You are now a sqlite data analyst, and you are given a database schema as follows:

    【Schema】
    【DB_ID】 retail_world
【Schema】
# Table: Orders
[
(OrderID:INTEGER, Primary Key, Examples: [10248, 10249, 10250]),
(CustomerID:INTEGER, Examples: [90, 81, 34]),
(EmployeeID:INTEGER, Examples: [5, 6, 4]),
(OrderDate:DATETIME, Examples: [1996-07-04 00:00:00]),
(ShipperID:INTEGER, Examples: [3, 1, 2])
]
# Table: Suppliers
[
(SupplierID:INTEGER, Primary Key, Examples: [1, 2, 3]),
(SupplierName:TEXT, Examples: [Exotic Liquid]),
(ContactName:TEXT, Examples: [Charlotte Cooper, Shelley Burke, Regina Murphy]),
(Address:TEXT, Examples: [49 Gilbert St., P.O. Box 78934, 707 Oxford Rd.]),
(City:TEXT, Examples: [Londona, New Orleans, Ann Arbor]),
(PostalCode:TEXT, Examples: [EC1 4SD, 70117, 48104]),
(Country:TEXT, Examples: [UK, USA, Japan]),
(Phone:TEXT, Examples: [(171) 555-2222, (100) 555-4822, (313) 555-5735])
]
# Table: Customers
[
(CustomerID:INTEGER, Primary Key, Examples: [1, 2, 3]),
(CustomerName:TEXT, Examples: [Alfreds Futterkiste]),
(ContactName:TEXT, Examples: [Maria Anders, Ana Trujillo, Antonio Moreno]),
(Address:TEXT, Examples: [Obere Str. 57]),
(City:TEXT, Examples: [Berlin, México D.F., London]),
(PostalCode:TEXT, Examples: [12209, 5021, 5023]),
(Country:TEXT, Examples: [Germany, Mexico, UK])
]
# Table: OrderDetails
[
(OrderDetailID:INTEGER, Primary Key, Examples: [1, 2, 3]),
(OrderID:INTEGER, Examples: [10248, 10249, 10250]),
(ProductID:INTEGER, Examples: [11, 42, 72]),
(Quantity:INTEGER, Examples: [12, 10, 5])
]
# Table: Employees
[
(EmployeeID:INTEGER, Primary Key, Examples: [1, 2, 3]),
(LastName:TEXT, Examples: [Davolio, Fuller, Leverling]),
(FirstName:TEXT, Examples: [Nancy, Andrew, Janet]),
(BirthDate:DATE, Examples: [1968-12-08]),
(Photo:TEXT, Examples: [EmpID1.pic, EmpID2.pic, EmpID3.pic]),
(Notes:TEXT)
]
# Table: Shippers
[
(ShipperID:INTEGER, Primary Key, Examples: [1, 2, 3]),
(ShipperName:TEXT, Examples: [Speedy Express, United Package, Federal Shipping]),
(Phone:TEXT, Examples: [(503) 555-9831, (503) 555-3199, (503) 555-9931])
]
# Table: Products
[
(ProductID:INTEGER, Primary Key, Examples: [1, 2, 3]),
(ProductName:TEXT, Examples: [Chais, Chang, Aniseed Syrup]),
(SupplierID:INTEGER, Examples: [1, 2, 3]),
(CategoryID:INTEGER, Examples: [1, 2, 7]),
(Unit:TEXT, Examples: [10 boxes x 20 bags, 24 - 12 oz bottles, 12 - 550 ml bottles]),
(Price:REAL, Examples: [18.0, 19.0, 10.0])
]
# Table: Categories
[
(CategoryID:INTEGER, Primary Key, Examples: [1, 2, 3]),
(CategoryName:TEXT, Examples: [Beverages, Condiments, Confections]),
(Description:TEXT)
]
【Foreign keys】
Orders.EmployeeID=Employees.EmployeeID
Orders.CustomerID=Customers.CustomerID
Orders.ShipperID=Shippers.ShipperID
OrderDetails.OrderID=Orders.OrderID
OrderDetails.ProductID=Products.ProductID
Products.CategoryID=Categories.CategoryID
Products.SupplierID=Suppliers.SupplierID

    【Question】
    What is the average sales for each categories? average sales = AVG(ProductSales)

    【Evidence】
    average sales = AVG(ProductSales)

    Please read and understand the database schema carefully, and generate an executable SQL based on the user's question and evidence. 

SQL: SELECT AVG(ProductSales) FROM `Sales by Category` GROUP BY CategoryName