AP Statistics : AP Statistics
Study concepts, example questions & explanations for AP Statistics
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Example Questions
Example Question #2 : How To Find Z Scores For A Data Set
The z-score is also known as the standard score.
The average temperature for all the days preceding the last for the month of February was 55 degrees Farhenheit, with a standard deviation of 5 degrees.
On the last day, the temperature was 73 degrees F. What is the z-score for the temperature on the last day?
To find the z-score, follow the formula
or
Example Question #41 : Univariate Data
A population has a standard deviation of 
A z score is unique to each value within a population.
To find a z score, subtract the mean of a population from the particular value in question, then divide the result by the population's standard deviation.
Example Question #1 : Data Sets And Z Scores
Natalie took her university placement examinations in Spanish and math. In Spanish, she scored 82; in math, she scored 86. The results of the Spanish exam had a mean of 72 and a standard deviation of 8. The results of the math exam had a mean of 68 and a standard deviation of 12. On which exam did Natalie do better, compared with the rest of her peers taking these placement exams?
The Math exam
None of the other answers, as z-scores cannot be calculated for this question
She did equally well on both exams
The Spanish exam
The Math exam
We need to calculate Natalie's z-scores for both her Spanish and math exams. Calculating z-scores is as follows:
Her z-score for the Spanish exam is 
Example Question #1 : 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 scored an 86? [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, 86, 
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 : Data Sets And Z Scores
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 : Data Sets And Z Scores
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 minutes lowere 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.
This week her time was two minutes lower than her average time.
This week her time was two standard deviations lower than her time last week.
This week her time was two standard deviations lower than her average time.
The z-score = 
Example Question #1 : Bivariate 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 #1 : Bivariate Data
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
There is a strong association between the two variables.
Correlation is measured on a scale of 
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 
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