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Math 2 with Support
Review – Sampling and Comparing Data
Name _______________________
MM2D1.a Pose a questions and collect sample data from at least two different populations.
1. Keyshon is collecting data to discover the average number of books that high-school boys read each week
in his town. Which sample below is the least biased?
a) a sample consisting of every tenth boy from an alphabetical listing of all students in his school only
b) a sample consisting of 50 randomly selected boys from each of the high schools in town
c) a sample consisting of 50 volunteers from each of the high schools in town
d) a sample consisting of students on Keyshon’s baseball team
For each of the following scenarios, tell what type of sampling was done (self-selected, convenience,
systematic, or random) and whether the sample is biased or biased and why.
2. A team wants to know who the fans think was the team’s most valuable player during the season. Fans can
vote on the team’s website.
Because the question is posted on the team’s website and you must volunteer to go to the website and vote,
this is a self-selected sample. All self-selected samples are biased.
3. The managers of a movie theater chain want to find the number of movies people in the community usually
see in a theater each month. The managers have the ticket seller at each theater survey customers when
they purchase their tickets.
This sample is a convenience sample because the tickets sellers conveniently ask everyone that walks by.
Every convenience sample is biased.
4. The managers of a company with 500 employees want to know how the employees feel about some
proposed changes. The managers use a computer to generate a list of 50 employees to survey from a
database that includes all the employees.
This is a random sample because a computer is randomly selecting the people to survey. All random samples
are unbiased.
5. A university is conducting a survey to determine whether a public library has hours that satisfies most of
their patrons. At the library, students survey every 10th patron that exits the library.
This is a systematic sample because the students have created a system of selecting every 10 th patron to
interview. All systematic samples are unbiased.
6. A bicycling club wants to gather information about biking condition in the city. A survey for bicycle
riders is posted on club’s website.
Again, a survey posted on a website is a voluntary survey so this is a self-selected sample. Again, selfselected samples are biased.
7. A survey of the school’s lunch menu is being conducted. Every third student entering the cafeteria is
surveyed and asked “Do you think the lunch menu should include grilled chicken instead of pizza because
grilled chicken is healthier?”
Asking every third student being surveyed is a systematic sample because you have developed a system in
order to choose your interviewees. This is an unbiased sample.
MM2D1.d Compare the means and standard deviations of random samples with the corresponding
population parameters.
1. The class average on a math test was 75 and the standard deviation was 4.2. Find the z-score for a test
68  75
 1.67
4.2
score of 68.
2. The heights of 3 year olds at a preschool averaged 32.4 in., with a standard deviation of 1.5 in. Estimate
the probability that a randomly selected 3-year-old is between 31.4 in. and 34.9 in. in height.
31.4  32.4
 .67
1.5
34.9  32.4
 1.67
1.5
Look up these values on the z-table then subtract: 0.9525-0.2514= 0.7011
3. There are 150 volunteers at a hospital. Lian selected 10 random samples of 8 volunteers each and asked
them their ages. The sample means she found are shown below. What is a good estimate of the mean age of
the entire population of volunteers.
x
X
X
Find the average of the averages: 15.8
x
X
X
X
X
X
X
14
15
16
17
4. What does a normal distribution look like?
A bell curve
5. For a large population, the mean is 13.7 and the standard deviation is 8.9. One random sample produced
data values of 19, 8, 12, 17, 16, 25, 5, 18, 21, 7. Another random sample had data values of 12, 15, 17, 20, 13,
11, 18, 9, 15, 14.
a. Calculate the mean and standard deviation of the first sample.
Mean: 14.8
Standard Deviation: 6.23
b. Calculate the mean and standard deviation of the second sample.
Mean: 14.4
Standard Deviation: 3.17
c. Compare the means and standard deviations of the samples to the population mean. Are they the same?
Are they close? Are the samples representative of the population?
The means are both above the population mean, and neither of them are very close. The standard deviations
are less which means they are closer together. I don’t think either sample is a very good representation of
the population.
6. Does a sample have more or less variability than a population?
A sample has less variability than a population.
EOCT Practice
1. Your school newspaper is conducting a survey about music. Which survey question is least likely to lead to
biased results?
a) Do you listen to boring classical music?
b) What is your favorite type of music?
c) Do you agree that fun dance music should be played at school dances instead of loud rock music?
d) Do you, like most people your age, watch music videos?
2. A cosmetic company makes a face wash for 3 different skin types. The average number of bottles
produced each day is listed in the table. A quality control inspector needs to choose a sample of bottles to
inspect. Which method will most likely be representative of all the bottles?
Skin Type
Normal to Dry
Combination/Oily
Sensitive
a)
b)
c)
d)
Bottles
2200
1600
1200
For each type, choose the last 15 bottles produced
Randomly choose 25 of each type
Choose the first 50 bottles produced, regardless of type
Randomly choose 44 normal to dry, 32 combination/oily, and 24 sensitive
3. Central High School is spending a portion of their budget on upgrading the computers in the lab. The
school wants to survey a sample of the school population about the upgrades. Which of the following would
be the best way to obtain an unbiased sample of 100 students?
a) Have students fill out a voluntary survey at lunch. Collect the first 100 surveys.
b) Interview every 3rd person to enter a Computer Science class on Tuesday.
c) Put every student’s ID number into a computer and select 100 students at random.
d) Interview the first 100 students who come into the school from their buses.
4. Suppose the test scores on an exam show a normal distribution with a mean of 82 and a standard
deviation of 5. Within what range do about 95% of the scores fall?
a)
b)
c)
d)
72  x  92
77  x  87
67  x  97
77.9  x  86.1
5. During boot camp, the drill sergeant measured the weight of the men in his unit. He found the average
weight of the men to be 142 pounds and the standard deviation to be 14 pounds. If there are 100 men in the
unit how many men would be expected to weigh less than 128 pounds?
a) 32
b) 16
c) 5
d) 34