Question

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.

Answer 1

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