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.
The mean absolute deviation (MAD) is calculated by finding the absolute differences between each data point and the mean, summing the absolute differences, and dividing by the number of data points.
To calculate the MAD, Leon would do the following steps:
1. Find the absolute difference between each data point and the mean:
|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
2. Sum the absolute differences: 2.8 + 8.8 + 0.2 + 6.2 + 5.2 = 23.2
3. Divide the sum by the number of data points: 23.2 / 5 = 4.64
Therefore, the final equation that Leon would use in determining the mean absolute deviation is:
MAD = 4.64
Note that the MAD should also be rounded to the nearest tenth, which is why the MAD value is given as 4.6.
To determine the mean absolute deviation, Leon would use the following equation:
Mean Absolute Deviation (MAD) = Σ |x - μ| / n
where Σ represents the sum, x represents each individual value, μ represents the mean, and n represents the total number of values.
In this case, Leon's data is as follows: 18, 24, 15, 9, 10.
The mean (μ) is given as 15.2.
Plugging these values into the equation:
MAD = (|18 - 15.2| + |24 - 15.2| + |15 - 15.2| + |9 - 15.2| + |10 - 15.2|) / 5
Calculating the absolute differences:
MAD = (2.8 + 8.8 + 0.2 + 6.2 + 5.2) / 5
Simplifying:
MAD = 23.2 / 5
Calculating the mean absolute deviation:
MAD = 4.64
Therefore, the final equation that Leon would use in determining the mean absolute deviation is:
MAD = 4.64