Find the mean absolute deviation for the set of data. Round to the
nearest hundredth if necessary. Then describe what the mean
absolute deviation represents.
1.
ANSWER:
17.88 moons; Sample answer: The average distance each data value is
from the mean is 17.88 moons.
2.
ANSWER:
158.75 gigabytes; Sample answer: The average distance each data value
is from the mean is 158.75 gigabytes.
3.The table shows the lengths of the longest bridges in the United States
and in Europe. Find the mean absolute deviation for each set of data.
Round to the nearest hundredth if necessary. Then write a few sentences
comparing their variation.
ANSWER:
United States: 9.77 km; Europe: 2.87 km; Sample answer: The mean
absolute deviation in bridge lengths in the U.S. is greater than the mean
absolute deviation of the bridge lengths in Europe. The lengths of the
bridges in Europe are closer to the mean.
Refer to the table that shows the recent population, in millions, of
the ten largest U.S. cities.
4.Find the mean absolute deviation. Round to the nearest hundredth.
ANSWER:
1.50 million
5.How many data values are closer than one mean absolute deviation away
from the mean?
ANSWER:
eight
6.Which population is farthest from the mean? How far away from the
mean is that population? Round to the nearest hundredth.
ANSWER:
8.40 million; 5.86 million
7.Are there any populations that are more than twice the mean absolute
deviation from the mean? Explain.
ANSWER:
yes; Sample answer: Twice the mean absolute deviation is 2 1.50
million, or 3.00 million. Since 5.86 million > 3.00 million, the population of
8.4 million is greater than 3.00 million away from the mean.
Be Precise Look up the word deviate in a dictionary or online.
8.What does the word deviate mean? How can it help you remember what
the mean absolute deviation refers to?
ANSWER:
to differ from; Sample answer: The mean absolute deviation describes
how the data values differ from the mean.
9.How does the word absolute help you to remember how to calculate the
mean absolute deviation?
ANSWER:
Sample answer: It helps me to remember to take the absolute value of
the difference between each data value and the mean.
10.Reason Abstractly Create two sets of data, each with five values, that
satisfy the following conditions.
The mean absolute deviation of Set A is less than the mean absolute
deviation of Set B.
The mean of Set A is greater than the mean of Set B.
ANSWER:
Sample answer: Set A: 12, 13, 15, 16, 19; Set B: 4, 8, 10, 15, 23
Persevere with Problems Refer to the table that shows the
recorded speeds of several cars on a busy street.
11.Calculate the mean absolute deviation both with and without the data
value of 55. Round to the nearest hundredth if necessary.
ANSWER:
with the data value of 55: 5.33 miles per hour; without the data value of
55: 2 miles per hour
12.Explain how including the value of 55 affects the mean absolute
deviation.
ANSWER:
Sample answer: When the value of 55 was included, the mean absolute
deviation increased. Because the value of 55 is so much greater than the
other data values, the larger mean absolute deviation shows that the data
are more spread out when the value of 55 is included as opposed to when
it is not included.
13.Construct an ArgumentExplainwhythemeanabsolutedeviationis
calculated using absolute value.
ANSWER:
Sample answer: The mean absolute deviation is the average distance that
each data value is from the mean. Since distance cannot be negative, the
absolute values of the differences are used.
14.Thetableshowsthehightemperaturefor6days.
Which of the following is the mean absolute deviation for the set of data?
A. 4°F
B. 4.8°F
C. 10°F
D. 68°F
ANSWER:
A
Use Math ToolsFindthemeanabsolutedeviationforthesetof
data. Round to the nearest hundredth if necessary. Then describe
what the mean absolute deviation represents.
15.
ANSWER:
$26.76; The average distance each data value is from the mean is
$26.76.
16.
ANSWER:
2.02 Grand Slam titles; The average distance each data value is from the
mean is 2.02 Grand Slam titles.
CopyandSolveFind the mean absolute deviation for each set of
data. Round to the nearest hundredth. Then write a few sentences
comparing their variation.
17.The table shows the amount of money raised by the homerooms for two
grade levels at a middle school.
ANSWER:
Sixth Grade: $10.67; Seventh Grade: $16.67; Sample answer: The mean
absolute deviation of the money raised by the sixth grade homerooms is
less than the mean absolute deviation of the money raised by the seventh
grade homerooms. The amounts of the money raised by the sixth grade
homerooms are closer to the mean.
