In order to get 4.8 you would need a ratio of 1:4 4stars:5tars, or 20% 4stars to 80% 5stars. This ignores any ratings less than 4 such as 1, 2 or 3... So for every 5 guests, 4 need to give 5 stars to achieve 4.8.
So the algebraic calculation to work out how many 5 star ratings you need to get to 4.8 is:
N(4) + M(5) + 5(X) = T
N+M+X
N = number of 4 star ratings
M = number of 5 star ratings
T = Target rating required
X = Unknown variable which we are trying to work out...
NB:-Where something is in a bracket it is multiplied to, e.g. N(4) is N x 4 so if N = 2 it is 2(4) = 8
So, for example, If someone had 50 guests made up of 10 four star ratings and 40 five star ratings that works out at 4.8
Calculation is:
10(4) + 40(5). = 4.8
50
Now if this host wanted a 4.9 rating, the algebraic calculation they would need to do is:
N(4) +M(5) +5(X) = 4.9
N+M+X
So, in this example...
N=10 (four star ratings)
M = 40 (five star ratings)
T = 4.9 (target rating)
X = Unknown number of 5 stars we need to get to T (target rating)
So when you plug the numbers in..
10(4)+40(5)+5(X) =4.9
10+40+X
Simplifying, we get:
= 240+5X = 4.9
50+X
= 240+5X=4.9 (50+X)
= 240+5X = 245+4.9X
= 0.1X=5
X= 5
0.1
X = 50. Therefore, in this case it will take 50 5 stars ratings to get from 4.8 to 4.9.
To check the maths you can substitute X for 50 back into the original equation
10(4)+40(5)+5(X)
50+X
So if X = 50 we get...
10(4)+40(5)+5(50)
50+50
= 4.9 so we now know that our equation was right and to get from 4.8 based on our number of guests and ratings we need a further 50 five stars.
So if you know the number of guests you have had and their ratings you can calculate it. I simplified the calculation by ignoring 3 stars etc but it is easy to add to the equation, just create a separate letter for that category.
It's quite late and I've typed this quite fast so I hope i haven't made too many typos but it gives you the gist, and you should just be able to plug whatever your numbers are into the general equation to give you the number of 5 stars you need.
Drew