Calculate the mean deviation of 5, 3, 0, 7, 2, 1

Analyze the question: Mean deviation is the average of the absolute differences between each value and the mean.

Concept: Mean deviation = Σ|x − x̄| / n

Solution:

Step 1: Find the mean. Sum = 5 + 3 + 0 + 7 + 2 + 1 = 18 n = 6 Mean x̄ = 18 / 6 = 3

Step 2: Find the absolute deviations |x − 3|.

• |5 − 3| = 2
• |3 − 3| = 0
• |0 − 3| = 3
• |7 − 3| = 4
• |2 − 3| = 1
• |1 − 3| = 2

Step 3: Add them up. 2 + 0 + 3 + 4 + 1 + 2 = 12

Step 4: Divide by n. Mean deviation = 12 / 6 = 2.0

Answer: The mean deviation is 2.

Tip: Do not confuse mean deviation with the plain sum of deviations (Σ(x − x̄)), which is always 0 (that is why option A is a trap). Always take the absolute values before averaging. Also, a quick check: the signed deviations (+2, 0, −3, +4, −1, −2) add up to 0, which confirms your mean is right.