18.The table shows the number of points scored each game for two
different basketball teams.
ANSWER:
Lakeside Panthers: 7.67 points; Jefferson Eagles: 10 points; Sample
answer: The mean absolute deviation of the number of points scored by
the Panthers is less than the mean absolute deviation of the number of
points scored by the Eagles. The number of points scored by the
Panthers is closer to the mean.
19.The table shows the prices for parking at various beaches along the same
coastline.
Which of the following is the mean absolute deviation for the set of data?
A. $0.25
B. $0.66
C. $2.50
D. $2.55
ANSWER:
B
20.Which of the following is true concerning the mean absolute deviation of
a set of data?
F. It describes the variation of the data values around the median.
G. It describes the absolute value of the mean.
H. It describes the average distance between each data value and the
mean.
I. It describes the variation of the data values around the mode.
ANSWER:
H
21.Short Response The table shows the number of Calories in several
sandwiches at a restaurant. Find the mean absolute deviation for the set
of data. Round to the nearest hundredth.
ANSWER:
45.33 Calories
Divide.
22.86÷5=__________
ANSWER:
17.2
23.95÷4=__________
ANSWER:
23.75
24.105÷6=__________
ANSWER:
17.5
25.94.5÷15=__________
ANSWER:
6.3
26.72÷5=__________
ANSWER:
14.4
27.40.6÷7=__________
ANSWER:
5.8
28.59.5÷7=__________
ANSWER:
8.5
29.126÷8=__________
ANSWER:
15.75
30.146÷5=__________
ANSWER:
29.2
31.The table shows the number of different cones Delightful Dips ice cream
shop sold in one afternoon. What is the total number of cones sold?
ANSWER:
235 cones
32.The hiking club wanted to cover a different trail each day for a week. On
Monday they hiked 2.3 miles, on Tuesday they hiked 1.8 miles, on
Wednesday they hiked 3.2 miles, on Thursday they hiked 1.4 miles and
on Friday they hiked 2.8 miles. What is the total distance they hiked?
ANSWER:
11.5 miles
Find the mean absolute deviation for the set of data. Round to the
nearest hundredth if necessary. Then describe what the mean
absolute deviation represents.
1.
ANSWER:
17.88 moons; Sample answer: The average distance each data value is
from the mean is 17.88 moons.
2.
ANSWER:
158.75 gigabytes; Sample answer: The average distance each data value
is from the mean is 158.75 gigabytes.
3.The table shows the lengths of the longest bridges in the United States
and in Europe. Find the mean absolute deviation for each set of data.
Round to the nearest hundredth if necessary. Then write a few sentences
comparing their variation.
ANSWER:
United States: 9.77 km; Europe: 2.87 km; Sample answer: The mean
absolute deviation in bridge lengths in the U.S. is greater than the mean
absolute deviation of the bridge lengths in Europe. The lengths of the
bridges in Europe are closer to the mean.
Refer to the table that shows the recent population, in millions, of
the ten largest U.S. cities.
4.Find the mean absolute deviation. Round to the nearest hundredth.
ANSWER:
1.50 million
5.How many data values are closer than one mean absolute deviation away
from the mean?
ANSWER:
eight
6.Which population is farthest from the mean? How far away from the
mean is that population? Round to the nearest hundredth.
ANSWER:
8.40 million; 5.86 million
7.Are there any populations that are more than twice the mean absolute
deviation from the mean? Explain.
ANSWER:
yes; Sample answer: Twice the mean absolute deviation is 2 1.50
million, or 3.00 million. Since 5.86 million > 3.00 million, the population of
8.4 million is greater than 3.00 million away from the mean.
Be Precise Look up the word deviate in a dictionary or online.
8.What does the word deviate mean? How can it help you remember what
the mean absolute deviation refers to?
ANSWER:
to differ from; Sample answer: The mean absolute deviation describes
how the data values differ from the mean.
9.How does the word absolute help you to remember how to calculate the
mean absolute deviation?
ANSWER:
Sample answer: It helps me to remember to take the absolute value of
the difference between each data value and the mean.
10.Reason Abstractly Create two sets of data, each with five values, that
satisfy the following conditions.
The mean absolute deviation of Set A is less than the mean absolute
deviation of Set B.
