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
11.8
11.8
1.7
1.7
7.0
7.0
9.3
To find the mean absolute deviation, you need to find the average of the absolute differences between each data point and the mean of the dataset.
First, find the mean (average) of the dataset:
Mean = (8.4 + 9.4 + 14.2 + 5.6 + 8.3 + 9.0 + 10.2)/7 = 65.1/7 ≈ 9.3.
Next, find the absolute difference between each data point and the mean:
|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
Find the average of these absolute differences:
(0.9 + 0.1 + 4.9 + 3.7 + 1.0 + 0.3 + 0.9)/7 ≈ 2.143.
Rounded to the nearest tenth, the mean absolute deviation is 2.1.
Therefore, the correct response is:
2.1
To find the mean absolute deviation (MAD) of a dataset, follow these steps:
Step 1: Calculate the mean (average) of the dataset.
To find the mean, add up all the numbers in the dataset and divide the sum by the total number of values.
Mean = (8.4 + 9.4 + 14.2 + 5.6 + 8.3 + 9.0 + 10.2) / 7 = 65.1 / 7 = 9.3
Step 2: Find the absolute deviation for each number.
Absolute deviation is the absolute value of the difference between the mean and each individual value in the dataset.
Absolute Deviations:
|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
Step 3: Calculate the mean of the absolute deviations.
Add up all the absolute deviations and divide the sum by the total number of values.
MAD = (0.9 + 0.1 + 4.9 + 3.7 + 1.0 + 0.3 + 0.9) / 7 = 11.8 / 7 = 1.7
Therefore, the mean absolute deviation of the given dataset is approximately 1.7 (rounded to the nearest tenth).