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Curriculum 2.0 Algebra 2: Unit 6-Topic 1, SLT 1
Name:
Normal Curves and Standard Deviation Sample Answers
Date:
Period:
1. What does the standard deviation tell us about a distribution?
The standard deviation tells us how spread out the data is, or how far the data is away from the mean.
Each of the distribution shown below are normal distributions with the same mean but a different standard
deviation.
2. How does changing the standard deviation affect a normal curve? Why does it have this effect?
The larger the standard deviation (e.g., SD=1 in this example) the more spread out the data. The peak of the
data is also lower. This happens because 68% of the distribution is 1 standard deviation from the mean
and 95% of the distribution is within 2 standard deviations of the mean.
Adapted from the Mathematics Vision Project
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Curriculum 2.0 Algebra 2: Unit 6-Topic 1, SLT 1
Name:
Normal Curves and Standard Deviation Sample Answers
Date:
Period:
3. What does the mean tell us about a distribution?
The mean tells us where the center, or balancing point, of the data is located.
Each of the distribution shown below are normal distributions with the same standard deviation but a different
means.
4. How does changing the mean affect a normal curve? Why does it have this effect?
Changing the mean does not change the shape of the curve, but changes where the peak is located.
Adapted from the Mathematics Vision Project
Page 2 of 3
Curriculum 2.0 Algebra 2: Unit 6-Topic 1, SLT 1
Name:
Normal Curves and Standard Deviation Sample Answers
Date:
Period:
5. Now that you have figured out some of the features of a normal distribution, determine if the following
statements are true or false. In each case, explain your answer.
a. A normal distribution depends on the mean and the standard deviation.
True/False Why?
True. The mean tells where the peak of the distribution is and the standard deviation determines how
spread out the distribution is.
b. The mean, median, and mode are equal in a normal distribution.
True/False Why?
True. A normal distribution is symmetric with a single peak, so the values for these measures of center
will be the same.
c. A normal distribution is bimodal.
True/False Why?
False. A bimodal distribution would have two peaks, but a normal distribution only has one.
d. In a normal distribution, 50% of the population is within one standard deviation of the mean.
True/False Why?
False. 68% of the distribution is within 1 standard deviation of the mean in a normal distribution.
Adapted from the Mathematics Vision Project
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