Univariate Data - AP Statistics
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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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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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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 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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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 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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Let 
be a positive integer.
Find the median of the set.
Let
Find the median of the set.
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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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?
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
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
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
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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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?
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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