Question

For the given 5 values, 35, 70, 30, 62, 58, the 3-year moving averages are:

• A. 45, 55, 50
• B. 40, 54, 60
• C. 55, 60, 65
• D. 45, 54, 50

Hint:

Moving averages are useful for smoothing out short-term fluctuations and highlighting the underlying trend in time series data.

Answer 1

The Correct Option is D

Step 1: Understanding the Concept:
A 3-year moving average involves taking the mean of three consecutive data points, shifting the window forward by one year at each step.

Step 2: Detailed Explanation:
Values: \( x_1=35, x_2=70, x_3=30, x_4=62, x_5=58 \).
1st average: \( (35+70+30) / 3 = 135 / 3 = 45 \).
2nd average: \( (70+30+62) / 3 = 162 / 3 = 54 \).
3rd average: \( (30+62+58) / 3 = 150 / 3 = 50 \).

Step 3: Final Answer:
The moving averages are 45, 54, and 50.