Hi,

You have to write Trigger on Contact object to fulfill your requirement.

see below sample trigger as per your requirement.

Apex Trigger:

trigger tskUpdateAccRatingtrigger on Contact(after insert, after update,after delete) {
    List<Contact> lstContact = [select id,AccountId from Contact where id in: trigger.newmap.keyset()];
    set<Id> sAccId = new set<Id>();
    for(Contact t: lstContact){
        if(t.AccountId != null){
            sAccId.add(t.AccountId);
        }
    }
    if(sAccId != null && sAccId.size() > 0){
        List<Account> lstAccount = [select id, (select id,Rating__c from Contacts) from Account where id in: sAccId];
        if(lstAccount.size() > 0){
            for(Account acc: lstAccount){
                Decimal decrating = 0;
                Integer intSumRating = 0;
                for(Contact con: acc.Contacts){
                    intSumRating += Integer.valueOf(con.Rating__c);
                }
                if(acc.Contacts.size() > 0){
                    decrating = decimal.valueOf(intSumRating/acc.Contacts.size());
                }
                acc.Averate_ContactRating__c = decrating;
            }            
            update lstAccount;
        }
    }
}

Hit Kudos if this provides you with useful information and if this is what you where looking for then please mark it as a solution for other benefits.

Thank You,
Hitesh Patel
SFDC Certified Developer & Administrator
My Blog:- http://mrjavascript.blogspot.in/