Lesson 12
Standard Deviation
Problem 1
The shoe size for all the pairs of shoes in a person's closet are recorded.
- 7
- 7
- 7
- 7
- 7
- 7
- 7
- 7
- 7
- 7
- What is the mean?
- What is the standard deviation?
Solution
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Problem 2
Here is a data set:
- 1
- 2
- 3
- 3
- 4
- 4
- 4
- 4
- 5
- 5
- 6
- 7
- What happens to the mean and standard deviation of the data set when the 7 is changed to a 70?
- For the data set with the value of 70, why would the median be a better choice for the measure of center than the mean?
Solution
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Problem 3
Which of these best estimates the standard deviation of points in a card game?
5 points
20 points
50 points
500 points
Solution
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Problem 4
The mean of data set A is 43.5 and the MAD is 3.7. The mean of data set B is 12.8 and the MAD is 4.1.
- Which data set shows greater variability? Explain your reasoning.
- What differences would you expect to see when comparing the dot plots of the two data sets?
Solution
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(From Unit 1, Lesson 11.)Problem 5
Select all the distribution shapes for which the mean and median must be about the same.
bell-shaped
bimodal
skewed
symmetric
uniform
Solution
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(From Unit 1, Lesson 10.)Problem 6
What is the IQR?
5 branches
7 branches
10 branches
12 branches
Solution
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(From Unit 1, Lesson 11.)Problem 7
The data represent the number of cans collected by different classes for a service project.
- 12
- 14
- 22
- 14
- 18
- 23
- 42
- 13
- 9
- 19
- 22
- 14
- Find the mean.
- Find the median.
- Eliminate the greatest value, 42, from the data set. Explain how the measures of center change.
Solution
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(From Unit 1, Lesson 9.)