Leon counts the number of bugs he finds on his tomato plants each day and collects the following data: 18, 24, 15, 9, 10. The mean is 15.2. What is the final equation that he would use in determining the mean absolute deviation? Round each value to the nearest tenth.(2 points)
The equation to determine the mean absolute deviation (MAD) is:
MAD = (|data point 1 - mean| + |data point 2 - mean| + |data point 3 - mean| + ... + |data point n - mean|) / n
Using the given data points and mean, the equation would be:
MAD = (|18 - 15.2| + |24 - 15.2| + |15 - 15.2| + |9 - 15.2| + |10 - 15.2|) / 5
To determine the mean absolute deviation (MAD), you need to find the absolute difference between each data point and the mean, and then calculate the average of those differences.
Step 1: Find the absolute differences for each data point:
- Data points: 18, 24, 15, 9, 10
- Mean: 15.2
Absolute differences:
|18 - 15.2| = 2.8
|24 - 15.2| = 8.8
|15 - 15.2| = 0.2
|9 - 15.2| = 6.2
|10 - 15.2| = 5.2
Step 2: Calculate the average of the absolute differences:
(2.8 + 8.8 + 0.2 + 6.2 + 5.2) / 5 = 23.2 / 5 ≈ 4.6
Therefore, the final equation that Leon would use in determining the mean absolute deviation is:
MAD = 4.6