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

Step 1: Understanding the Concept:
A moving average is a technique used to smooth out short-term fluctuations in data and highlight longer-term trends or cycles. A "three-year moving average" is calculated by taking the average of three consecutive data points.
Step 2: Key Formula or Approach:
For a data series \(y_1, y_2, y_3, y_4, \dots\), the three-period moving averages are calculated as: - First moving average = \(\frac{y_1 + y_2 + y_3}{3}\) - Second moving average = \(\frac{y_2 + y_3 + y_4}{3}\) - Third moving average = \(\frac{y_3 + y_4 + y_5}{3}\), and so on.
Step 3: Detailed Explanation:
The given data values are 15, 18, 21, 27, 39.
First three-year moving average: This will be the average of the first three values (15, 18, 21). \[ \text{Average}_1 = \frac{15 + 18 + 21}{3} = \frac{54}{3} = 18 \] Second three-year moving average: This will be the average of the next three values (18, 21, 27). \[ \text{Average}_2 = \frac{18 + 21 + 27}{3} = \frac{66}{3} = 22 \] Third three-year moving average: This will be the average of the last three values (21, 27, 39). \[ \text{Average}_3 = \frac{21 + 27 + 39}{3} = \frac{87}{3} = 29 \] Step 4: Final Answer:
The sequence of the three-year moving averages is 18, 22, 29.