The mean of a set of numbers is $\overline{\mathrm{X}}$. If each number is divided by 3, then the new mean is

Let ${\mathrm{x}}_1,{\mathrm{x}}_2,\dots ,{\mathrm{x}}_{\mathrm{n}}$ n be n numbers. Then $\overline{\mathrm{X}}=\frac{1}{\mathrm{n}}\sum _{\mathrm{i}=1}^{\mathrm{n}} {\mathrm{x}}_{\mathrm{i}}$

If each number is divided by 3, then the new mean, $\overline{\mathrm{Y}}$ is given by

$\overline{\mathrm{Y}}=\frac{1}{\mathrm{n}}\sum _{\mathrm{i}=1}^{\mathrm{n}} \left(\frac{{\mathrm{x}}_{\mathrm{i}}}{3}\right)=\frac{1}{3}\left(\frac{1}{\mathrm{n}}\sum _{\mathrm{i}=1}^{\mathrm{n}} {\mathrm{x}}_{\mathrm{i}}\right)=\frac{\overline{\mathrm{X}}}{3}$