Leon counts the number of bugs he finds on his tomato plant 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 the determining the mean absolute deviation? Round each value to the nearest tenth.
To determine the mean absolute deviation, Leon will use the following formula:
Mean Absolute Deviation = Σ |x - μ| / n
Where:
Σ = Summation
x = Each individual data point
μ = Mean
n = Total number of data points
First, calculate the absolute deviations for each data point:
|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
Next, sum up the absolute deviations:
2.8 + 8.8 + 0.2 + 6.2 + 5.2 = 23.2
Then, divide the sum by the total number of data points (5 in this case):
Mean Absolute Deviation = 23.2 / 5
Mean Absolute Deviation = 4.64
Therefore, the final equation that Leon would use in determining the mean absolute deviation for the data set {18,24,15,9,10} is:
Mean Absolute Deviation = 4.64