Algebra 1 Unit 1 Teacher Guide Merged.docx

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Lesson 16 Practice Problems

457. Problem 1 Statement

Here are the statistics for the high temperatures in a city during October:

– mean of 65.3 degrees Fahrenheit
– median of 63.5 degrees Fahrenheit
– standard deviation of 9.3 degrees Fahrenheit
– IQR of 7.1 degeres Fahrenheit
Recall that the temperature , measured in degrees Celsius, is related to the
temperature , measured in degrees Fahrenheit, by = 5 ( − 32).

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a. Describe how the value of each statistic changes when 32 is subtracted from the
temperature in degrees Fahrenheit.

b. Describe how the value of each statistic further changes when the new values
are multiplied by 5.

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c. Describe how to find the value of each statistic when the temperature is
measured in degrees Celsius.

Solution

d. Subtracting 32 from the temperature in degrees Fahrenheit will decrease the
mean and median by 32 but it will not change the standard deviation or the
IQR.

e. Multiplying the new values (which have been shifted by 32) by 5 will multiply

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the mean and the median by 5. Both the standard deviation and the IQR

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are multplied by 5.

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f. For the mean and median, subtract 32 from the given values and then multiply
by 5. For the standard deviation and IQR, multiply the given values by 5.

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(From Unit 1, Lesson 15.)

458. Problem 2 Statement

Here is a box plot.

Give an example of a box plot that has a greater median and a greater measure of
variability, but the same minimum and maximum values.

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Solution
The minimum should be 15, the maximum 95, the median greater than 50, and the
interquartile range larger than 15.
Sample response:

(From Unit 1, Lesson 15.)

459. Problem 3 Statement

The mean vitamin C level for 20 dogs was 7.6 milligrams per liter, with a standard
deviation of 2.1 milligrams per liter.

One dog’s vitamin C level was not in the normal range. It was 0.9 milligrams per liter,
which is a very low level of vitamin C.

a. If the value 0.9 is eliminated from the data set, does the mean increase or
decrease?

b. If the value 0.9 is eliminated from the data set, does the standard deviation
increase or decrease?

Solution

c. The mean will increase because 0.9 milligrams per liter is below the mean of
7.6 milligrams per liter.

d. The standard deviation will decrease because 0.9 milligrams per liter is very far
from the mean, so the new data set will be more concentrated around the
center when that value is removed.

(From Unit 1, Lesson 14.)

460. Problem 4 Statement

The data set represents the number of hours that fifteen students walked during a
two-week period.

6 6 7 8 8 8 9 10
10 12 13 14 15 16 30

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The median is 10 hours and the IQR is 6 hours. Are there any outliers in the data?
Explain or show your reasoning.

Solution

Yes, 30 is an outlier since 10 + 1.5 • 6 = 19 and 30 > 19.

(From Unit 1, Lesson 14.)

461. Problem 5 Statement

Here are some summary statistics about the number of accounts that follow some
bands on social media.

– mean: 15,976 followers
– median: 16,432 followers
– standard deviation: 3,279 followers
– IQR: 5,274 followers
a. Give an example of a number of followers that a very popular band might have

that would be considered an outlier for this data. Explain or show your
reasoning.
b. Give an example of a number of followers that a relatively unknown band might
have that would be considered an outlier for this data. Explain or show your
reasoning.
Solution

c. Sample response: 30,000 followers since it is an outlier if the number of
followers is greater than 16, 432 + 1.5 • 5, 274, or 24,343 followers.

d. Sample response: 5,000 followers since it is an outlier if the number of
followers is less than 16, 432 − 1.5 • 5, 274, or 8,521 followers.

(From Unit 1, Lesson 14.)

462. Problem 6 Statement

The weights of one population of mountain gorillas have a mean of 203 pounds and
standard deviation of 18 pounds. The weights of another population of mountain
gorillas have a mean of 180 pounds and standard deviation of 25 pounds. Andre says
the two populations are similar. Do you agree? Explain your reasoning.

Solution

Sample response: I agree with Andre. Even though the weights of the two populations
have different means, the standard deviation lets me know that many gorillas in the
first population weigh less than 203 pounds, and many gorillas in the second

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population weigh more than 180 pounds. The populations have weights that overlap,
so I think they are similar.

(From Unit 1, Lesson 13.)

463. Problem 7 Statement

The box plot represents the distribution of the amount of change, in cents, that 50
people were carrying when surveyed.

The box plot represents the distribution of the same data set, but with the maximum,
203, removed.

The median is 25 cents for both plots. After examining the data, the value 203 is
removed since it was an error in recording.

a. Explain why the median remains the same when 203 cents was removed from
the data set.

b. When 203 cents is removed from the data set, does the mean remain the same?
Explain your reasoning.

Solution
c. The median remains the same because removing an extreme value from a data
set tends not to have much effect or no effect on the median. In this case, there
may be multiple people carrying 25 cents.
d. The mean decreases because 203 cents is greater than the mean of the data set.

(From Unit 1, Lesson 10.)

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