RANDOM SAMPLES AND BIASED 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.

Examples : 

Identify the population. Determine whether each sample is a random sample or a biased sample. Explain your reasoning.

A. Roberto wants to know the favorite sport of adults in his hometown. He surveys 50 adults at a baseball game.

The population is adults in Roberto’s hometown.

The sample is biased.

Because, people who don’t like baseball will not be represented in this sample.

B.  Paula wants to know the favorite type of music for students in her class. She puts the names of all students in a hat, draws 8 names, and surveys those students.

The population is students in Paula’s class.

The sample is random.

Because, each student has an equal chance of being selected.

C.  Paula wants to know the favorite type of music for students in her class. She selected 5 her close friends as a sample and asked their favorite type of music. 

The population is students in Paula’s class.

The sample is biased.

Because, all the students do not have equal chance of being a part of the sample. 

D.  Mr. David is the principal of a school and he wants to check how many students are good in math in 7th grade. He takes the attendance of 7th grade and selects 5 students for a math quiz.   

The population is students in 7th grade. 

The sample is random.

Because, each student has an equal chance of being selected.

E. How might you choose a sample of size 20 to determine the preferred practice day of all the players in a soccer league ?

Place the names of all the players in a hat. Draw 20 names.

F. For a survey, a company manager assigned a number to each of the company’s 500 employees, and put the numbers in a bag. The manager chose 20 numbers and surveyed the employees with those numbers. Did the manager choose a random sample ?

Yes; every employee had an equal chance of being selected.

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