The first m-year moving average of the data 10, 20, 30, 40, 50 is 30. The value of \(m\) is
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 5
The first m-year moving average is the mean of the first m values, here 10, 20, …, 10m:
\( \displaystyle \frac{10(1 + 2 + \dots + m)}{m} = 30 \)
\( \displaystyle \frac{10}{m} \cdot \frac{m(m+1)}{2} = 30 \)
\( 5(m + 1) = 30 \)
\( m = 5 \)
Check: \(\frac{10 + 20 + 30 + 40 + 50}{5} = \frac{150}{5} = 30\).