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.
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 values in the dataset and divide the sum by the number of values.
8.4 + 9.4 + 14.2 + 5.6 + 8.3 + 9.0 + 10.2 = 65.1
65.1 / 7 = 9.3 (rounded to one decimal place)
Step 2: Find the absolute deviation for each value.
For each value in the dataset, subtract the mean from that value and take the absolute value of the result. If there are negative values, make sure to use the positive value for the calculation.
|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 deviation values and divide by the number of values.
0.9 + 0.1 + 4.9 + 3.7 + 1.0 + 0.3 + 0.9 = 11.8
11.8 / 7 = 1.6857... (approximated to four decimal places)
Step 4: Round the mean absolute deviation to the nearest tenth.
The mean absolute deviation is approximately 1.7 (rounded to the nearest tenth).
Therefore, the mean absolute deviation of the given dataset is 1.7.