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 determine the 4-year moving averages from sales data \(a, b, c, d, e, f, g, h\), we calculate the average of sales over four consecutive years. The computations are as follows:

The first average covers years 1 through 4: \(\frac{a + b + c + d}{4}\).

The second average covers years 2 through 5: \(\frac{b + c + d + e}{4}\).

The third average covers years 3 through 6: \(\frac{c + d + e + f}{4}\).

The fourth average covers years 4 through 7: \(\frac{d + e + f + g}{4}\).

The fifth average covers years 5 through 8: \(\frac{e + f + g + h}{4}\).

Comparing these to the provided choices:

• (A) \(\frac{a + b + c + d}{4}\): Matches the first computed average.
• (B) \(\frac{a + c + d + e}{4}\): Does not match any computed average.
• (C) \(\frac{c + d + f + h}{4}\): Does not match any computed average.
• (D) \(\frac{b + c + d + e}{4}\): Matches the second computed average.

Therefore, the correct options are:

(A) and (D) only