Question

Directions:
Directions for the following 4 questions: The table below shows the sales (in thousands of units) of four products P, Q, R and S of a company over three years. Study the table and answer the questions that follow. Year | P | Q | R | S 2021 | 20 | 30 | 25 | 15 2022 | 25 | 35 | 20 | 20 2023 | 30 | 40 | 30 | 25

What is the average yearly sales (in thousands) of product S over the three years?

• A. 18
• B. 22
• C. 25
• D. 20

Hint:

Try assuming a trial average and see whether the deviations of the three yearly values above and below it cancel out to zero - that confirms the true average.

Answer 1

The Correct Option is D

Step 1: Instead of adding the three values and dividing by 3, use the assumed-mean (deviation) method to find the average of product S's sales.
Step 2: Product S's sales over the three years are $15$, $20$, $25$ (in thousands of units). Assume a trial mean of $20$.
Step 3: Find the deviation of each value from this assumed mean: $15-20=-5$, $20-20=0$, $25-20=+5$.
Step 4: Sum the deviations: $-5+0+5=0$.
Step 5: Since the deviations from the assumed mean sum to exactly zero, the assumed mean of $20$ must be the actual average. Average yearly sales of S $=20$ thousand units. \[\boxed{20}\]