Number of observations $n = 10$. Initial mean $\overline{x} = 15$. Each observation is increased by a constant $k = 3$.

If every value in a data set is increased/decreased by a constant $k$, the mean of the data set also increases/decreases by exactly that same constant $k$.

Many students try to calculate the sum of all 10 observations first ($10 imes 15 = 150$), add $3$ to each of the 10 observations ($150 + 30 = 180$), and then divide by 10, which is time-consuming and prone to calculation errors.

This property also holds for multiplication: if each observation is multiplied by a factor $k$, the new mean is $\overline{x}_{new} = \overline{x}_{old} imes k$. This is frequently tested in Variance and Standard Deviation questions as well.