Question

If ${\displaystyle \overline{x}}$ is the mean of x₁, x₂ ............x_n and ${\displaystyle \overline{y}}$ is the mean of y₁, y₂, …….y_n and ${\displaystyle \overline{z}}$ is the mean of x₁, x₂ ............x_n, y₁, y₂, ……….y_n then ${\displaystyle \overline{z}}$ =?

Options

• ${\displaystyle \frac{\overline{x}+\overline{y}}{2}}$

• ${\displaystyle \overline{x}+\overline{y}}$

• ${\displaystyle \frac{\overline{x}+\overline{y}}{n}}$

• ${\displaystyle \frac{\overline{x}+\overline{y}}{2n}}$

Answer 1

${\displaystyle \frac{\overline{x}+\overline{y}}{2}}$

Explanation:

Z = ${\displaystyle \frac{nx+ny}{2n}}$

= ${\displaystyle \frac{n(\overline{x}+\overline{y})}{2n}}$

= ${\displaystyle \frac{\overline{x}+\overline{y}}{2}}$