Observe the following table:
| Year | 2010 | 2011 | 2012 | 2013 | 2014 | 2015 |
| Annual Sale | 40 | 50 | 60 | 70 | 80 | 90 |
If the three-year moving averages of the above observations are A, B, C, D respectively, then the largest value of the three-year moving averages is :
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → D
A three-year moving average is the mean of three consecutive years, placed against the middle year. Six years give four such averages:
\( \displaystyle A=\frac{40+50+60}{3}=50\ \ (2011) \)
\( \displaystyle B=\frac{50+60+70}{3}=60\ \ (2012) \)
\( \displaystyle C=\frac{60+70+80}{3}=70\ \ (2013) \)
\( \displaystyle D=\frac{70+80+90}{3}=80\ \ (2014) \)
The largest is D = 80.
Shortcut: The sales increase every year, so each moving average is larger than the one before; the last one, D, is the largest without any calculation.