If the mean of five observations x, x + 2, x + 4, x + 6 and x + 8 is 11, then the mean of first three observations is :

1. 9

2. 11

3. 13

4. none of these

By formula,

$\Rightarrow \text{Mean} = \dfrac{\sum x_i}{n} \\[1em] \Rightarrow 11 = \dfrac{x + (x + 2) + (x + 4) + (x + 6) + (x + 8)}{5} \\[1em] \Rightarrow 11 \times 5 = 5x + 20 \\[1em] \Rightarrow 55 = 5x + 20 \\[1em] \Rightarrow 55 - 20 = 5x \\[1em] \Rightarrow 5x = 35 \\[1em] \Rightarrow x = \dfrac{35}{5} \\[1em] \Rightarrow x = 7.$

Mean of first three observations, x = 7, x + 2 = 7 + 2 = 9, x + 4 = 7 + 4 = 11

$\text{Mean} = \dfrac{\sum x_i}{n} \\[1em] = \dfrac{7 + 9 + 11}{3} \\[1em] = \dfrac{27}{3} \\[1em] =9.$

Hence, option 1 is the correct option.