I have a question about distribution on histogram. Let's just say me and my friends emptied our pockets of coins and recorded the year marked on each coin. And teh distribution of dates would be skewed to the left. WHy is that? I thought that the coins were made roughly around same time therefore mean should be shifted to the right.

The odds are not equal for the dates on the coins. Old coins are worn out ,lost,collected so the odds are rarer to have an 1850 coin vs a 1950 coin vs 1990 coin or 2001 coin.
Figuring old is to the left and new to the right. Having a coin made this year is possible but at this writing a 2006 coin is not possible ...as they've not been made yet.
Coins will always be skewed to the older side.

'sometimes there will be gaps too..
Like a 1975 US quarter dollar...None were made but roughly 2x as many 1976 quarters were made for the bicentennial.