Understanding Sampling

Understanding Sampling

7th Grade Math Topics, Data Collection Project

Vocabulary

​When you hear the term population, you may think about the number of people living in a city or country. In statistics, population has a different meaning. A population is a group of individuals or objects that you want to study.

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You may want to gather information about characteristics or attributes of a population. It may be difficult or impossible to survey every member of a population so only a sample, or part of a population, can be surveyed.

Vocabulary (continued)

The best kind of sample to pick is a random sample. In this type, every member of the population has an equal chance of being chosen. As a result, random samples are usually representative of the larger population being studied.

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In statistics, an inference is an estimate or prediction about the population that is based on a sample. If the people in a sample are representative of the larger population, then the inferences you make based are your sample are likely to be true of that population.

Vocabulary (continued)

In contrast, a biased sample is not representative of the population. A sample is biased if some members of the population are more likely to be chosen than others. 

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For example, if you survey only students gathered by the bike rack at your school about whether or not they walk to school, that is a biased sample.​

Multiple Choice

A group of individuals or objects that you want to study is called....

• Population

• Sample

• Random Sample

• Biased Sample

Multiple Choice

Part of the population you wish to study is called...

• Inference

• Sample

• Random Sample

• Biased Sample

Multiple Choice

If your sample is not representative of the population, it is called a...

• Inference

• Random Sample

• Biased Sample

Example: Determine if the sample is representative.

​Mark wants to estimate the average age of vehicles driven in his town. He reviews a list of registered vehicles and notices that there are many more cars than trucks. Then he creates a sample by randomly choosing 100 cars and 100 trucks from the list. 

1. Identify the population.

2. Describe the sample.

3. Compare the characteristics of the sample with the population.​

Subject | Subject

Some text here about the topic of discussion

Example: Make the best choice.

Ruth is studying the characteristics of American popular songs from 1900 to 1945. She obtains a list of 500 songs published during this period. She wants to select 30 songs to include in her sample. Which of these methods will result in a random sample?

1. Choose the first 15 songs and the last 15 songs.

2. Number the songs from 001 to 500. Use a computer to generate 30 random three-digit whole numbers between 1 and 500. Select those songs.

3. Choose a number from 1 to 5 by drawing a slip of paper from a hat. Beginning with that number, choose every 10th song on the list.​

Subject | Subject

Some text here about the topic of discussion

Multiple Choice

Sherri wants to know how the 1,090 students at her school feel about after-school art programs. She needs to select a sample that is representative of the school to conduct a survey. Which of these samples is most likely to represent the population?

• 50 students in the spring musical

• Every 10th student that walks into school until you reach 50 students

• 50 students who are studying art

• 50 students at a school football game

Multiple Choice

Some students are conducting surveys to find out if adults in their town will vote to fund a new city park. Which of the following samples will be most representative of the voting population?

• Lavonne asks 20 parents of her friends.

• Quentin asks every other person leaving the library until he has asked 20 people.

• Latoya collects a list of adults in the town, assigns each of them a number, and uses a random number generator to pick 20 adults.

• Vince sends surveys to 50 local business owners and receives 20 responses.

Multiple Choice

Which of the following methods will result in a random sample?

• Paolo assigns a number to each student at school. He writes the numbers on slips of paper, randomly chooses 20 numbers, and surveys those students.

• Paolo puts up a sign that asks students to voluntarily record the number of pets they have. He takes the first 20 students.

• Paolo randomly surveys one boy and one girl at each lunch table during school lunch until he has surveyed 20 people.

• Paolo asks 20 out of 40 teachers at the school to randomly choose one student for the survey.

Poll

Rate your understanding of sampling.

• I understand this really well!

• I feel pretty good about it.

• I'm not sure.

• What just happened?!