Name_________________________________________________ Date____________________________
Math 7: Populations and Samples
HOMEWORK #_____________
1) Identify the population and the sample. Determine if the sample is random or biased and explain why.
a) Paul and his friends average their test grades and find that their group average is 95. They pridict
the class average will be 95. The teacher announces that the average grade of all of students in the
class is 83.
Population: The entire class
Sample: Paul and his friends
Biased Sample
Biased Sample: Only Paul and his friends are included. Other students could not be picked.
b) Nancy wants to know the national average price of gas so she averages the prices of gas at stations
near her home. It comes out $3.03. Nancy hears a report that the national average price of
gasoline is $2.82.
Population: All gas stations in the country
Sample: Gas stations near her home
Biased Sample
Biased Sample: Only the gas stations near her home were surveyed. Other stations could not be
picked.
2) Determine whether each sample is a random sample or a biased sample. Explain.
a) Carol wants to find out the favorite foods of students at her middle school. She asks the boys’
basketball team about their favorite foods.
Biased Sample: Students who are not on the team won’t be selected.
b) Dallas wants to know what exploratory classes the students at his school like best. He survey’s
students who are leaving Mrs. Zeblisky’s Forensic Science exploratory.
Biased Sample: Students who aren’t in that class won’t be selected.
c) To choose a sample for a survey of seventh graders, the student council puts pieces of paper with
the names of all the seventh graders in a bag and selects 20 names.
Random Sample: All seventh graders have an equal chance of being selected.
3) Members of a polling organization survey 700 of the 7,453 registered voters in a town by randomly
choosing names form a list of all registered voters. Does this type of sample have a good chance of
representing the entire population?
Yes, the sample is more likely to represent the population because the sample is random.
4) Determine whether each question may be biased. Explain.
a) Joey wants to find out what sport seventh grade girls like most. He asks girls, “Is basketball your
favorite sport?”
Biased: Only one of the possible choices is given as an option. The possible sports don’t have a
chance to be picked based on that wording.
b) Jae wants to find out what type of art her fellow students enjoy the most. She asks her classmates,
“What is your favorite type of art?”
Not Biased: Based on the wording, any type of art may be selected.
5) Below is a chart that displays two different sampling methods that were used to determine how many
students go to the school football games. The results of those surveys are listed next to them.
Determine which sampling method below will better represent the entire population. Justify your
answer.
Sample Answer: Collin’s method better represents the entire student population because he used a random
sample. Any student could have been asked. Karl’s method was biased because the only people that had a
chance to be asked were those that were near him at lunch. It is possible his sample could have been limited
to things like just his friends or kids in his grade.
6) 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?
60 students were surveyed.
This is a random sample because every student had the same chance of being picked.