Concept explainers
a.
To Find: To find the mean absolute deviation of the given data.
a.
Answer to Problem 9IP
The mean absolute deviation is 2
Explanation of Solution
Given information:Wood planks made by the carpenter.
Formula used: For Mean:
Calculation:
Calculation of Mean
Thus, mean is 5.5
Now, calculation of mean absolute deviation
4 | 1.5 | |
8 | 2.5 | |
7 | 1.5 | |
3 | 2.5 | |
Total | 0 | 8 |
Thus, mean absolute deviation is 2
Hence, the required mean absolute deviation is 2.
b.
To Find:To find the mean absolute deviation of the given data in feet.
b.
Answer to Problem 9IP
Mean absolute deviation is 6
Explanation of Solution
Given information:Wood planks made by the carpenter.
Formula used: For Mean:
Calculation:
Taking 1 yard equal to 3 feet the new data became
12, 24, 21, 9
Calculation of Mean
Thus, mean is 16.5
Now, calculation of mean absolute deviation
12 | 4.5 | |
24 | 7.5 | |
21 | 4.5 | |
9 | 7.5 | |
Total | 0 | 24 |
Thus, mean absolute deviation is 6
Hence, the required mean absolute deviation is 6
c.
To Compare:To compare the difference in mean absolute deviation of the given data in both conditions.
c.
Answer to Problem 9IP
The reason is multiple of 3.
Explanation of Solution
Given information:Mean absolute deviation in both cases.
In the first case when data is given in yards mean absolute deviation is 2 and mean is 5.5 while in the second case when data is given in feet mean absolute deviation is 6 and mean is 16.5.
Comparing this, it can be concluded that the values are affected by a multiple of 3 and this is happened because of one yard is equal to three feet. So, every observation in yard is changed to feet with a multiple of 3.
Hence, mean absolute deviation is changed by three times by converting the data yards into feet.
Chapter 10 Solutions
Glencoe Math Accelerated, Student Edition
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