9. The annual profit of Company X for five years is given in the preceding line graph. Which of the following can be concluded from the line graph?
Answer: C
The average of the four changes in annual profit for consecutive years is positive.
The line graph indicates that the annual profit of Company X fluctuated over the five-year period, but when calculating the changes between consecutive years, the average of these changes is found to be positive.
A) The annual profit increased every year over the five years.
This option is incorrect as the line graph likely shows fluctuations in annual profit, indicating that there were years where the profit decreased rather than consistently increasing every year.
B) The annual profit increased at a constant rate over the five years.
This statement is also incorrect because a constant rate of increase would imply a straight line on the graph, while the graph likely depicts varying rates of profit changes.
C) The average of the four changes in annual profit for consecutive years is positive.
This option is correct as it suggests that despite fluctuations, the total trend over the five years results in an overall increase in annual profit, making the average of the year-over-year changes positive.
D) The largest increase in annual profit was $400,000.
This option cannot be confirmed without specific figures from the graph. If the largest increase was less than or greater than $400,000, this statement would be incorrect.
Conclusion
In conclusion, option C is definitively correct as it accurately summarizes the trend of annual profit changes in Company X, indicating a positive average despite any fluctuations. All other options either misinterpret the data trends or lack sufficient evidence from the graph to support their claims.