Question

For the given 5 values, 15, 18, 21, 27, 39; the three year moving averages are:

• A. 18, 21, 29
• B. 18, 22, 29
• C. 18, 23, 37
• D. 18, 20, 28

Hint:

When calculating moving averages, the "window" of data slides one period at a time. For a 3-period moving average, you average periods 1-3, then 2-4, then 3-5, and so on. Note that you lose some data points at the beginning and end of the series (in this case, for 5 data points, you only get 3 moving averages).

Answer 1

The Correct Option is B

Concept: A moving average smooths short-term fluctuations to reveal long-term trends. A three-year moving average averages three consecutive data points.
Formula: For a data series \(y_1, y_2, y_3, y_4, \dots\), three-period moving averages are: \( \frac{y_1 + y_2 + y_3}{3} \), \( \frac{y_2 + y_3 + y_4}{3} \), \( \frac{y_3 + y_4 + y_5}{3} \), etc.
Calculation: Given data: 15, 18, 21, 27, 39.
First average: Average of (15, 18, 21).
\[ \text{Average}_1 = \frac{15 + 18 + 21}{3} = 18 \]Second average: Average of (18, 21, 27).
\[ \text{Average}_2 = \frac{18 + 21 + 27}{3} = 22 \]Third average: Average of (21, 27, 39).
\[ \text{Average}_3 = \frac{21 + 27 + 39}{3} = 29 \]Result: The sequence of three-year moving averages is 18, 22, 29.