I agree with Vince, but I think 'half a dozen' does not have to mean exáctly 6 when used in a phrase.

For example: "You have made that mistake half a dozen times now!"

In my perception should indicate that the mistake is made about six times, but probably the exact number is not counted. I am not 100% sure about this though.

A dozen is precisely 12.

Half-a-dozen = 6

Baker's dozen = 13

A score = 20.

A gross = 144.

"A dozen" usually means "exactly twelve."

Like some other numbers, it can also be used in an imprecise way as an indefinite: "If I've told you once, I've told you a dozen times, please don't put dishes in the dishwasher without rinsing them first." You would never use it that way if you actually knew the correct number. You would never knowingly call ten pennies "a dozen."

The plural, "dozens," is obviously an indefinite use.

A "baker's dozen" is thirteen, supposedly from time when it was a serious offense for bakers to give short measure and threw in an extra just to be sure.

It's rarely heard nowadays, but a dozen dozen, i.e. 144, is a "gross," a dozen dozen dozen, i.e. 1728, is "a great gross," and the original meaning of the word "grocer" is "a store that buys things by the gross."

Because twelve is evenly divisible by two, three, four, and six it is in some ways a more convenient number than ten, and before the introduction of the International System, many of the traditional weights and measures were based on multiples of twelve. In the 1930s there was a "duodecimal society" that advocated changing to a number system with base 12 instead of 10, and pointed out that in a system with base 12, and suggested that if the goal was to make arithmetic easy, it would be better to keep the traditional measurements and switch to base-12 numbers than to keep base-10 numbers and switch to the metric system.

I agree with you, Marc.

Similarly, I wouldn't expect the plural "dozens" to be an exact multiple of 12 either.

If we are talking about something which often comes in a set of 12 (or 6) such as eggs, then it's more likely an exact number is meant.