Univariate Data - AP Statistics
Card 0 of 240
Obtain a normal distribution table or calculator for this problem.
Approximate the 
-percentile on the standard normal distribution.
Obtain a normal distribution table or calculator for this problem.
Approximate the
The 
-percentile is the value such that 
percent of values are less than it.
Using a normal table or calculator (such as R, using the command qnorm(0.9)), we get that the approximate 
-percentile is about 
.
The
Using a normal table or calculator (such as R, using the command qnorm(0.9)), we get that the approximate
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Find the first and third quartile for the set of data
Find the first and third quartile for the set of data
In order to find the first and third quartiles, we haave to find the 25th and 75th percentiles, respectively.
To find the 
percentile, we find the product of 
and the number of items 
in the set.
We then round that number 
up if it is not a whole number, and the 
term in the set is the 
percentile.
For this problem, to find the 
and 
percentile, we first find that there are 14 items in the set. We find their respective products to be
and
As such, the 
and 
percentiles are the fourth and eleventh terms in the set, or
In order to find the first and third quartiles, we haave to find the 25th and 75th percentiles, respectively.
To find the
We then round that number
For this problem, to find the
As such, the
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Obtain a normal distribution table or calculator for this problem.
Approximate the -percentile on the standard normal distribution.
Obtain a normal distribution table or calculator for this problem.
Approximate the
The -percentile is the value such that percent of values are less than it.
Using a normal table or calculator (such as R, using the command qnorm(0.9)), we get that the approximate -percentile is about .
The
Using a normal table or calculator (such as R, using the command qnorm(0.9)), we get that the approximate
Compare your answer with the correct one above
Find the first and third quartile for the set of data
Find the first and third quartile for the set of data
In order to find the first and third quartiles, we haave to find the 25th and 75th percentiles, respectively.
To find the percentile, we find the product of and the number of items in the set.
We then round that number up if it is not a whole number, and the term in the set is the percentile.
For this problem, to find the and percentile, we first find that there are 14 items in the set. We find their respective products to be
and
As such, the and percentiles are the fourth and eleventh terms in the set, or
In order to find the first and third quartiles, we haave to find the 25th and 75th percentiles, respectively.
To find the
We then round that number
For this problem, to find the
As such, the
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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
Which answer is closest to the standard deviation of the number of birds to visit the bird feeder over the four days?
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
Which answer is closest to the standard deviation of the number of birds to visit the bird feeder over the four days?
Standard deviation is essentially the average distance from the mean of a group of numbers. There are a number of steps in computing standard deviation, but the steps are not too complicated if you take them one at a time. First, find the mean of the values. Second, subtract the mean from the first value and square the result. Do this for all remaining values. Third, add these results together. Fourth, divide this value by the number of values. Finally, find the square root of the result.
1: 
2: 
3: 
4: 
5: 
Standard deviation is essentially the average distance from the mean of a group of numbers. There are a number of steps in computing standard deviation, but the steps are not too complicated if you take them one at a time. First, find the mean of the values. Second, subtract the mean from the first value and square the result. Do this for all remaining values. Third, add these results together. Fourth, divide this value by the number of values. Finally, find the square root of the result.
1:
2:
3:
4:
5:
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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 variance of the number of birds that visited the bird feeder over the four days?
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 variance of the number of birds that visited the bird feeder over the four days?
Variation measures the average difference between values within a group. The process is not complicated but there are four steps that can take time. First, find the mean of the values. Second, subtract the mean from the first value and square the result. Do this for all remaining values. Third, add these results together. Fourth, divide this value by the number of values in the group minus one (in this case, there are four days).
1: 
2: 
3: 
4: 
Note that to find the standard deviation, we would simply take one additional step of finding the square root of the variance.
Variation measures the average difference between values within a group. The process is not complicated but there are four steps that can take time. First, find the mean of the values. Second, subtract the mean from the first value and square the result. Do this for all remaining values. Third, add these results together. Fourth, divide this value by the number of values in the group minus one (in this case, there are four days).
1:
2:
3:
4:
Note that to find the standard deviation, we would simply take one additional step of finding the square root of the variance.
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The standard deviation of a population is 7.5. What is the variance of the population?
The standard deviation of a population is 7.5. What is the variance of the population?
This question illustrates the close relationship between the concepts of variance and standard deviation. We can find variance even though we do not know the values in the population if we know the standard deviation. Simply square the standard deviation to find the variance.
