Find the standard deviation of 5, 4, 3, 2, 1

Analyze the question: We need the standard deviation of the data set 5, 4, 3, 2, 1.

Concept: For JAMB, standard deviation is usually the population form:

SD = √[Σ(x − x̄)² / n]

Solution:

1. Mean: x̄ = (5 + 4 + 3 + 2 + 1) / 5 = 15/5 = 3

2. Deviations from the mean (x − x̄): 2, 1, 0, −1, −2

3. Squared deviations: 4, 1, 0, 1, 4. Sum = 10

4. Variance = 10 / 5 = 2

5. Standard deviation = √2

(If you divided by n − 1 for a sample, you would get √(10/4) = √2.5, which is not among the options. This confirms JAMB wants the population formula, dividing by n.)

Answer: The standard deviation is √2, which is option A.

Tip: For any 5 consecutive integers, the deviations are always 2, 1, 0, −1, −2, so the SD is √2. Remember: variance = (sum of squared deviations) ÷ n, then take the square root.