Given the data set $\{10,12,14,16,18\}$, what is the mean absolute deviation?

• A. $2$
• B. $4$
• C. $1.5$
• D. $3$

Answer: (A)

Verified step by step guidance

1. First, calculate the mean (average) of the data set {10, 12, 14, 16, 18}. Use the formula for the mean: \(\text{Mean} = \frac{\sum x_i}{n}\), where \(x_i\) are the data points and \(n\) is the number of data points.
2. Next, find the absolute deviations of each data point from the mean. This means subtract the mean from each data point and take the absolute value: \(|x_i - \text{Mean}|\) for each \(x_i\).
3. Then, sum all the absolute deviations you calculated in the previous step: \(\sum |x_i - \text{Mean}|\).
4. Finally, calculate the mean absolute deviation (MAD) by dividing the sum of absolute deviations by the number of data points: \(\text{MAD} = \frac{\sum |x_i - \text{Mean}|}{n}\).
5. Interpret the result as the average distance of the data points from the mean, which gives a measure of variability in the data set.