Make sure you fill up half a tank
With the Jazz weighing 1100 Kg saving weight of half a tank of fuel (less than 20kg) is hardly going to make any measurable difference, in any case I try never to let my tank get less than half empty because without fuel a car is just an expensive ornament.
A fast warmup and avoiding using brakes, avoiding excessive acceleration and speed above 50 if possible will give best payback.
Most engines do less than 20mpg until they warm up, and with short journeys your car never gets warm. Suggest you zero the trip and take it for a decent run (more than 20 to 30 miles) driving carefully and see how the consumption goes. It is important to zero the trip (I do it every time I fill up) because the mpg indication is at its most accurate and sensitive when trip at zero, as the miles build up on trip it gets very sluggish to change and after about 100 miles mpg readout hardly changes whether you are going downhill, uphill driving carefully or not. This effect is because the fuel usage data (the injector open time taken from ECU) is averaged out over the total miles on the trip and as the miles build up and change in instantaneous fuel usage is swamped by averaging it over more miles. The mpg readout normally updates about every 10 seconds.
In fact if you zero the trip from cold and drive say 5 miles you will see 'cold mpg' if you then zero trip with engine warmed up you should see a marked difference in mpg. Winter is not a good time to check MPG as the results are normally disappointing.