Univariate Data Descriptors - AP Statistics
Card 0 of 168
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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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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Find the range for the set.
Find the range for the set.
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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Let 
be a positive integer.
What is the range of the set.
Let
What is the range of the set.
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
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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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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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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