If each of the observations $x_1, x_2, \ldots, x_n$ is increased or decreased by $k$, where $k$ is a…

If each of the observations $x_1, x_2, \ldots, x_n$ is increased or decreased by $k$, where $k$ is a positive number, then the variance of the da
  1. increases by $\mathrm{k}$
  2. do not change
  3. is equal to $\mathrm{k}^2$
  4. is equal to $2 \mathrm{k}$

Solution

If each of the observations $x_1, x_2, \ldots x_n$ is increased or decreased by $k$ then mean and variance of the obtained data remains unchanged.

Asked in: AP EAMCET 2023 (17 May Shift 1)

Practice more Statistics questions on Aicharya