AP Statistics : Data
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Example Questions
Example Question #4 : How To Find Z Scores For A Data Set
The following data set represents Mr. Marigold's students' scores on the final. The standard deviation for this data set is 8.41. How many standard deviations are you away from the mean if you got all the questions right? [find your z-score]
To calculate the z-score, first we need to find the mean of the data set. By adding together and dividing by 26, we get 81.15.
To calculate your z-score and discover how close your score is to the mean in terms of standard deviations, use this formula:
where x is your data point, 100, 
Example Question #1 : How To Find Z Scores For A Data Set
This year's harvest, the apples had a mean mass of 
What is the z-score of the apple you picked?
To find the z-score, we follow the formula
For this problem we see that
Substituting for these values we see
Example Question #11 : How To Find Z Scores For A Data Set
The observed times (in minutes) it takes a swimmer to complete a race are normally distributed. The z-score for her swimming time this week is 
This week her time was two standard deviations lower than her average time.
This week her time was two minutes lower than her average time.
This week her time was two minutes lowere than her time last week.
This week her time was two standard deviations lower than her time last week.
This week her time was two minutes lower than her best time ever.
This week her time was two standard deviations lower than her average time.
The z-score = 
Example Question #51 : Data
Which of the following correlation coefficients indicates the strongest relationship between variables?
Correlation coefficients range from 1 to -1. The closer to either extreme, the stronger the relationship. The closer to 0, the weaker the relationship.
Example Question #2 : How To Find Correlation
It is found that there is a correlation of exactly 
There is enough evidence, with a correlation of 
The association between the two variables is positive
Correlation is measured on a scale of 
There is a strong association between the two variables.
All of the answer choices are correct
There is enough evidence, with a correlation of
Under no circumstance will correlation ever equate to causation, regardless of how strong the correlation between two variables is. In this case, all other answer choices are correct.
Example Question #1 : How To Find Correlation
In a medical school, it is found that there is a correlation of 
i. There is a positive association between the two variables.
ii. There is a strong correlation between the two variables.
iii. Coffee consumption in medical school students causes students to sleep less each night.
i, ii, and iii
iii only
ii only
i and ii
i and iii
ii only
Since the correlation is negative, there must be a negative association between the two variables (therefore statement i is incorrect). Statement ii is correct since a correlation of 
Example Question #1 : How To Find Correlation
Which of the following shows the least correlation between two variables?
The strength of correlation is measured on an absolute value scale of 
A correlation of 
Example Question #2 : Bivariate Data
Which of the following correlation coefficients implies the strongest relationship between variables:
A high correlation coefficient regardless of sign implies a stronger relationship. In this case 
Example Question #3 : How To Find Correlation
A national study on cell phone use found the following correlations:
-The correlation between the number of texts sent each day and a person's average credit card debt is 
-The correlation between the number of texts sent each day and the number of books read each month is 
Which of the following statements are true?
i. As the number of texts sent each day increases, average credit card debt increases.
ii. Sending more texts causes people to read less.
iii. A person's average credit card debt is related more strongly to the number of texts sent each day than the number of books read each month is related to the number of texts sent each day.
i and iii
i and ii
ii and iii
ii
iii
i and iii
i is correct because there is a positive correlation between the number of texts sent each day and average credit card debt.
ii is incorrect because the word "cause" was used in the statement. Correlation does not mean causation. There is a relationship between the number of texts sent each day and the number of books that a person reads each month. However, the number of texts sent each day does not cause a person to read a certain number of books each month.
iii is correct because the absolute values of the correlations indicate which correlation is stronger. 
Example Question #1 : Bivariate Data
A basketball coach wants to determine if a player's height can predict the number of points the player scores in a season. Which statistical test should the coach conduct?
P-score
T-test
Correlation
Linear regression
ANOVA
Linear regression
Linear regression is the best option for determining whether the value of one variable predicts the value of a second variable. Since that is exactly what the coach is trying to do, he should use linear regression.
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