Question

Let x₁, x₂, x₃, x₄, x₅ be the observations with mean m and standard deviations. The standard deviation of the observation kx₁, kx₂, kx₃, kx₄, kx₅, is
(a) k + s

(b) $\frac{s}{k}$

c) $\left|k\right|s$

(d) s

Answer 1

Given, x₁, x₂, x₃, x₄, x₅ be the observations with mean m and standard deviations s.
Then variance of x₁, x₂, x₃, x₄ and x₅ is s².
∴ Variance of kx₁, kx₂, kx₃, kx_4, and kx₅ has variance k²s².
∴ Standard deviation of kx₁, kx₂, kx₃, kx_4, and kx₅ is$\sqrt{k^2{s}^2}$
i.e |k|s
Hence, the correct answer is option C.