If ∑i=1⁹(xi - 5) = 9 and ∑i=1⁹(xi - 5)² = 45, then the standard deviation of the 9 items x₁, x₂, ...., x₉ is

∑i=1⁹(xi - 5) = 9 ∴ ∑i=1⁹xi - 45 = 9 ∴ ∑i=1⁹xi = 54
Hence, mean of xi's = μ = ∑i=1⁹xi/9 = 6
Also, ∑i=1⁹(xi - 5)² = 45 ∴ ∑i=1⁹(x²i - 10xi + 25) = 45
∴ ∑i=1⁹x²i - 10∑i=1⁹xi + 225 = 45
∴ ∑i=1⁹x²i - 10 × 54 + 225 = 45
∴ ∑i=1⁹x²i - 540 + 225 = 45
∴ ∑i=1⁹x²i = 360
∴ ∑i=1⁹x²i/9 = 40
Now, Standard deviation of xi's = √(∑i=1⁹x²i/9 - μ²) = √(40 - 6²) = √(40 - 36) = √4 = 2
This is the required answer.