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
To find the mean absolute deviation, we first need to find the mean of the dataset. Calculating the mean:
(8.4 + 9.4 + 14.2 + 5.6 + 8.3 + 9.0 + 10.2) / 7 = 9.22857142857
Next, we subtract the mean from each data point, take the absolute value, and calculate the mean of those absolute values:
|8.4 - 9.22857142857| = 0.82857142857
|9.4 - 9.22857142857| = 0.17142857143
|14.2 - 9.22857142857| = 4.97142857143
|5.6 - 9.22857142857| = 3.62857142857
|8.3 - 9.22857142857| = 0.92857142857
|9.0 - 9.22857142857| = 0.22857142857
|10.2 - 9.22857142857| = 0.97142857143
(0.82857142857 + 0.17142857143 + 4.97142857143 + 3.62857142857 + 0.92857142857 + 0.22857142857 + 0.97142857143) / 7 = 1.8387755102
Rounded to the nearest tenth, the mean absolute deviation of the dataset is 1.8. Answer: \boxed{1.8}.
To find the mean absolute deviation of a dataset, follow these steps:
1. Find the mean (average) of the dataset by adding up all the numbers and dividing by the total count.
8.4 + 9.4 + 14.2 + 5.6 + 8.3 + 9.0 + 10.2 = 65.1
65.1 / 7 = 9.3
2. Subtract the mean from each value in the dataset to find the deviation for each number.
8.4 - 9.3 = -0.9
9.4 - 9.3 = 0.1
14.2 - 9.3 = 4.9
5.6 - 9.3 = -3.7
8.3 - 9.3 = -1.0
9.0 - 9.3 = -0.3
10.2 - 9.3 = 0.9
3. Take the absolute value of each deviation to ensure that all values are positive.
|-0.9| = 0.9
|0.1| = 0.1
|4.9| = 4.9
|-3.7| = 3.7
|-1.0| = 1.0
|-0.3| = 0.3
|0.9| = 0.9
4. Find the average deviation by adding up all the absolute deviations and dividing by the total count.
0.9 + 0.1 + 4.9 + 3.7 + 1.0 + 0.3 + 0.9 = 11.8
11.8 / 7 = 1.6857 (rounded to 1.7)
Therefore, the mean absolute deviation of the given dataset is approximately 1.7.