Mean Absolute Deviation Practice
Complete this assessment to review what you've learned. It will not count toward your grade.
2 of 52 of 5 Items
Question
The number of words Mr. Ahmad’s students read per minute is 109, 89, 112, 98, 101, 105, 120, 106. What is the mean absolute deviation of the dataset? Round the answer to the nearest tenth.(1 point)
To find the mean absolute deviation, we first need to find the mean of the dataset.
Sum of all the numbers = 109 + 89 + 112 + 98 + 101 + 105 + 120 + 106 = 840
Mean = Sum of all the numbers / Total number of numbers
= 840 / 8
= 105
Next, we find the absolute deviation for each number by subtracting the mean from each number:
Absolute deviation for 109 = |109 - 105| = 4
Absolute deviation for 89 = |89 - 105| = 16
Absolute deviation for 112 = |112 - 105| = 7
Absolute deviation for 98 = |98 - 105| = 7
Absolute deviation for 101 = |101 - 105| = 4
Absolute deviation for 105 = |105 - 105| = 0
Absolute deviation for 120 = |120 - 105| = 15
Absolute deviation for 106 = |106 - 105| = 1
Now, we find the sum of the absolute deviations:
Sum of absolute deviations = 4 + 16 + 7 + 7 + 4 + 0 + 15 + 1 = 54
Lastly, we find the mean of the absolute deviations:
Mean absolute deviation = Sum of absolute deviations / Total number of numbers
= 54 / 8
= 6.8
Therefore, the mean absolute deviation of the dataset is 6.8 (rounded to the nearest tenth).
Mean Absolute Deviation Practice
Complete this assessment to review what you've learned. It will not count toward your grade.
3 of 53 of 5 Items
Question
Use the table to answer the question.
Data Point Absolute Deviation
5 17.3
10 12.3
45
12 10.3
27
35 12.7
The table lists Jude’s data for how many people walk into a store each half hour. The mean is 22.3. Identify the absolute deviation for each missing value. Round each value to the nearest tenth.
(1 point)
Data Point Absolute Deviation
5 17.3
10 12.3
45
12 10.3
27
35 12.7
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Use the table to answer the question.
Data Point Absolute Deviation
5 17.3
10 12.3
45
12 10.3
27
35 12.7
The table lists Jude’s data for how many people walk into a store each half hour. The mean is 22.3. Identify the absolute deviation for each missing value. Round each value to the nearest tenth.
(1 point)
Data Point Absolute Deviation
5 17.3
10 12.3
45
12 10.3
27
35 12.7
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To find the missing absolute deviation values, we need to use the formula for absolute deviation:
Absolute deviation = |data point - mean|
We are given the mean as 22.3.
For the missing value 45:
Absolute deviation = |45 - 22.3| = 22.7
For the missing value 27:
Absolute deviation = |27 - 22.3| = 4.7
Therefore, the missing absolute deviation values are:
Data Point Absolute Deviation
5 17.3
10 12.3
45 22.7
12 10.3
27 4.7
35 12.7
Leon counts the number of bugs he finds on his tomato plants each day and collects the following data: 18, 24, 15, 9, 10. The mean is 15.2. What is the final equation that he would use in determining the mean absolute deviation? Round each value to the nearest tenth.(2 points)
÷
=
To find the mean absolute deviation, the equation used is:
Mean Absolute Deviation = (Sum of absolute deviations / Total number of data points)
The absolute deviation for each data point is calculated by subtracting the mean from each data point and taking the absolute value.
For the given data points: 18, 24, 15, 9, 10
The mean is 15.2.
Now, we calculate the absolute deviation for each data point:
Absolute deviation for 18 = |18 - 15.2| = 2.8
Absolute deviation for 24 = |24 - 15.2| = 8.8
Absolute deviation for 15 = |15 - 15.2| = 0.2
Absolute deviation for 9 = |9 - 15.2| = 6.2
Absolute deviation for 10 = |10 - 15.2| = 5.2
Next, we add up all the absolute deviations:
Sum of absolute deviations = 2.8 + 8.8 + 0.2 + 6.2 + 5.2 = 23.2
Lastly, we divide the sum of absolute deviations by the total number of data points:
Mean Absolute Deviation = 23.2 / 5 = 4.6
Therefore, the final equation that Leon would use in determining the mean absolute deviation is:
Mean Absolute Deviation = 23.2 ÷ 5 = 4.6 (rounded to the nearest tenth).
What is the sum of the absolute deviations in the following dataset: 63, 25, 74, 52, 63, 12, 46? The mean of the dataset is 47.9. Round to the nearest tenth.(1 point)
To find the sum of the absolute deviations, we first need to calculate the absolute deviation for each data point. The absolute deviation is found by subtracting the mean from each data point and taking the absolute value.
Given dataset: 63, 25, 74, 52, 63, 12, 46
Mean of the dataset: 47.9
Absolute deviation for 63 = |63 - 47.9| = 15.1
Absolute deviation for 25 = |25 - 47.9| = 22.9
Absolute deviation for 74 = |74 - 47.9| = 26.1
Absolute deviation for 52 = |52 - 47.9| = 4.1
Absolute deviation for 63 = |63 - 47.9| = 15.1
Absolute deviation for 12 = |12 - 47.9| = 35.9
Absolute deviation for 46 = |46 - 47.9| = 1.9
Now, we sum up all the absolute deviations:
Sum of absolute deviations = 15.1 + 22.9 + 26.1 + 4.1 + 15.1 + 35.9 + 1.9 = 121.1
Therefore, the sum of the absolute deviations in the dataset is 121.1 (rounded to the nearest tenth).
Find the mean absolute deviation of the following dataset: 8.4, 9.4, 14.2, 5.6, 8.3, 9.0, 10.2. Round the answer to the nearest tenth.(1 point)
Responses
9.3
9.3
7.0
7.0
11.8
11.8
1.7
To find the mean absolute deviation, we first need to find the mean of the dataset.
Given dataset: 8.4, 9.4, 14.2, 5.6, 8.3, 9.0, 10.2
Sum of all the numbers = 8.4 + 9.4 + 14.2 + 5.6 + 8.3 + 9.0 + 10.2 = 65.1
Mean = Sum of all the numbers / Total number of numbers
= 65.1 / 7
≈ 9.3
Next, we find the absolute deviation for each number by subtracting the mean from each number:
Absolute deviation for 8.4 = |8.4 - 9.3| = 0.9
Absolute deviation for 9.4 = |9.4 - 9.3| = 0.1
Absolute deviation for 14.2 = |14.2 - 9.3| = 4.9
Absolute deviation for 5.6 = |5.6 - 9.3| = 3.7
Absolute deviation for 8.3 = |8.3 - 9.3| = 1.0
Absolute deviation for 9.0 = |9.0 - 9.3| = 0.3
Absolute deviation for 10.2 = |10.2 - 9.3| = 0.9
Now, we find the sum of the absolute deviations:
Sum of absolute deviations = 0.9 + 0.1 + 4.9 + 3.7 + 1.0 + 0.3 + 0.9 = 11.8
Lastly, we find the mean of the absolute deviations:
Mean absolute deviation = Sum of absolute deviations / Total number of numbers
= 11.8 / 7
≈ 1.7
Therefore, the mean absolute deviation of the dataset is 1.7 (rounded to the nearest tenth).