Question

For the given five values 12, 15, 18, 24, 36; the three-year moving averages are:

• A. 15, 25, 21
• B. 15, 27, 19
• C. 15, 19, 26
• D. 15, 19, 30

Hint:

Moving averages are widely used in time series analysis to smooth out short-term fluctuations and highlight longer-term trends or cycles. In this case, the three-year moving average takes the average of three consecutive data points. It’s useful in predicting future values based on past trends. Always ensure that you're correctly calculating the average by considering the correct number of data points in each set for moving averages.

Answer 1

The Correct Option is C

The three-year moving average is calculated by taking the average of three consecutive numbers. 

First moving average:

\( \text{Average} = \frac{12 + 15 + 18}{3} = \frac{45}{3} = 15. \)

Second moving average:

\( \text{Average} = \frac{15 + 18 + 24}{3} = \frac{57}{3} = 19. \)

Third moving average:

\( \text{Average} = \frac{18 + 24 + 36}{3} = \frac{78}{3} = 26. \)

Thus, the three-year moving averages are 15, 19, 26.

Answer 2

The three-year moving average is calculated by taking the average of three consecutive numbers.

Step 1: First moving average:

To calculate the first moving average, we take the average of the first three numbers, which are 12, 15, and 18: \[ \text{Average} = \frac{12 + 15 + 18}{3} = \frac{45}{3} = 15. \] Therefore, the first moving average is 15.

Step 2: Second moving average:

For the second moving average, we take the next set of three consecutive numbers, which are 15, 18, and 24: \[ \text{Average} = \frac{15 + 18 + 24}{3} = \frac{57}{3} = 19. \] Therefore, the second moving average is 19.

Step 3: Third moving average:

For the third moving average, we take the next set of three consecutive numbers, which are 18, 24, and 36: \[ \text{Average} = \frac{18 + 24 + 36}{3} = \frac{78}{3} = 26. \] Therefore, the third moving average is 26.

Conclusion: Thus, the three-year moving averages are 15, 19, and 26. The moving average helps smooth out fluctuations and provides a better understanding of the trend over time.