Data - AP Statistics
Card 1 of 552
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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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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Use the following five number summary to determine if there are any outliers in the data set:
Minimum: 
Q1: 
Median: 
Q3: 
Maximum: 
Use the following five number summary to determine if there are any outliers in the data set:
Minimum:
Q1:
Median:
Q3:
Maximum:
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An observation is an outlier if it falls more than 
above the upper quartile or more than 
below the lower quartile.
. The minimum value is 
so there are no outliers in the low end of the distribution.
. The maximum value is 
so there are no outliers in the high end of the distribution.
An observation is an outlier if it falls more than
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For a data set, the first quartile is 
, the third quartile is 
and the median is 
.
Based on this information, a new observation can be considered an outlier if it is greater than what?
For a data set, the first quartile is
Based on this information, a new observation can be considered an outlier if it is greater than what?
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Use the 
criteria:
This states that anything less than 
or greater than 
will be an outlier.
Thus, we want to find
where 
.
Therefore, any new observation greater than 115 can be considered an outlier.
Use the
This states that anything less than
Thus, we want to find
Therefore, any new observation greater than 115 can be considered an outlier.
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Which values in the above data set are outliers?
Which values in the above data set are outliers?
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Step 1: Recall the definition of an outlier as any value in a data set that is greater than 
or less than 
.
Step 2: Calculate the IQR, which is the third quartile minus the first quartile, or 
. To find 
and 
, first write the data in ascending order.
. Then, find the median, which is 
. Next, Find the median of data below 
, which is 
. Do the same for the data above 
to get 
. By finding the medians of the lower and upper halves of the data, you are able to find the value, 
that is greater than 25% of the data and 
, the value greater than 75% of the data.
Step 3: 
. No values less than 64.
. In the data set, 105 > 104, so it is an outlier.
Step 1: Recall the definition of an outlier as any value in a data set that is greater than
Step 2: Calculate the IQR, which is the third quartile minus the first quartile, or
Step 3:
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You are given the following information regarding a particular data set:
Q1: 
Q3: 
Assume that the numbers 
and 
are in the data set. How many of these numbers are outliers?
You are given the following information regarding a particular data set:
Q1:
Q3:
Assume that the numbers
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In order to find the outliers, we can use the 
and 
formulas.
Only two numbers are outside of the calculated range and therefore are outliers: 
and 
.
In order to find the outliers, we can use the
Only two numbers are outside of the calculated range and therefore are outliers:
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Use the following five number summary to answer the question below:
Min: 
Q1: 
Med: 
Q3: 
Max: 
Which of the following is true regarding outliers?
Use the following five number summary to answer the question below:
Min:
Q1:
Med:
Q3:
Max:
Which of the following is true regarding outliers?
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Using the 
and 
formulas, we can determine that both the minimum and maximum values of the data set are outliers.
This allows us to determine that there is at least one outlier in the upper side of the data set and at least one outlier in the lower side of the data set. Without any more information, we are not able to determine the exact number of outliers in the entire data set.
Using the
This allows us to determine that there is at least one outlier in the upper side of the data set and at least one outlier in the lower side of the data set. Without any more information, we are not able to determine the exact number of outliers in the entire data set.
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A certain distribution has a 1st quartile of 8 and a 3rd quartile of 16. Which of the following data points would be considered an outlier?
A certain distribution has a 1st quartile of 8 and a 3rd quartile of 16. Which of the following data points would be considered an outlier?
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An outlier is any data point that falls 
above the 3rd quartile and below the first quartile. The inter-quartile range is 
and 
. The lower bound would be 
and the upper bound would be 
. The only possible answer outside of this range is 
.
An outlier is any data point that falls
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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
Tap to reveal answer
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
Tap to reveal answer
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 study is trying to determine if a particular medication (Y) is effective in weight loss. Patients participating in the study were randomly assigned to groups A, B, C, D, or E. Group A will receive one dose of Y, Group B will receive two doses of Y, Group C will receive three doses of Y, Group D will receive four doses of Y, and Group E will serve as the control group.
