It's no big secret that Google loves to use algorithms and crazy hard mathematical equations for its return of search results, in both organic and local results. This is no different when Google computes its review average.
MEAN (Average)
The issue here isn't the fact that Google is returning an incorrect review average, the problem is that you are assuming they are using average calculator based on a simple formula called 'MEAN'.
To calculate the Mean
Add the numbers together and divide by the number of numbers. (The sum of values divided by the number of values).
To determine the Median
Arrange the numbers in order, find the middle number. (The middle value when the values are ranked).
To determine the Mode
Count how many times each value occurs the highest is the mode. (The most frequently occurring value)
Bayesian Average, or Similar
Google is using a far more complex formula to work out your average, and many people believe its a modified Bayesian average formula that predicts the probability of next few reviews, a simpler way of getting your head around this is to think, Google is predicting a negative review, It's unrealistic to assume that your business will always be 5.0, 4.6 and so on.
A site withbusiness could 5 reviews, 5 stars may have with a average rating of 5 stars.0, while another business may have the exact same number of reviews, and the exact score from visitors, but have a lower reviewcompletely different average rating, this is because the formulaGoogle is complexusing Bayesian average or something similar, not simple and takingor a modified Bayesian formula. Google for example does, can, or could take into other factors into consideration, such as time, dates and how frequent they aredate, frequency, volume and how many you have... but we won't know this for sure since this information is not disclosed witheven the public,niche of the business.
Google is not afar from being transparent company in terms of their algorithmswhen it comes to disclosing algorithm information, so sometimes you just need to accept it, or attempt to understand it the best you can.
It's extremely unlikely that someone is going to pick a 4.7 over a 4.5, Google knows this... People are for more likely consider the amount of reviews a better indicator. The only thing you can do about it is keep up the good work! everyone else is in the same boat.
You will find more information about Bayesian and Google Local Reviews on Google.