Question

The mean deviation from the mean for the set of observations \(-1, 0, 4\) is

• A. less than 3
• B. less than 1
• C. greater than 2.5
• D. greater than 4.9

Hint:

Mean deviation measures the average absolute distance of each data point from the mean.

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
Mean deviation from the mean = \(\frac{1}{n} \sum |x_i - \bar{x}|\).

Step 2: Detailed Explanation:
Mean \(\bar{x} = \frac{-1 + 0 + 4}{3} = \frac{3}{3} = 1\). Deviations: \(|-1 - 1| = 2\), \(|0 - 1| = 1\), \(|4 - 1| = 3\). Sum of absolute deviations = \(2 + 1 + 3 = 6\). Mean deviation = \(\frac{6}{3} = 2\).

Step 3: Final Answer:
2 is less than 3, which corresponds to option (A).