Find the mean deviation of 20, 25, 21, 27, 28, 29, to the nearest whole number

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

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

Step 1: Find the mean Sum = 20 + 25 + 21 + 27 + 28 + 29 = 150 n = 6 Mean = 150 / 6 = 25

Step 2: Find the absolute deviations

• |20 − 25| = 5
• |25 − 25| = 0
• |21 − 25| = 4
• |27 − 25| = 2
• |28 − 25| = 3
• |29 − 25| = 4

Step 3: Add and divide Σ|x − x̄| = 5 + 0 + 4 + 2 + 3 + 4 = 18

Mean deviation = 18 / 6 = 3

Tip: Always find the mean first, then take absolute values (ignore negative signs) before averaging. If the deviations are not whole numbers, round only at the end. A quick check: the positive and negative deviations should cancel out. Here the deviations below the mean are −5 − 4 = −9, and those above are 2 + 3 + 4 = 9, so the mean of 25 is right.