Question

For predicting the straight-line trend in the sales of washing machines (in thousands) on the basis of 8 consecutive years' data, the company calculates 4-year moving averages. If the sales of washing machines for respective years are \( a, b, c, d, e, f, g, \) and \( h \), then which of the following averages will be computed?
(A) \( \frac{a + b + c + d}{4} \)  
(B) \( \frac{a + c + d + e}{4} \)  
(C) \( \frac{c + d + f + h}{4} \)  
(D) \( \frac{b + c + d + e}{4} \)  
Choose the correct answer from the options given below:

• A. (A), (B), and (D) only
• B. (C) and (D) only
• C. (A) and (D) only
• D. (B), (C), and (D) only

Answer 1

The Correct Option is C

To solve the problem of determining which 4-year moving averages will be computed from the sales data \(a, b, c, d, e, f, g, h\), we must understand the concept of a 4-year moving average. Here, it's calculated by taking the average of sales figures over 4 consecutive years. We proceed with computing the averages as follows:

The first average is for the years 1 to 4: \(\frac{a + b + c + d}{4}\).

The second average is for the years 2 to 5: \(\frac{b + c + d + e}{4}\).

The third average is for the years 3 to 6: \(\frac{c + d + e + f}{4}\).

The fourth average is for the years 4 to 7: \(\frac{d + e + f + g}{4}\).

The fifth average is for the years 5 to 8: \(\frac{e + f + g + h}{4}\).

Comparing these with the given choices:

• (A) \(\frac{a + b + c + d}{4}\): Correct, as it corresponds to the first average.
• (B) \(\frac{a + c + d + e}{4}\): Incorrect, does not correspond to any of the computed averages.
• (C) \(\frac{c + d + f + h}{4}\): Incorrect, does not correspond to any of the computed averages.
• (D) \(\frac{b + c + d + e}{4}\): Correct, as it corresponds to the second average.

Thus, the correct options are:

(A) and (D) only

Answer 2

A 4-year moving average is computed by taking the average of consecutive 4 years' data. For 8 years of data ($a, b, c, d, e, f, g, h$), the moving averages would be:
1. First 4-year average:
$\frac{a + b + c + d}{4}$
2. Second 4-year average:
$\frac{b + c + d + e}{4}$
3. Third 4-year average:
$\frac{c + d + e + f}{4}$
4. Fourth 4-year average:
$\frac{d + e + f + g}{4}$
Analyzing given options
- Option (A): $\frac{a + b + c + d}{4}$ is a valid 4-year moving average (first average).
- Option (B): $\frac{a + c + d + f}{4}$ is incorrect because it does not use 4 consecutive years of data.
- Option (C): $\frac{c + d + f + h}{4}$ is incorrect because it skips some years and does not represent a valid 4-year moving average.
- Option (D): $\frac{b + c + d + e}{4}$ is a valid 4-year moving average (second average).
Conclusion The correct options are:
(A) and (D)