Interesting thing: the word guesstimate was first coined by
statisticians.
My personal understanding of when it would be appropriate is when you have a formula for something, and there are some unknowns, but some of the inputs are guesses. So you
guess as to the factors, and then do the calculations, then that's your guesstimate. The reason they coined the term would have been that in statistician terms "estimate" means an output that you gained by putting in measurements for the unknowns, not guesses. The need for a new term was because "estimate" means a specific thing when your doing stats. A guess is something you pluck out of the air, an estimate is something you take measurements for and plug them into an equation, and a guesstimate is something where you don't have data for some of the measurements, so you plug in guesses for those.
https://en.wikipedia.org/wiki/Guesstimatehttps://en.wikipedia.org/wiki/Estimation"using the value of a statistic derived from a sample to estimate the value of a corresponding population parameter".
So if you don't actualy have the sample data to plug into the equation, you're not actually producing a proper estimate. Even so, you may be required to given an estimation, so you plug in some reasonable-sounding guess. Hence, a guesstimate instead of a proper estimate. Yeah, so the term shouldn't be thrown around randomly, but it does have a specific and concrete meaning in that field, because
estimate has a narrower definition when working in that field, so this term ended up getting split out.