Which group will be receiving the placebo (a sugar pill)?
A study is trying to determine if a particular medication (Y) is effective in weight loss. Patients participating in the study were randomly assigned to groups A, B, C, D, or E. Group A will receive one dose of Y, Group B will receive two doses of Y, Group C will receive three doses of Y, Group D will receive four doses of Y, and Group E will serve as the control group.
Which group will be receiving the placebo (a sugar pill)?
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The control group in an experiment typically receives placebo treatments (in this case - Group E). Since all of the other groups are receiving at least one dose of the medication, they are considered to be experimental groups.
The control group in an experiment typically receives placebo treatments (in this case - Group E). Since all of the other groups are receiving at least one dose of the medication, they are considered to be experimental groups.
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To test if vitamin C actually makes people feel better, a vitamin company decides to run a 5-day study where they give one group of 100 sick participants vitamin C pills and another group of 100 sick people placebo pills, and monitored another group of 100 sick people who took no pills.
At the end of the 5-day experiment, 90 participants in the vitamin C group reported feeling better. 30 participants in the no-pill group felt better after the 5-day period. Interestingly, 50 participants in the placebo group felt better after the 5-day period.
What could explain these numbers?
To test if vitamin C actually makes people feel better, a vitamin company decides to run a 5-day study where they give one group of 100 sick participants vitamin C pills and another group of 100 sick people placebo pills, and monitored another group of 100 sick people who took no pills.
At the end of the 5-day experiment, 90 participants in the vitamin C group reported feeling better. 30 participants in the no-pill group felt better after the 5-day period. Interestingly, 50 participants in the placebo group felt better after the 5-day period.
What could explain these numbers?
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The placebo effect is when effects are seen in a group of people who did not actually receive a treatment.
In the vitamin C group, 90 participants felt better.
Naturally (no-pill), 30 participants felt better.
With the placebo, 50 participants felt better. Since more people felt better with the placebo than with no treatment at all, it appears that some percentage of people believed that they would feel better with a pill and actually began to feel better due to the placebo effect.
The placebo effect is when effects are seen in a group of people who did not actually receive a treatment.
In the vitamin C group, 90 participants felt better.
Naturally (no-pill), 30 participants felt better.
With the placebo, 50 participants felt better. Since more people felt better with the placebo than with no treatment at all, it appears that some percentage of people believed that they would feel better with a pill and actually began to feel better due to the placebo effect.
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On a residual plot, the 
-axis displays the and the 
-axis displays .
On a residual plot, the
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A residual plot shows the difference between the actual and expected value, or residual. This goes on the y-axis. The plot shows these residuals in relation to the independent variable.
A residual plot shows the difference between the actual and expected value, or residual. This goes on the y-axis. The plot shows these residuals in relation to the independent variable.
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Let us suppose a company wants to evaluate whether a new medical device works better than current devices. It conducts a small experiment to assess the effectiveness of the new device. To conduct the experiment, the company randomly assigns one group to the new medical device, which requires users to stay well hydrated, and the other group to the old device.
How should we control for confounding variables?
Let us suppose a company wants to evaluate whether a new medical device works better than current devices. It conducts a small experiment to assess the effectiveness of the new device. To conduct the experiment, the company randomly assigns one group to the new medical device, which requires users to stay well hydrated, and the other group to the old device.
How should we control for confounding variables?
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When comparing the effectiveness of a treatment, one should try to ensure that only the treatment varies across groups. In this case, the new device is compared to an old device. However, the new device also requires that users stay well hydrated. If we observe any positive effects from the new device, we won't know whether the new device is effective, or if merely staying well hydrated is actually what is effective. To rule out this confounding variable, we should also ask the group using the old machine condition to stay hydrated as well.
