Question

Mean Absolute Deviation Practice 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.

Answer 1

To calculate the mean absolute deviation, Leon would use the following equation:

Mean Absolute Deviation = Σ|X - Mean| / n

Where:
- Σ represents the sum of
- X represents each individual data point
- Mean represents the mean of the data set
- n represents the total number of data points

Plugging in the values from Leon's data set and the mean:

Mean = 15.2
n = 5
Data set: 18, 24, 15, 9, 10

Calculating 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

Adding these absolute deviations together:
2.8 + 8.8 + 0.2 + 6.2 + 5.2 = 23.2

Calculating the mean absolute deviation:
Mean Absolute Deviation = 23.2 / 5 = 4.6

Therefore, the final equation that Leon would use in determining the mean absolute deviation is:

Mean Absolute Deviation = 4.6