There is no one hard and fast answer to your question. The amount of acceptable variance could depend on a variety of factors. One would be the size of your sample, and a sample size of 30 is generally considered the minimum for a statistically significant result. Another factor would be whether the observations were in something where the golden ratio might reasonably be expected to appear, such as in biological systems or in the works of an artist who was known to use the golden ratio.

When I do my digital image analysis with my PhiMatrix software, I generally like the variance to be only a pixel or two on images of anywhere from 600 to 6000 pixels, so that would be a variance of only +/- 0.003 to .00016. If your suggested variance of +/- .05 is meant to indicate a range of 1.568 to 1.668 then I would consider that much to large a range to still call the results as golden ratios. A variance of +/- 0.005 would in my opinion yield more accurate conclusions.

On the other extreme, some will tell you that nothing can be the golden ratio because it has an infinite number of digits. While theoretically correct, it a ridiculous position to take in real world applications because nothing can be measured with infinite precision, nor is there a need for it to be. If I use a golden ratio on a design on my computer screen with pixel level accuracy, it’s still a golden ratio in concept and in application, and the exact golden ratio will fall within the golden ratio dividing line that I have created. It’s just a question of how much accuracy I need for a particular purpose.

I’d recommend you look at other studies in the field of your study and seek to achieve results of similar accuracy. My book, available at https://bit.ly/goldenratiobook has a more detail discussion on your question. Your might also find these articles to be helpful:

https://www.goldennumber.net/golden-ratio-misconceptions-by-george-markowsky-reviewed/
See the section “Flawed assumptions can lead to flawed conclusions”

https://www.goldennumber.net/golden-ratio-design-beauty-face-evidence-facts/

Re “what is the mathematical concept behind this,” here are some pages that may help:

https://www.goldennumber.net/golden-ratio/
https://www.goldennumber.net/what-is-phi/
https://www.goldennumber.net/life-design/
https://www.goldennumber.net/plants/

It’s a broad topic, so there are many aspects to it. Both articles have links to other articles that you can go to when you find a topic of interest.

As to doing it in a creative way, here are some ideas:

https://www.goldennumber.net/school-projects-interviews/
https://www.goldennumber.net/do-it-yourself/
https://www.goldennumber.net/content-images-use/

The application of the golden ratio to beauty is one of the most visited topics on this site, so yes that may make it more interesting. See the articles at https://www.goldennumber.net/category/face-beauty/.

You may also find my PhiMatrix software to be useful. See http://www.phimatrix.com/nature-animals-golden-ratio/ for examples. You can download it from http://www.phimatrix.com/download/. A free two week trial is available, along with a 50% educational discount if purchased. See http://www.phimatrix.com/education/ for details.

That should get you started. If you have other questions let me know. I wish you the best with your project.

or do you think in order for my project to be more creative it would be better if i did the project with the human faces and the golden ratio?

It relates to real life whenever we understand and appreciate what we see in nature and then apply it to our own creations. This has taken place in art and just about every field of design. The purpose it usually for that which is created to be innately pleasing to our perceptions.