The mean of Set A is greater than the mean of Set B.
ANSWER:
Sample answer: Set A: 12, 13, 15, 16, 19; Set B: 4, 8, 10, 15, 23
Persevere with Problems Refer to the table that shows the
recorded speeds of several cars on a busy street.
11.Calculate the mean absolute deviation both with and without the data
value of 55. Round to the nearest hundredth if necessary.
ANSWER:
with the data value of 55: 5.33 miles per hour; without the data value of
55: 2 miles per hour
12.Explain how including the value of 55 affects the mean absolute
deviation.
ANSWER:
Sample answer: When the value of 55 was included, the mean absolute
deviation increased. Because the value of 55 is so much greater than the
other data values, the larger mean absolute deviation shows that the data
are more spread out when the value of 55 is included as opposed to when
it is not included.
13.Construct an ArgumentExplainwhythemeanabsolutedeviationis
calculated using absolute value.
ANSWER:
Sample answer: The mean absolute deviation is the average distance that
each data value is from the mean. Since distance cannot be negative, the
absolute values of the differences are used.
14.Thetableshowsthehightemperaturefor6days.
Which of the following is the mean absolute deviation for the set of data?
A. 4°F
B. 4.8°F
C. 10°F
D. 68°F
ANSWER:
A
Use Math ToolsFindthemeanabsolutedeviationforthesetof
data. Round to the nearest hundredth if necessary. Then describe
what the mean absolute deviation represents.
15.
ANSWER:
$26.76; The average distance each data value is from the mean is
$26.76.
16.
ANSWER:
2.02 Grand Slam titles; The average distance each data value is from the
mean is 2.02 Grand Slam titles.
CopyandSolveFind the mean absolute deviation for each set of
data. Round to the nearest hundredth. Then write a few sentences
comparing their variation.
17.The table shows the amount of money raised by the homerooms for two
grade levels at a middle school.
ANSWER:
Sixth Grade: $10.67; Seventh Grade: $16.67; Sample answer: The mean
absolute deviation of the money raised by the sixth grade homerooms is
less than the mean absolute deviation of the money raised by the seventh
grade homerooms. The amounts of the money raised by the sixth grade
homerooms are closer to the mean.
18.The table shows the number of points scored each game for two
different basketball teams.
ANSWER:
Lakeside Panthers: 7.67 points; Jefferson Eagles: 10 points; Sample
answer: The mean absolute deviation of the number of points scored by
the Panthers is less than the mean absolute deviation of the number of
points scored by the Eagles. The number of points scored by the
Panthers is closer to the mean.
19.The table shows the prices for parking at various beaches along the same
coastline.
Which of the following is the mean absolute deviation for the set of data?
A. $0.25
B. $0.66
C. $2.50
D. $2.55
ANSWER:
B
20.Which of the following is true concerning the mean absolute deviation of
a set of data?
F. It describes the variation of the data values around the median.
G. It describes the absolute value of the mean.
H. It describes the average distance between each data value and the
mean.
I. It describes the variation of the data values around the mode.
ANSWER:
H
21.Short Response The table shows the number of Calories in several
sandwiches at a restaurant. Find the mean absolute deviation for the set
of data. Round to the nearest hundredth.
ANSWER:
45.33 Calories
Divide.
22.86÷5=__________
ANSWER:
17.2
23.95÷4=__________
ANSWER:
23.75
24.105÷6=__________
ANSWER:
17.5
25.94.5÷15=__________
ANSWER:
6.3
26.72÷5=__________
ANSWER:
14.4
27.40.6÷7=__________
ANSWER:
5.8
28.59.5÷7=__________
ANSWER:
8.5
29.126÷8=__________
ANSWER:
15.75
30.146÷5=__________
ANSWER:
29.2
31.The table shows the number of different cones Delightful Dips ice cream
shop sold in one afternoon. What is the total number of cones sold?
ANSWER:
235 cones
32.The hiking club wanted to cover a different trail each day for a week. On
Monday they hiked 2.3 miles, on Tuesday they hiked 1.8 miles, on
Wednesday they hiked 3.2 miles, on Thursday they hiked 1.4 miles and
on Friday they hiked 2.8 miles. What is the total distance they hiked?
ANSWER:
11.5 miles
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11-4 Mean Absolute Deviation
