A WoW script snippet that shows how to calculate the average item level of a unit. Call RequestAverageItemLevel with a unitID to request inspect data for the unit and calculate the unit's average item level once that data is available. The results are printed to chat. This hasn't been tested, so please notify me if it doesn't work.

CalculateAverageItemLevel.lua

local SPECID_FURY = 72 -- Fury's specialisation ID, as returned by GetInspectSpecialization

-- Calculate and return a unit's average item level using the formula described on this page:
-- http://www.wowpedia.org/API_GetAverageItemLevel
-- Should only be called after INSPECT_READY fired for the unit
local function CalculateAverageItemLevel(unit)
	local totalIlvl = 0
	local mainHandEquipLoc, offHandEquipLoc
	
	for slot = INVSLOT_FIRST_EQUIPPED, INVSLOT_LAST_EQUIPPED do -- For every slot,
		if slot ~= INVSLOT_BODY and slot ~= INVSLOT_TABARD then -- If this isn't the shirt/tabard slot,
			local id = GetInventoryItemID(unit, slot) -- Get the ID of the item in this slot
			if id then -- If we have an item in this slot,
				local _, _, _, itemLevel, _, _, _, _, itemEquipLoc = GetItemInfo(id) -- Get the item's ilvl and equip location
				totalIlvl = totalIlvl + itemLevel -- Add it to the total
				
				if slot == INVSLOT_MAINHAND then -- If this is the main or off hand, store the equip location for later use
					mainHandEquipLoc = itemEquipLoc
				elseif slot == INVSLOT_OFFHAND then
					offHandEquipLoc = itemEquipLoc
				end
			end
		end
	end
	
	local numSlots
	if mainHandEquipLoc and offHandEquipLoc then -- The unit has something in both hands, set numSlots to 17
		numSlots = 17
	else -- The unit either has something in one hand or nothing in both hands
		local equippedItemLoc = mainHandEquipLoc or offHandEquipLoc
		
		local _, class = UnitClass(unit)
		local isFury = class == "WARRIOR" and GetInspectSpecialization() == SPECID_FURY
		
		-- If the user is holding a one-hand weapon, a main-hand weapon or a two-hand weapon as Fury, set numSlots to 17; otherwise set it to 16
		
		numSlots = (
			equippedItemLoc == "INVTYPE_WEAPON" or 
			equippedItemLoc == "INVTYPE_WEAPONMAINHAND" or
			(equippedItemLoc == "INVTYPE_2HWWEAPON" and isFury)
		) and 17 or 16
	end
	
	return totalIlvl / numSlots -- Return the average
end

-- Print out the arguments according to the first format string argument
local function printf(formatStr, ...)
	print(formatStr:format(...))
end

local f = CreateFrame("Frame") -- Create a frame to receive events
f:SetScript("OnEvent", function(self, event, ...) -- When an event fires, call the method of the same name
	self[event](self, ...)
end)

f:RegisterEvent("INSPECT_READY") -- Fires when the inspect data we requested is ready

function f:INSPECT_READY(guid)
	local inspectUnit = self.inspectUnit
	if inspectUnit and UnitGUID(inspectUnit) == guid then -- If this is the unit we requested information for,
		self.inspectUnit = nil
		
		local avIlvl = CalculateAverageItemLevel(inspectUnit) -- Calculate the unit's average item level
		printf("%s has an average item level of %.2f!", UnitName(inspectUnit), avIlvl) -- Print this out to chat
		ClearInspectPlayer() -- Tell the game that we're done with this unit's data.
	end
end

-- Request the average item level of a unit to be calculated
local function RequestAverageItemLevel(unit)
	f.inspectUnit = unit
	NotifyInspect(unit)
	printf("Requesting item level of %s (unitID %s)...", UnitName(unit), unit)
end