Given Evelyn's scores: $5.1$, $5.6$, $5.8$, and $7$, what is the mean absolute deviation of her scores?

• A. $0.675$
• B. $0.65$
• C. $0.725$
• D. $0.8$

Answer: (A)

Verified step by step guidance

1. First, calculate the mean (average) of Evelyn's scores. To do this, sum all the scores and then divide by the number of scores. The formula is: \[ \text{Mean} = \frac{5.1 + 5.6 + 5.8 + 7}{4} \]
2. Next, find the absolute deviation of each score from the mean. This means subtracting the mean from each score and taking the absolute value (ignoring negative signs). For each score \(x_i\), calculate: \[ |x_i - \text{Mean}| \]
3. After finding all the absolute deviations, sum these values together. This gives the total absolute deviation.
4. Finally, calculate the mean absolute deviation (MAD) by dividing the total absolute deviation by the number of scores. The formula is: \[ \text{MAD} = \frac{\sum |x_i - \text{Mean}|}{n} \] where \(n\) is the number of scores.
5. Interpret the result as the average distance of Evelyn's scores from the mean, which gives a measure of variability in her scores.