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.
Responses
11.8
7.0
9.3
1.7
To find the mean absolute deviation (MAD) of a dataset, follow these steps:
1. Find the mean (average) of the dataset.
- Add up all the numbers in the dataset: 8.4 + 9.4 + 14.2 + 5.6 + 8.3 + 9.0 + 10.2 = 65.1
- Divide the sum by the number of elements in the dataset: 65.1 / 7 = 9.3
2. Calculate the absolute deviation of each number from the mean.
- Subtract the mean from each number in the dataset, and take the absolute value.
- |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. Find the mean of the absolute deviations.
- Add up all the absolute deviations: 0.9 + 0.1 + 4.9 + 3.7 + 1.0 + 0.3 + 0.9 = 11.8
- Divide the sum by the number of elements in the dataset: 11.8 / 7 = 1.7
Therefore, the mean absolute deviation of the given dataset is 1.7 (rounded to the nearest tenth). Select response 1.7.
To find the mean absolute deviation (MAD) of a dataset, you need to 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. In this case, the dataset is: 8.4, 9.4, 14.2, 5.6, 8.3, 9.0, and 10.2.
Mean = (8.4 + 9.4 + 14.2 + 5.6 + 8.3 + 9.0 + 10.2) / 7
Mean = 64.1 / 7
Mean = 9.1571 (rounded to 4 decimal places)
Step 2: Calculate the absolute deviation for each value.
To find the absolute deviation for each value, subtract the mean from each value and take the absolute value of the result. In this case, subtract 9.1571 from each of the values:
|8.4 - 9.1571| = 0.7571
|9.4 - 9.1571| = 0.2429
|14.2 - 9.1571| = 5.0429
|5.6 - 9.1571| = 3.5571
|8.3 - 9.1571| = 0.8571
|9.0 - 9.1571| = 0.1571
|10.2 - 9.1571| = 1.0429
Step 3: Calculate the mean of the absolute deviations.
To find the mean of the absolute deviations, add up all the absolute deviations and divide the sum by the total number of values:
(0.7571 + 0.2429 + 5.0429 + 3.5571 + 0.8571 + 0.1571 + 1.0429) / 7
= 11.7 / 7
= 9.3 (rounded to the nearest tenth)
Therefore, the mean absolute deviation of the given dataset is 9.3.