normal and average both are nouns.

normal and average both are adjectives.

normal is not a verb while average is a verb.

normal (noun)	average (noun)
something regarded as a normative example	a statistic describing the location of a distribution
	(sports) the ratio of successful performances to opportunities
	an intermediate scale value regarded as normal or usual

normal (adjective)	average (adjective)
conforming with or constituting a norm or standard or level or type or social norm; not abnormal	approximating the statistical norm or average or expected value
in accordance with scientific laws	lacking special distinction, rank, or status; commonly encountered
being approximately average or within certain limits in e.g. intelligence and development	lacking exceptional quality or ability
forming a right angle	around the middle of a scale of evaluation
	relating to or constituting the most frequent value in a distribution
	relating to or constituting the middle value of an ordered set of values (or the average of the middle two in a set with an even number of values)

normal (verb)	average (verb)
	amount to or come to an average, without loss or gain
	achieve or reach on average
	compute the average of