This question illustrates the close relationship between the concepts of variance and standard deviation. We can find variance even though we do not know the values in the population if we know the standard deviation. Simply square the standard deviation to find the variance.
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Alice recorded the outside temperature at noon each day for one week. These were the results.
Monday: 78
Tuesday: 85
Wednesday: 82
Thursday: 84
Friday: 82
Saturday: 79
Sunday: 80
What is the standard deviation of the temperatures?
Alice recorded the outside temperature at noon each day for one week. These were the results.
Monday: 78
Tuesday: 85
Wednesday: 82
Thursday: 84
Friday: 82
Saturday: 79
Sunday: 80
What is the standard deviation of the temperatures?
There are five steps to finding the standard deviation of a group of values. First, find the mean of the values. Second, subtract the mean from the first value and square the result. Do this for all remaining values. Third, add these results together. Fourth, divide this value by the number of values minus one. Finally, find the square root of the result.
There are five steps to finding the standard deviation of a group of values. First, find the mean of the values. Second, subtract the mean from the first value and square the result. Do this for all remaining values. Third, add these results together. Fourth, divide this value by the number of values minus one. Finally, find the square root of the result.
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Alice recorded the outside temperature at noon each day for one week. These were the results.
Monday: 78
Tuesday: 85
Wednesday: 82
Thursday: 84
Friday: 82
Saturday: 79
Sunday: 80
What is the variance of the temperatures?
Alice recorded the outside temperature at noon each day for one week. These were the results.
Monday: 78
Tuesday: 85
Wednesday: 82
Thursday: 84
Friday: 82
Saturday: 79
Sunday: 80
What is the variance of the temperatures?
There are four steps to finding the variance of values within a group. First, find the mean of the values. Second, subtract the mean from the first value and square the result. Do this for all remaining values. Third, add these results together. Fourth, divide the result by the number of values in the group minus one (in this case, there are seven days, so you must divide by six).
There are four steps to finding the variance of values within a group. First, find the mean of the values. Second, subtract the mean from the first value and square the result. Do this for all remaining values. Third, add these results together. Fourth, divide the result by the number of values in the group minus one (in this case, there are seven days, so you must divide by six).
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The average height of 
females in a class is 
inches, with a standard deviation of 
inches. In the same class, the average height of 
boys is 
inches, with a standard deviation of 
inches. What is the mean height of both males and females?
The average height of
To find the mean of the whole population, multiply the female's average by the number of females, and then multiply the male's average by the number of males. Sum up these products and divide by the total number of males AND females:
To find the mean of the whole population, multiply the female's average by the number of females, and then multiply the male's average by the number of males. Sum up these products and divide by the total number of males AND females:
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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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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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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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Six homes are for sale and have the following dollar values in thousands of dollars:
535
155
305
720
315
214
What is the range of the values 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 range of the values of the six homes?
The range is the simplest measurement of the difference between values in a data set. To find the range, one simply subtracts the lowest value from the greatest value, ignoring the others. Here, the lowest value is 155 and the greatest is 720.
The range is the simplest measurement of the difference between values in a data set. To find the range, one simply subtracts the lowest value from the greatest value, ignoring the others. Here, the lowest value is 155 and the greatest is 720.
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Alice recorded the outside temperature at noon each day for one week. These were the results.
Monday: 78
Tuesday: 85
Wednesday: 82
Thursday: 84
Friday: 82
Saturday: 79
Sunday: 80
What is the range of temperatures?
Alice recorded the outside temperature at noon each day for one week. These were the results.
Monday: 78
Tuesday: 85
Wednesday: 82
Thursday: 84
Friday: 82
Saturday: 79
Sunday: 80
What is the range of temperatures?
The range is the simplest measurement of the difference between values in a data set. To find the range, simply subtract the lowest value from the greatest value, ignoring the others.
The range is the simplest measurement of the difference between values in a data set. To find the range, simply subtract the lowest value from the greatest value, ignoring the others.
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A business tracked the number of customer calls received over a period of five days. What was the range of customer calls received daily?
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 range of customer calls received daily?
Day 1: 57
Day 2: 63
Day 3: 48
Day 4: 49
Day 5: 59
The range is the simple measurement of the difference between values in a dataset.
To find the range, simply subtract the lowest value from the greatest value, ignoring the others.
The range is the simple measurement of the difference between values in a dataset.
To find the range, simply subtract the lowest value from the greatest value, ignoring the others.
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