The importance of the presence of the statistician for the presentation of a result.

Unfortunately it appears that your manager used your analysis in a way it was not intended. That can definitely be problematic as it usually is given much more significance than it should, because of the formal nature of the science. Unfortunately, the technical specialist does not often get to decide who presents their analysis to directors.

I have had similar issues with people misrepresenting my work so there are a few things I typically do to try and avoid this situation. The first is to ask the customer, in this case your manager, how is your analysis being used. Understanding the audience and purpose can provide insight into what supporting information should be presented with the raw data. For a mean value such as this case, I would typically want to include a variance and visual distribution at a minimum, along with any disclaimers about the underlying data sources.

Directors usually don't want to see the detailed analysis so it is important to have a 1 page executive summary of your results and how they should be interpreted. The detailed analysis can be provided as back-up material if needed. I would make a point to your manager that if they are the ones to present a summary of your data to the director, then they should at least meet with you to discuss the analysis and its limitations before they misrepresent your work, to avoid situations such as this in the future.