Maths problem: how to do (a), (b) thanks?

(a)
First of all, we calculate the mean as
μ
= [(k + 4) + (k - 3) + (k + 1) + (k - 7) + k] ÷ 5
= k - 1.

The variance is then
σ²
= [(k + 4 - μ)² + (k - 3 - μ)² + (k + 1 - μ)² + (k - 7 - μ)² + (k - μ)²] ÷ 5
= [(5)² + (-2)² + (2)² + (-6)² + (1)²] ÷ 5
= (25 + 4 + 4 + 36 + 1) ÷ 5
= 70 ÷ 5
= 14.

The s.d. is σ = √14.

(b)
Standard deviation is a measure of dispersion.
For each datum added to the same number, the dispersion among the data remains the same, so the new s.d. is still σ = √14.

(c)
For each datum multiply to the same number, the dispersion among the data is also scaled by the same number, so the new s.d. is 3σ = 3√14.