Populations and Samples

Warm Up Heidi decides to use a random sample to determine her classmates’ favorite color. She asks, “Is green your favorite color?” Is Heidi’s question biased? If so, give an example of an unbiased question that would serve Heidi better. Determine which sampling method will better represent the entire population. Justify your answer.

A population is the entire group of objects, individuals, or events about which information is being gathered. A sample is a part of the population. The size and way a sample is chosen can affect whether or not the sample is representative of the population. In a random sample, every person, object, or event has an equal chance of being selected. A biased sample does not accurately represent the population.

To determine the favorite bicycle brand of students at her school, Rhonda surveys 25 students as they leave a neighborhood bike shop. Is Rhonda’s sample a random sample or a biased sample? Explain

Identify the population Identify the population. Determine whether each sample is a random sample or a biased sample. Explain your reasoning. Gino wants to know how most people in his neighborhood get to work. He surveys 100 people getting off the bus at a bus stop near his house. Raylene wants to know the favorite ice cream flavor of the employees at her company. She surveys 150 employees chosen at random from a list of all employees.

How can you use a sample to gain information about a population How can you use a sample to gain information about a population? Select a sample that represents the population, and survey the sample using an unbiased question.

Can a sample be both random and biased Can a sample be both random and biased? Yes; if a random sample is too small, it may be biased if it does not accurately represent the population.

If you want to know how often people in your town travel as part of their job, why will surveying people at the airport produce a biased sample?

Can a survey question be biased if the information included is true Can a survey question be biased if the information included is true? Yes, true information can still be used to influence people to respond a certain way to a question. For example, “A glass of water has less calories than a glass of soda. Which is the better drink to have with meals?” is a biased question.

What could be the negative effects of using a biased survey question What could be the negative effects of using a biased survey question? The biased survey question could produce answers that are not truly representative of the entire population.

How can you make sure you are using unbiased samples and unbiased questions when surveying people? To have an unbiased sample, select people who are unlikely to answer the survey with a certain response. To write an unbiased question, make sure the words you choose do not make it more likely that people will respond with a certain answer.

Local residents were surveyed about adding stoplights at the corner of Main Street and Perry Avenue. Determine whether each survey question may be biased. Explain. Are stoplights needed at the intersection of Main and Perry? Fewer accidents occur at intersections with stoplights than at intersections that do not have them. Would you be in favor of having stoplights installed to make the intersection at Main and Perry safer? Installing a new stoplight will require detours that will decrease traffic to local businesses for up to a month. Should stoplights be installed at the corner of Main and Perry? Should stoplights be installed at the corner of Main and Perry?

Barbara surveyed students in her school by looking at an alphabetical list of the 600 student names, dividing them into groups of 10, and randomly choosing one from each group. How many students did she survey? What type of sample is this? Barbara found that 35 of the survey participants had pets. About what percent of the students she surveyed had pets? Is it safe to believe that about the same percent of students in the school have pets? Explain your thinking.

Exit Ticket Determine whether each sample is a random sample or a biased sample. Explain. Carlos chooses 50 movies at random from a list of all his movies to determine the average runtime of the movies in his collection. Lisa asks 75 people at a neighborhood fast-food restaurant about the last meal they ate, in order to find out the eating habits of people in her neighborhood. To determine the favorite subject of students at his school, Jason surveys 30 students who ride his bus about their favorite subject. Determine whether each question may be biased. Explain. Would a theme park with expensive ticket prices be a good place for a field trip? What is your favorite horror movie?