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:
Step 1: Find the mean (average) of the dataset. Add up all the values and divide by the 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 value in the dataset. To do this, subtract the mean from each value and take the absolute value.
Absolute deviation = |8.4 - 9.3| = 0.9
Absolute deviation = |9.4 - 9.3| = 0.1
Absolute deviation = |14.2 - 9.3| = 4.9
Absolute deviation = |5.6 - 9.3| = 3.7
Absolute deviation = |8.3 - 9.3| = 1.0
Absolute deviation = |9.0 - 9.3| = 0.3
Absolute deviation = |10.2 - 9.3| = 0.9
Step 3: Find the mean of the absolute deviations. Add up all the absolute deviations and divide by the number of values.
Mean of absolute deviations = (0.9 + 0.1 + 4.9 + 3.7 + 1.0 + 0.3 + 0.9) / 7 = 11.8 / 7 = 1.6857 (rounded to 4 decimal places)
Therefore, the mean absolute deviation is approximately 1.7 (rounded to the nearest tenth). So the correct response is: 1.7.
To find the mean absolute deviation (MAD) of a dataset, you need to follow these steps:
Step 1: Add up all the numbers in the dataset.
8.4 + 9.4 + 14.2 + 5.6 + 8.3 + 9.0 + 10.2 = 65.1
Step 2: Find the mean (average) of the dataset by dividing the sum of the numbers by the total count of numbers.
65.1 / 7 = 9.3
Step 3: Calculate the absolute deviation for each number by subtracting the mean from each number and taking the absolute value. The absolute value ensures that the deviations are all positive.
|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
|9.0 - 9.3| = 0.3
|10.2 - 9.3| = 0.9
Step 4: Find the mean of these absolute deviations.
(0.9 + 0.1 + 4.9 + 3.7 + 1 + 0.3 + 0.9) / 7 = 11.8 / 7 = 1.6857...
Step 5: Round the mean absolute deviation to the nearest tenth.
Rounded to the nearest tenth, the mean absolute deviation is 1.7.
Therefore, the correct answer is 1.7.