Question

Find the mean: $y-2a$, $y-a$, $y+a$, $y+2a$.

Answer 1

Calculate the mean of the given expressions

Given expressions: $y-2a$, $y-a$, $y+a$, $y+2a$.

Thus, the number of expressions, $n=4$.

The sum of four expressions,

$\sum x=\left(y-2a\right)+\left(y-a\right)+\left(y+a\right)+\left(y+2a\right)$

$$\begin{gathered} \Rightarrow \sum x=4y+\left(-2a-a+a+2a\right) \\ \Rightarrow \sum x=4y \end{gathered}$$

The mean of the given data can be found by, $\overline{x}=\frac{\sum x}{n}$.

Thus, the mean of the given expressions, $\overline{x}=\frac{\sum x}{n}=\frac{4y}{4}=y$.

Therefore, the mean of the given expressions is $y$.