Univariate Data - AP Statistics
Card 0 of 20
A value has a 
-score of 
. The value is . . .
A value has a
The 
-score indicates how close a particular value is to the population mean and whether the value is above or below the mean. A positive 
-score is always above the mean and a negative 
-score is always below it. Here, we know the value is below the mean because we have a negative 
-score.
The
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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?
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?
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.
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.
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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 
and a standard deviation of 
. Sally's z-score is 
. What is her score on the test?
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 
we have 
.
The z-score equation is
To solve for
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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?
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.
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.
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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?
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.
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.
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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?
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 
on the test, we enter the given information into the z-score formula and solve for 
.
where 
is the z-score, 
is the mean, and 
is the standard deviation.
As such,
So you scored a 
on the test.
To find out your score
As such,
So you scored a
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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?
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, 
is the mean, 81.15, and 
is the standard deviation, which we are told is 8.41.
multiply both sides by 8.41
we can reasonably round this to 73.5, which is an actual score in the data set. That must be your grade.
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
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Find the Interquartile Range (IQR) for the following data.
Q1 = 2, Q3 = 6
IQR = Q3 - Q1 = 4
Find the Interquartile Range (IQR) for the following data.
Q1 = 2, Q3 = 6
IQR = Q3 - Q1 = 4
The Interquartile Range equation is Q3-Q1
First, make sure the data is in ascending order. Then split the data up so that it each quartile has 25% of the data, or think of it as splitting the data into 4 equal parts.
is the "middle" value in the first half of the rank-ordered data set.
is the median value in the overall set.
is the "middle" value in the second half of the rank-ordered data set.
The Interquartile Range equation is Q3-Q1
First, make sure the data is in ascending order. Then split the data up so that it each quartile has 25% of the data, or think of it as splitting the data into 4 equal parts.
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Find the interquartile range for the following data set:
Find the interquartile range for the following data set:
To find the interquartile range, first find the median. This will split the data set into the upper and lower halves. The median for this data set is 11.
Focusing on the lower half, we can find the median, which is the first quartile, Q1:
the median is 6
Focusing on the upper half, we can find the median, which is the third quartile, Q3:
the median is 22.
The interquartile range is just Q3 - Q1, in this case 
To find the interquartile range, first find the median. This will split the data set into the upper and lower halves. The median for this data set is 11.
Focusing on the lower half, we can find the median, which is the first quartile, Q1:
Focusing on the upper half, we can find the median, which is the third quartile, Q3:
The interquartile range is just Q3 - Q1, in this case
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Find the interquartile range for the following data set:
Find the interquartile range for the following data set:
To find the interquartile range, first find the median. This will split the data set into the upper and lower halves. The median for this data set is 15.
Focusing on the lower half, we can find the median, which is the first quartile, Q1:
the median is 6, found by taking the mean of the middle two numbers 5 and 7.
Focusing on the upper half, we can find the median, which is the third quartile, Q3:
the median is 22.5, found by taking the mean of the middle two numbers 22 and 23.
The interquartile range is just Q3 - Q1, in this case 
To find the interquartile range, first find the median. This will split the data set into the upper and lower halves. The median for this data set is 15.
Focusing on the lower half, we can find the median, which is the first quartile, Q1:
Focusing on the upper half, we can find the median, which is the third quartile, Q3:
The interquartile range is just Q3 - Q1, in this case
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Six homes are for sale and have the following dollar values in thousands of dollars:
535
155
305
720
315
214
What is the mean value of the six homes?
Six homes are for sale and have the following dollar values in thousands of dollars:
535
155
305
720
315
214
What is the mean value of the six homes?
The mean is calculated by adding all the values in a group together, then dividing the sum by the total number in the group. In this case, six homes are for sale. The six home values are added together 
, then that value is divided by six.
The mean is calculated by adding all the values in a group together, then dividing the sum by the total number in the group. In this case, six homes are for sale. The six home values are added together
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A bird watcher observed how many birds came to her bird feeder for four days. These were the results:
Day 1: 15
Day 2: 12
Day 3: 10
Day 4: 13
What is the mean number of birds?
A bird watcher observed how many birds came to her bird feeder for four days. These were the results:
Day 1: 15
Day 2: 12
Day 3: 10
Day 4: 13
What is the mean number of birds?
