The mean of the following scores 30, 32, 34, 36, 38, 40 and 42 What is the mean deviation?

Analyze the question: We need the mean deviation of the scores 30, 32, 34, 36, 38, 40, 42.

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

Step 1: Find the mean Sum = 30 + 32 + 34 + 36 + 38 + 40 + 42 = 252 n = 7 Mean = 252 ÷ 7 = 36

Step 2: Find the absolute deviations from 36

• |30 − 36| = 6
• |32 − 36| = 4
• |34 − 36| = 2
• |36 − 36| = 0
• |38 − 36| = 2
• |40 − 36| = 4
• |42 − 36| = 6

Sum of deviations = 6 + 4 + 2 + 0 + 2 + 4 + 6 = 24

Step 3: Mean deviation Mean deviation = 24 ÷ 7 = 3.428... ≈ 3.43

Checking against the options: The options are 4.21, 3.24, 3.42, and 4.54. Our value of 3.428... is closest to 3.42 (option C), which is what you get by truncating instead of rounding.

Tip: When the data are evenly spaced (an arithmetic progression) and symmetrical around the mean, the deviations come in matching pairs, so you can double the sum of one side. Here: 2(6 + 4 + 2) = 24. Also, the mean is just the middle value (36), so you can skip the addition. If your answer is a recurring decimal such as 3.428..., choose the nearest option.