A pure word (or perfect word), as defined by me, is a word where the sum of the position in the alphabet of each letter in the word is perfectly divisible by the total length of the word. For example,
abcb is a perfect word because 1 + 2 + 3 + 2 = 8, and 8 / 4 = 2.
Given a word as input, output whether or not it is a perfect word. The word may always be assumed to be lowercase.
This is code-golf, so shortest program in bytes wins.
abcb: truthy ccc: truthy aaa: truthy pure: truthy word: truthy bed: falsy code: falsy bode: falsy