AP Statistics : Data
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Example Questions
Example Question #1 : How To Find Descriptive Data From A Z Score
Your professor gave back the mean and standard deviation of your class's scores on the last exam.
Your friend says the z-score of her exam is 
What did she score on her exam?
The z-score is the number of standard deviations above the mean.
We can use the following equation and solve for x.
Two standard deviations above 75 is 85.
Example Question #4 : How To Find Descriptive Data From A Z Score
Your boss gave back the mean and standard deviation of your team's sales over the last month.
Your friend says the z-score of her number of sales is 
How many sales did she make?
The z-score is the number of standard deviations above or below the mean.
We can use the known information with the following formula to solve for x.
Example Question #3 : How To Find Descriptive Data From A Z Score
The following data set represents Mr. Marigold's students' scores on the final. The standard deviation for this data set is 8.41. If you scored 0.91 standard deviations worse than the mean, what was your score?
To work with a z-score, first we need to find the mean of the data set. By adding together and dividing by 26, we get 81.15.
We know that your score is 0.91 standard deviations WORSE than the mean, which means that your z-score is -0.91. We can use the following formula for the z-score:
where z is the z-score, x is your data point, 
multiply both sides by 8.41
Example Question #12 : Data Sets And Z Scores
Your teacher gives you the z-score of your recent test, and says that the mean score was a 60, with a standard deviation of 6. Your z-score was a -2.5. What did you score on the test?
To find out your score 
As such,
So you scored a 
Example Question #1 : Census And Studies
You are conducting the following series of observational studies to determine if generally understood parameters about a local population are accurate:
A. You stand on the sidewalk next to a stop sign to observe and record the number of cyclists and drivers who stop or don't stop.
B. You inform customers at a local fast food restaurant of your study to determine the proportion of healthy food choices from the menu and then observe their choices.
C. From your car in the mall parking lot, you observe the proportion of shoppers who hold the door open for the next person who enters or exits the mall.
D. To estimate the proportion of males and females in the local community, you observe spectators at a hockey match and count and record the gender in a randomly selected area of the crowd.
E. You review the daily sign-in sheets at a local fitness center to estimate the average number of workouts per week for residents of the local community.
Which observational study should yield the most accurate results?
Study A
Study E
Study B
Study D
Study C
Study C
Study C takes a representative sample of local residents, and it does so without affecting the outcomes.
Studies A and B are influenced by the person conducting the survey. Studies D and E are biased samples of the population.
Therefore, C should yield the most accurate results.
Example Question #1 : How To Conduct An Observational Study
What situation would most warrant the method of observational study to produce accurate results?
Testing the effectiveness of a new drug.
Observing how chocolate consumption affects mood.
Studying the social interactions between groups of baboons.
Studying the relationship between sleep deprivation and cold susceptibility.
None of the above.
Studying the social interactions between groups of baboons.
Obseverational study does not involve any interference with the group being studied, so watching baboons in their natural habit would be best suited for this method.
Example Question #1 : How To Conduct A Census
Kate would like to determine what flavors of ice cream are most popular among students in her AP Statistics class. In total, there are 100 students in the class. Which of the following would be an appropriate sampling methodology?
Randomly select several of the most popular students in the class to answer questions about their favorite ice cream flavor
Group students into several homogeneous groups and choose one group to survey in order to determine the class's favorite ice cream flavor
Obtain a census of the class and survey each person in the class to determine their favorite flavor of ice cream
Ask every fifth person that walks through the door what their favorite flavor of ice cream is before class starts
There is no effective way to obtain a representative sample from the target population
Obtain a census of the class and survey each person in the class to determine their favorite flavor of ice cream
In this situation, it is best to conduct a census in order to determine what the class's favorite flavor of ice cream is. Since there are only 100 students in the class, a sample of the class would be very small and may not be representative of the class as a whole.
Example Question #1 : Census And Studies
Census is to __________ as survey is to __________.
There are no similarities between these two.
population; sample
population; group
cluster; stratum
sample; population
population; sample
A census gathers data from an entire population of people. A survey targets a representative sample of a population.
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