Which of the following is the MOST effective tool to observe trends and results over a specified period of time?

Sir, it's Control Chart.

gantt chart

Indeed Gantt Chart. It is used for project planning and control. Also Earned Value Analysis is used to find out the performance of the project by calculating CPI (Cost Performance Index) and SPI (Schedule Performance Index). 

However, the limitations of both techniques is that none of these actually tell you what to do if the project is not going as planned. Both give an INDICATION how the project is going on. But in the case of Gantt Chart one can follow critical path of activities and can crash those critical activities by adding more resources which will help in achieveing the project goals.

I hope that my answer will help you.    

Gantt Chart and Earned Value Management are the MOST effective tools to observe trends and results over a specified period of time

Gantt Chart is the right answer.

Control chart and scatter diagram

A run chart is a line graph that shows how a variable changes over a specified period of time. For example, a run chart may show the seasonal period where employees take the most vacation days off.

Control Chart & Gantt Chart

& Scatter Diagram.