There is a long pipe to the fuel tank in the Jazz (tank is under front seats), this holds quite an amount of fuel - that is part of the reason for gauge staying on 'full' for a while, also when needle is on 'empty' and light comes on there is still about 6 to 7 litres in the tank, this is another reason why second half of tank 'seems' to go more quickly.
Having said that, every car that I have owned and driven seems to have a similar problem.
Driving my 1.4SE Jazz reasonably carefully, 50 miles round trip commute a day, mixed main road and town I get about 62 to 63 mpg on the readout, which equates to about 56 to 57mpg actual (measured by fuel used and miles), if I drive 'normally' I get about 53 to 54mpg indicated.