Find the mean deviation of 20, 30, 25, 40, 35, 50, 45, 40, 20 and 45

Step 1: Analyze the question We need the mean deviation, which is the average of the absolute differences between each value and the mean.

Step 2: Concept Mean deviation = Σ|x − x̄| / n

Step 3: Solution

Data: 20, 30, 25, 40, 35, 50, 45, 40, 20, 45 (n = 10)

Sum = 20 + 30 + 25 + 40 + 35 + 50 + 45 + 40 + 20 + 45 = 350

Mean x̄ = 350 / 10 = 35

Absolute deviations |x − 35|:

• 20 → 15
• 30 → 5
• 25 → 10
• 40 → 5
• 35 → 0
• 50 → 15
• 45 → 10
• 40 → 5
• 20 → 15
• 45 → 10

Sum of deviations = 15 + 5 + 10 + 5 + 0 + 15 + 10 + 5 + 15 + 10 = 90

Mean deviation = 90 / 10 = 9

Step 4: Answer The mean deviation is 9, which is option B.

Tip: Always find the mean first, then take absolute values (ignore negative signs) of the differences. Quick check: the signed deviations must sum to zero. Here the values below 35 contribute -45 (15+5+10+15) and those above contribute +45 (5+15+10+5+10), so the check works.