MATH SOLVE

2 months ago

Q:
# Which answer is the approximate standard deviation of the data set?

Accepted Solution

A:

Answer:3.4Step-by-step explanation:Standard deviation of a population is defined as:σ² = ∑(xᵢ − μ)² / nThe standard deviation of a sample is defined as:s² = ∑(xᵢ − x)² / (n - 1)It's not clear which one we have, so let's calculate both.First, we must find the mean.μ = (5+12+15+10+12+6+8+8) / 8μ = 9.5Now we find the squares of the differences:(5-9.5)² + (12-9.5)² + (15-9.5)² + (10-9.5)² + (12-9.5)² + (6-9.5)² + (8-9.5)² + (8-9.5)²= 80Divide by n:σ² = 80 / 8σ² = 10And take the square root:σ = √10σ ≈ 3.2That's not one of the answers, so let's try the standard deviation of a sample instead of a population.Instead of dividing by n, we'll divide by n-1:s² = 80 / 7And take the square root:s = √(80/7)s ≈ 3.4So that must be it.