How to remove a rating of vendor based on an insertion calculation I am currently inserting a star rating of various vendors using the following formula New New Rating Value = ((Overall Rating * Total Rating) + New Calculated ) / Total Rating where Overall Rating = Current Rating value Total Rating = No of reviews (ratings) currently present New Calculated = The new star rating value the user specified The above formula works for adding a new rating. My question is how would I remove a specific rating and return to the old value if I only have the `New Calculated` and the total Rating value (I wont have access to the earlier Overall Rating ?

If I understand correctly you have $$\frac {O\times T+N_c}T=N_r$$ yes?

Then, if you are given $N_r,N_c,T$ we get $$O=\frac {N_rT-N_c}T$$

Note: I am not entirely clear on the definition of $T=$ Total Rating. How is it the same even after you add a new rating? Shouldn't it have increased by $1$? Usually when you add a new element to a sample and seek to compute the new average given the old, you take into account that the sample size has increased by $1$.