If the mean of five observations $x+1,x+2,x+3, x+4$ and $x + 5$ is 15, then what is the mean of the first three observations?

14

The correct answer is Option (2) → 14

The five observations are:
$x+1, x+2, x+3, x+4, x+5$

Step 1: Use the given mean

Mean = 15

$\frac{(x+1)+(x+2)+(x+3)+(x+4)+(x+5)}{5} = 15$

$\frac{5x + 15}{5} = 15$

$x + 3 = 15 \Rightarrow x = 12$

Step 2: Find the first three observations

$x+1 = 13,\quad x+2 = 14,\quad x+3 = 15$

Step 3: Mean of the first three observations

$\frac{13 + 14 + 15}{3} = \frac{42}{3} = 14$