The mean is calculated by adding the values from the four days together, then dividing the sum by the total number of values. In this case, four values must be added:
The mean is calculated by adding the values from the four days together, then dividing the sum by the total number of values. In this case, four values must be added:
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What is the mode of the following list of numbers?
35, 17, 4, 25, 7, 4, 17, 26, 8, 17
What is the mode of the following list of numbers?
35, 17, 4, 25, 7, 4, 17, 26, 8, 17
The mode is the number that appears most frequently in a series of numbers. First, organize the numbers in order from least to greatest: 4, 4, 7, 8, 17, 17, 17, 25, 26, 35. The number 17 appears three times, more than any other number.
The mode is the number that appears most frequently in a series of numbers. First, organize the numbers in order from least to greatest: 4, 4, 7, 8, 17, 17, 17, 25, 26, 35. The number 17 appears three times, more than any other number.
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A sample consists of the following observations:
. What is the mean?
A sample consists of the following observations:
The mean is 
The mean is
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A business tracked the number of customer calls received over a period of five days. What was the mean number of customer calls received in a day?
Day 1: 57
Day 2: 63
Day 3: 48
Day 4: 49
Day 5: 59
A business tracked the number of customer calls received over a period of five days. What was the mean number of customer calls received in a day?
Day 1: 57
Day 2: 63
Day 3: 48
Day 4: 49
Day 5: 59
The mean is calculated by adding all the values in a data set, then dividing the sum by the total number in the group.
The mean is calculated by adding all the values in a data set, then dividing the sum by the total number in the group.
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Find the mean of the following set.
Find the mean of the following set.
To find the mean of a set, follow the formula
in this case
or
To find the mean of a set, follow the formula
in this case
or
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Number Crunchers Inc. has offices in New York and Wisconsin. The mean salary for office workers in New Work is $28,500. The mean salary for office workers in the Wisconsin office is $22,500. The New York office has 128 office workers and the Wisconsin office has 32 office workers. What is the mean salary paid to the office workers in Number Crunchers Inc.?
Number Crunchers Inc. has offices in New York and Wisconsin. The mean salary for office workers in New Work is $28,500. The mean salary for office workers in the Wisconsin office is $22,500. The New York office has 128 office workers and the Wisconsin office has 32 office workers. What is the mean salary paid to the office workers in Number Crunchers Inc.?
The total amount paid in salaries to the office workers is
,
which is paid to 
office workers. Thus, the mean salary paid to office workers is
.
The total amount paid in salaries to the office workers is
which is paid to
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Six homes are for sale and have the following dollar values in thousands of dollars:
535
155
305
720
315
214
What is the median value of the six homes?
Six homes are for sale and have the following dollar values in thousands of dollars:
535
155
305
720
315
214
What is the median value of the six homes?
The median is determined by ordering the values in the group from least to greatest: 155, 214, 305, 315, 535, 720. The value directly in the middle is the median. For instance, if there are five numbers, the third is the median. Here, we have an even number of values so there is no value directly in the middle. To find the median when there is no middle-most value, find the average of the two middle values. The mean is determined by adding the two values and dividing by two (the number in the group):
The median is determined by ordering the values in the group from least to greatest: 155, 214, 305, 315, 535, 720. The value directly in the middle is the median. For instance, if there are five numbers, the third is the median. Here, we have an even number of values so there is no value directly in the middle. To find the median when there is no middle-most value, find the average of the two middle values. The mean is determined by adding the two values and dividing by two (the number in the group):
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Suppose a basketball team plays six games and scores the following points: 69, 78, 82, 69, 98, 85. Find the median.
Suppose a basketball team plays six games and scores the following points: 69, 78, 82, 69, 98, 85. Find the median.
To find the median of a sample with an even sample size, order the values from smallest to largest, take the two values in the middle, add them, and divide that by zero.
69, 78, 82, 69, 98, 85
69, 69, {78, 82} 85, 98
(78+82) / 2 = 80
To find the median of a sample with an even sample size, order the values from smallest to largest, take the two values in the middle, add them, and divide that by zero.
69, 78, 82, 69, 98, 85
69, 69, {78, 82} 85, 98
(78+82) / 2 = 80
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Find the median of the set.
Find the median of the set.
The median is the middle value of the set in increasing order.
In this set of 11 entries, the median is the 6th entry of the set in increasing order, or 6.
The median is the middle value of the set in increasing order.
In this set of 11 entries, the median is the 6th entry of the set in increasing order, or 6.
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