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 mean is the sum of the observations divided by their number. The value of \(x\) is found from the mean of all five, and then the first three are averaged.
Finding \(x\) (from the mean of all five):
Sum \(=(x+1)+(x+2)+(x+3)+(x+4)+(x+5)=5x+15\)
Mean \(\displaystyle =\frac{5x+15}{5}=x+3\)
\(x+3=15\), so \(x=12\)
The first three observations (with \(x=12\)):
They are 13, 14 and 15
Their mean \(\displaystyle =\frac{13+14+15}{3}=\frac{42}{3}=14\)
Tip: Numbers that go up by the same step have their mean at the middle term: the mean of all five is \(x+3\), and the mean of the first three is their middle term, \(x+2=14\).