Random Samples and Populations

Module 11: Random Samples and Populations

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Lesson 11.1: Populations and Samples

When information is being gathered about a group, the entire group of objects, individuals, or events is called the population.  Because gathering information about each member of a large group can be difficult or impossible, researchers often study a part of the population, called a sample. 

The size of a sample and the way the sample is chosen can have an effect on whether the sample is representative of the population or not.  

One way that we can represent a random selection is to use number cubes (dice). 

Lesson 11.1: Populations and Samples

A sample in which every person, object, or event has an equal chance of being selected is called a random sample.  A random sample is more likely to be representative of the entire population than other types of samples.  When a sample does not accurately represent the population, it is called a biased sample. 

Lesson 11.1: Populations and Samples

Once you have selected a sample of the population, be sure that the data is gathered without bias. Make sure that the survey questions themselves do not sway people to respond in a certain way.  

-Would you like to waste the taxpayer’s money to build a frivolous skateboard park?

-Do you favor a new skateboard park?

-Studies have shown that having a safe place to go keeps kids out of trouble. Would you like to invest taxpayer’s money to build a skateboard park?

Multiple Choice

a sample that does not accurately represent the population

• population

• sample

• random sample

• biased sample

Multiple Choice

part of the group of objects, individuals, or events about which information is being gathered

• population

• sample

• random sample

• biased sample

Multiple Choice

the entire group of objects, individuals, or events about which information is being gathered

• population

• sample

• random sample

• biased sample

Multiple Choice

a sample in which every person, object, or event has an equal chance of being selected

• population

• sample

• random sample

• biased sample

Lesson 11.2: Making Inferences from a Random Sample

After obtaining a random sample of a population, you can make inferences about the population.  Random samples are usually representative and support valid inferences. 

Using the information from the random sample, you can create dot plots and box plots.  Both of these can help you make inferences about the population. 

You can use data based on a random sample, along with proportional reasoning, to make inferences or predictions about the population. 

Lesson 11.3: Generating Random Samples

We already talked about using number cubes (dice) to generate random samples.  Another way is to use a graphing calculator or online random number generator.  Just type random number generator into Google and they have some easy ones to use.  

Another way to choose random samples is to pull samples from a bag where pieces have been put to represent the population.  

Multiple Choice

Manny wants to know how many students at CTMS enjoy solving math problems. What is the best sampling method?

• ask for 20 volunteers to discuss whether they enjoy solving math problems
• ask the last 20 people to arrive at CTMS 
• Randomly ask 2 students in the hallway
• Ask every 20th student that walks into school

Multiple Choice

A school randomly chose ten English teachers and asked them which type of juice their students would prefer. Which reason best shows why this sample is biased?

• The sample didn't include students.
• The sample is too small.
• The sample can only be accurate if each teacher is included in the sample
• English teachers don't drink juice!

Multiple Choice

The manager of a book store surveys every 10th person who enters their store to see if the store should expand its hours.  What is the population?

• People who visit the bookstore.

• People who buy mystery novels.

• Residents of the town

• People who like to read.

Multiple Choice

Identify the Population:

Stokes County Schools randomly selected 23 teachers to find out which technology resource is the most effective for their students.

• 23 Teachers

• All teachers

• Students

• Stokes County Schools

Multiple Choice

Mrs. Boyd wants to find the average height of all her students in her classes. She decides to use the first 5 people who walk in the door. Is this a good representative sample?

• Yes
• No

Multiple Choice

Identify the Sample:
A restaurant wants to know if customers buy dessert when they eat out. As people leave the restaurant one evening, 20 people are surveyed at random. Eight people say they usually order dessert when they eat out. The restaurant concluded that most customers do not order dessert.

• 20 customers
• All customers
• 8 customers
• Dessert

Multiple Choice

A beverage company wanted to see if people in the United States like their new logo.  Which choice BEST represents a sample?

• A selection of shoppers from different states.
• Every person in the United States.
• 153 male and female employees
• A selection of logo artists.

Multiple Choice

_______ is the entire group of objects or individuals considered for a survey.

• Sample
• Population
• Random Sample
• Quartile

Multiple Choice

_______ is a part of a group being surveyed.

• Sample
• Population
• Random Sample
• Quartile

Multiple Choice

The entire group studied.

• sample

• population

Multiple Choice

What would be the sample in this example?

Surveyors in a mall choose shoppers to ask about products they prefer.

• the surveyors

• all shoppers in the mall

• the shoppers who were asked their preferences

Multiple Choice

What would be the population in this example?

Surveyors in a mall choose shoppers to ask about products they prefer.

• the surveyors

• all shoppers in the mall

• the shoppers who were asked their preferences