. Simple random sample

2. Systematic random sample3. 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 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.

ExampleResearchers 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 20th 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 sampleWhatever is “convenient” or

“easy”.

Voluntary Response SampleMembers of the population volunteer to participate.

GPS devices are attached to every goose on one lake in Canada.

ExampleResearchers 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.

ExampleA 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?