Univariate Data - AP Statistics
Card 1 of 240
Let 
be a positive integer.
Find the median of the set.
Let
Find the median of the set.
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The median is the middle value of the set in increasing order.
In this set of 8 (or any even number) entries, the median is the mean of the two middle entries of the set in increasing order
or
The median is the middle value of the set in increasing order.
In this set of 8 (or any even number) entries, the median is the mean of the two middle entries of the set in increasing order
or
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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?
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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?
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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
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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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Find the range for the set.
Find the range for the set.
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To find the range, subtract the minimum value from the maximum value
minimum: 
maximum: 
So,
maximum - minimum = 
To find the range, subtract the minimum value from the maximum value
minimum:
maximum:
So,
maximum - minimum =
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The 70th and 80th percentiles of a set of scores are 78 and 86, respectively; the interquartile range of the scores is 41. Which of these scores is more likely than the others to be at the 25th percentile?
The 70th and 80th percentiles of a set of scores are 78 and 86, respectively; the interquartile range of the scores is 41. Which of these scores is more likely than the others to be at the 25th percentile?
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The interquartile range of a set of scores is the difference between the third and first quartile - that is, the difference between the 75th and 25th percentiles. The 75th percentile is between 78 and 86, so, if 41 is subtracted from those numbers, the upper and lower bounds of the 25th percentile can be found.
Of our choices, only 40 falls in this range.
The interquartile range of a set of scores is the difference between the third and first quartile - that is, the difference between the 75th and 25th percentiles. The 75th percentile is between 78 and 86, so, if 41 is subtracted from those numbers, the upper and lower bounds of the 25th percentile can be found.
Of our choices, only 40 falls in this range.
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Your class' scores on a recent quiz was listed on the board.
Calculate the 
percentile.
Your class' scores on a recent quiz was listed on the board.
Calculate the
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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 
percentile, we find that there are 20 items in the set. We find the product to be
Since 
in order to find the 
percentile we find the 
term in the set, which is
To find the
We then round that number
For this problem, to find the
Since
in order to find the
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Your gym class' shot put distances are listed in the set below.
Which score is the 
percentile?
Your gym class' shot put distances are listed in the set below.
Which score is the
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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 
percentile, we find that there are 
items in the set. We find the product to be
Since 
in order to find the 
percentile we find the 
term in the set, which is
To find the
We then round that number
For this problem, to find the
Since
in order to find 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
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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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Let 
be a positive integer.
What is the range of the set.
Let
What is the range of the set.
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To find the range, subtract the minimum value from the maximum value
minimum: 
maximum: 
So,
maximum - minimum = 
To find the range, subtract the minimum value from the maximum value
minimum:
maximum:
So,
maximum - minimum =
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Find the range for the set of data
Find the range for the set of data
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The range is equal to the absolute difference between the minimum and maximum value.
We find the range to be
The range is equal to the absolute difference between the minimum and maximum value.
We find the range to be
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A sample consists of the following observations:
. What is the mean?
A sample consists of the following observations:
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The mean is 
The mean is
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Find the median of the set.
Find the median of the set.
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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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Find the median of the set
Find the median of the set
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The median is the middle value of the set in increasing order.
In this set of 6 (or any even number of) entries, the median is the mean of the two middle entries of the set in increasing order
or
The median is the middle value of the set in increasing order.
In this set of 6 (or any even number of) entries, the median is the mean of the two middle entries of the set in increasing order
or
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The following data set represents Mr. Marigold's students' scores on the final. If you got a 90 on the final, what percentile does that place you in?
The following data set represents Mr. Marigold's students' scores on the final. If you got a 90 on the final, what percentile does that place you in?
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Your percentile is the percent of the data set that is at your score or below.
There are 26 students in this particular class.
Of those students, 23 students were at a 90 or below.
, or 
.
Your percentile is the percent of the data set that is at your score or below.
There are 26 students in this particular class.
Of those students, 23 students were at a 90 or below.
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The following data set represents Mr. Marigold's students' scores on the final. If you are in the 46th percentile, what did you score?
The following data set represents Mr. Marigold's students' scores on the final. If you are in the 46th percentile, what did you score?
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If you scored in the 46th percentile, that means that 46% of your classmates scored the same as or worse than you.
This class has 26 students, and 46% of 26 is about 12.
Starting at 66 and counting 12 students forward would give you a 78.
This means that if you scored a 78, 12 students either had the same score or worse, so that is the 46th percentile.
If you scored in the 46th percentile, that means that 46% of your classmates scored the same as or worse than you.
This class has 26 students, and 46% of 26 is about 12.
Starting at 66 and counting 12 students forward would give you a 78.
This means that if you scored a 78, 12 students either had the same score or worse, so that is the 46th percentile.
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The following data set represents Mr. Marigold's students' scores on the final. If you are in the 96th percentile, what did you score?
The following data set represents Mr. Marigold's students' scores on the final. If you are in the 96th percentile, what did you score?
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If you scored in the 96th percentile, that means that 96% of your classmates scored the same as or worse than you.
This class has 26 students, and 96% of 26 is about 25.
If 25 of your classmates did the same as or worse than you, that means only one person did better than you - nice work.
You must have gotten a 92, because it's the second-best score.
If you scored in the 96th percentile, that means that 96% of your classmates scored the same as or worse than you.
This class has 26 students, and 96% of 26 is about 25.
If 25 of your classmates did the same as or worse than you, that means only one person did better than you - nice work.
You must have gotten a 92, because it's the second-best score.
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The following data set represents Mr. Marigold's students' scores on the final. If you got a 74 on the final, what percentile does that place you in?
The following data set represents Mr. Marigold's students' scores on the final. If you got a 74 on the final, what percentile does that place you in?
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If you scored a 74, you can count and discover that eight students did worse than or the same as you.
There are a total of 26 students in the class, so 8 students would be
or around 
.
This places you in the 31st percentile.
If you scored a 74, you can count and discover that eight students did worse than or the same as you.
There are a total of 26 students in the class, so 8 students would be
This places you in the 31st percentile.
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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?
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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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Find the first and third quartile for the set of data
Find the first and third quartile for the set of data
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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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