Here is a simple tool that is free, easy to use, and gives you some useful statistic about your twitter account.
Just enter your twitter account name and click Graph my Tweets. It generates following statistics.
Average tweets / day – Simple average of your tweets on daily basis
Average tweets / month – Simple average of your tweets on monthly basis
Tweet Density / weekday – Graph of tweets by week day
Time of day – Tweet statistics by time of day
It also gives some other useful statistics about your replies and retweets.
It essentially has the same functionality as Twoolr’s free version.
However, the product development has been discontinued.
Nevertheless, its useful for basic statistics.