AP Statistics : Univariate Data
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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 #4 : 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 : 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 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 minutes lowere than her time last week.
This week her time was two minutes lower than her average time.
This week her time was two standard deviations lower than her average time.
This week her time was two standard deviations lower than her average time.
The z-score = 
Example Question #11 : Data Sets And Z Scores
There are four suspects in a police line-up, and one of them committed a robbery. The suspect is described as "abnormally tall". In this case, "abnormally" refers to a height at least two standard deviations away from the average height. Their heights are converted into the following z-scores:
Suspect 1: 2.3
Suspect 2: 1.2
Suspect 3: 0.2
Suspect 4: -1.2.
Which of the following suspects committed the crime?
Suspect 1
Suspect 4
Suspect 2
Suspect 3
Suspect 1
Z-scores describe how many standard deviations a given observation is from the mean observation. Suspect 1's z-score is greater than two, which means that his height is at least two standard deviations greater than the average height and thus, based on the description, Suspect 1 is the culprit.
Example Question #1 : How To Find Descriptive Data From A Z Score
A value has a 
the same as the population mean
below the population mean
above the population mean
two standard deviations from the population mean
one standard deviation from the population mean
below the population mean
The 
Example Question #2 : How To Find Descriptive Data From A Z Score
All of the students at a high school are given an entrance exam at the beginning of 9th grade. The scores on the exam have a mean of 
The z-score equation is 
To solve for 
Example Question #12 : Data Sets And Z Scores
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 #11 : Data Sets And Z Scores
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 
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