Samples & Populations

Samples & Populations

By Ashley Alexopoulos

​Samples should be:

​

• representative of the population

  • if the sample is representative, surveying the sample can more accurately make generalizations about the population

• randomly selected

  • this helps prevent "bias"​ which would skew the results and lead to inaccurate generalizations about the population

Multiple Choice

A _________ is the entire set someone is interested in studying.

• Sample

• Statistic

• Population

• Bias

Multiple Choice

A _________ is a subset of the population to be surveyed.

• Population

• Bias

• Sample

• Statistic

Multiple Select

Which of the following are reasons why a random sample would be preferred over surveying the entire population?

• Surveying the population is expensive

• Surveying the population takes too much time

• Surveying the population can be hard to manage

• Surveying the population might not be possible

Multiple Choice

Select the sampling method that would most fairly represent the people in the viewing area.

• 100 people that are trying out for a reality TV show

• 100 students at your middle school

• Every 100th person at a shopping mall

Multiple Choice

A student wants to know which type of pizza high school students prefer. Which of the following is a good, representative sample of the population?

• All 10th graders in the school

• 20 students from each grade level

• The teachers at the school

• The students who walk to school

Multiple Choice

A beverage company wants to see if people in the US like their new logo. Which of the following represents the population?

• 2000 people ages 5-13

• A selection of logo artists

• A selection of shoppers from different states

• All of the people in the US

Multiple Choice

A beverage company wants to see if people in the US like their new logo. Which of the following represents the best choice for a sample?

• 2000 people ages 5-13

• A selection of logo artists

• A selection of shoppers from different states

• All of the people in the US

Multiple Choice

A survey company wants to know if the people in a state think that pollution is too high. Which choice represents the population?

• A selection of people who live in small towns

• Everyone who lives in the state

• A selection of people from each city in the state

Multiple Choice

You want to know how most people get home from school. You go to the bus stop and ask students how they get home. This is a good representative sample.

• TRUE

• FALSE

Multiple Choice

Ana wants to know what the average student thinks about her school's tardy policy. Which group of students should she survey as a representative sample for the most accurate results?

• 30 randomly selected students

• 30 of her friends

• 30 students who are often tardy

• 30 students who are not often tardy

​Biased vs. Unbiased

​

A biased sample is selected based on non-random criteria. For example, in a "convenience sample," participants are selected based on accessibility and availability. Or in a "voluntary response sample," people volunteer to participate which skews the results.

​

An unbiased sample means that everyone in the population has an equal chance of being selected and represented. ​

Multiple Choice

All samples lead to good predictions about the entire population

• TRUE

• FALSE

Multiple Select

To get valid results, a sample must be:

• BIASED

• UNBIASED

• RANDOM

• EASY

Multiple Choice

A school surveys all 7th grade boys to determine what to sell in the school store.  This sample is _________.

• BIASED

• UNBIASED

Multiple Select

Chloe and Ella want to know the favorite subject of people at their school, so they place everyone's name on a piece of paper and draw 30 names from a bag.

• BIASED SAMPLE

• RANDOM SAMPLE

• UNBIASED SAMPLE

Multiple Choice

Carlos wants to know the favorite sport of people at his school, so he asks his baseball team.

• BIASED

• UNBIASED

Multiple Choice

I surveyed 100 people at a grocery store by selecting every 3rd person that entered, does this sample represent the local population?

• Yes. It is random and unbiased.

• No. It is random, but it's also biased.

• No. It is not random, and is biased.

• No. It is unbiased, but it is not random.

​Survey questions can be biased too!

Multiple Choice

Which survey question is most likely to result in unbiased results?

• Which do you like better, delicious apples or boring oranges?

• Which do you prefer, apples or oranges?

• Do you prefer apples, like I do, or oranges?

• Don't you prefer apples to oranges?

Multiple Choice

To evaluate the defect rate of its memory chips, an integrated circuit manufacturer tests every 100th chip off the production line. Out of 10 chips tested, one chip is found to be defective. The manufacturer concludes that 3 chips out of 3,000 will be defective.

• Valid - Simple Random Sample

• Valid - Systematic Random Sample

• Invalid - Convenience Sample

• Invalid - Voluntary Response Sample

Multiple Choice

Students who wish to represent the school at a school board meeting are asked to stop by the office after lunch. 5 students show up.

• Valid - Simple Random Sample

• Valid - Systematic Random Sample

• Invalid - Convenience Sample

• Invalid - Voluntary Response Sample

Multiple Choice

To determine if the class understood the homework assignment, the math teacher checks the top 3 papers in the pile of collected homework. The teacher finds that all students understood the homework assignment.

• Valid - Simple Random Sample

• Valid - Systematic Random Sample

• Invalid - Convenience Sample

• Invalid - Voluntary Response Sample

Multiple Choice

A member of the cafeteria staff asks every fifth student leaving the cafeteria to rank 5 vegetables from most favorite to least favorite. She finds that corn is one of the favorite vegetables for students who eat at the cafeteria.

• Valid - Simple Random Sample

• Valid - Systematic Random Sample

• Invalid - Convenience Sample

• Invalid - Voluntary Response Sample

Multiple Choice

One bead for every member of the school orchestra is placed in a bag. All but 2 of the beads are white. Each member draws a bead from the bag, and the members who pick the non-white beads will represent the orchestra.

• Valid - Simple Random Sample

• Valid - Systematic Random Sample

• Invalid - Convenience Sample

• Invalid - Voluntary Response Sample