When comparing the effectiveness of a treatment, one should try to ensure that only the treatment varies across groups. In this case, the new device is compared to an old device. However, the new device also requires that users stay well hydrated. If we observe any positive effects from the new device, we won't know whether the new device is effective, or if merely staying well hydrated is actually what is effective. To rule out this confounding variable, we should also ask the group using the old machine condition to stay hydrated as well.
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An experiment was done by medical researchers to determine the association between drinking caffeine and severity of lung cancer. Results showed that there was a high association between the two variables. Which of the following could be a potential confounding variable in the experiment?
An experiment was done by medical researchers to determine the association between drinking caffeine and severity of lung cancer. Results showed that there was a high association between the two variables. Which of the following could be a potential confounding variable in the experiment?
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A confounding variable is one that could potentially have an effect on both the independent and dependent variables in a study. In this case, it is possible that there is an association between smoking and caffeine as well as smoking and lung cancer.
A confounding variable is one that could potentially have an effect on both the independent and dependent variables in a study. In this case, it is possible that there is an association between smoking and caffeine as well as smoking and lung cancer.
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A study finds that caffeine intake has a strong positive correlation with grades for college students. In other words, on average, the more caffeine intake a student has, the higher a grade the student gets.
Which of the following could potentially be a confounding variable in this experiment?
A study finds that caffeine intake has a strong positive correlation with grades for college students. In other words, on average, the more caffeine intake a student has, the higher a grade the student gets.
Which of the following could potentially be a confounding variable in this experiment?
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The only confounding variable in this experiment is the amount of sleep that each student gets. A confounding variable is one that has an impact on both the dependent and independent variable. It is possible that the amount of sleep a student gets is related to caffeine intake, which in turn affects the grade a student receives on a test or assignment.
The only confounding variable in this experiment is the amount of sleep that each student gets. A confounding variable is one that has an impact on both the dependent and independent variable. It is possible that the amount of sleep a student gets is related to caffeine intake, which in turn affects the grade a student receives on a test or assignment.
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An experiment testing the effects of caffeine on endurance performance in athletes assigns caffeine to a randomly selected group of athletes and has them exercise. Another trial was conducted in which the same group exercised without anything given to them to take. The results did not match the expected results. What should be done to improve this experiment?
An experiment testing the effects of caffeine on endurance performance in athletes assigns caffeine to a randomly selected group of athletes and has them exercise. Another trial was conducted in which the same group exercised without anything given to them to take. The results did not match the expected results. What should be done to improve this experiment?
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The placebo effect can potentially be a confounding variable. By knowingly taking a substance, participants may feel more energenized. By administering the same substance both trials, with the only thing changed being caffeine content, this corrects for this possible confounding variable.
The placebo effect can potentially be a confounding variable. By knowingly taking a substance, participants may feel more energenized. By administering the same substance both trials, with the only thing changed being caffeine content, this corrects for this possible confounding variable.
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A small local umbrella company is trying to test the effectiveness of their umbrellas by looking at how many umbrellas they sell each year.
In 2014, the company sold 2,000 umbrellas.
In 2015, they sold 1,500 umbrellas.
They assume that their umbrellas are less effective which is why sales decreased.
However, there could be many confounding factors. Which of the following is NOT a possible confounding factor?
A small local umbrella company is trying to test the effectiveness of their umbrellas by looking at how many umbrellas they sell each year.
In 2014, the company sold 2,000 umbrellas.
In 2015, they sold 1,500 umbrellas.
They assume that their umbrellas are less effective which is why sales decreased.
However, there could be many confounding factors. Which of the following is NOT a possible confounding factor?
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Any of these answers could explain why umbrella sales dropped. You cannot assume any specific cause explains a change in data like this-- further experimentation should be done rather than assuming cause and effect.
Any of these answers could explain why umbrella sales dropped. You cannot assume any specific cause explains a change in data like this-- further experimentation should be done rather than assuming cause and effect.
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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?
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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?
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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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