What is the mean absolute deviation of 49, 55, 52, 46, 47, 42, and 38?
56
To find the mean absolute deviation, you need to follow these steps:
1. Find the mean (average) of the given set of numbers.
Add all the numbers together: 49 + 55 + 52 + 46 + 47 + 42 + 38 = 329
Divide the sum by the total number of values (7 in this case): 329 ÷ 7 = 47
So, the mean is 47.
2. Find the absolute deviation for each number.
Subtract the mean from each number and take the absolute value (ignoring the negative sign if any).
For 49: |49 - 47| = 2
For 55: |55 - 47| = 8
For 52: |52 - 47| = 5
For 46: |46 - 47| = 1
For 47: |47 - 47| = 0
For 42: |42 - 47| = 5
For 38: |38 - 47| = 9
3. Find the mean of these absolute deviations.
Add all the absolute deviations together: 2 + 8 + 5 + 1 + 0 + 5 + 9 = 30
Divide the sum by the total number of values (7 in this case): 30 ÷ 7 ≈ 4.286
Therefore, the mean absolute deviation of the given set of numbers is approximately 4.286