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?
Answer & explanation
Correct answer: option 2
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
$\frac{13 + 14 + 15}{3} = \frac{42}{3} = 14$