In Animal Farm, why does Squealer quote facts and figures in his speeches?
Squealer is the propaganda arm of the pig leadership, and so uses his gift for persuasion to convince the other animals that things have changed, or that their memories of past events are faulty. He represents the government-controlled newspapers and radio of the Soviet Union, which reported on fabricated improvements for the working-class. As the pigs increase their oppression of the animals, Squealer takes up the role of commentator on farm production:
On Sunday mornings Squealer... would read out to them lists of figures proving that the production of every class of foodstuff had increased by two hundred per cent... The animals saw no reason to disbelieve him, especially as they could no longer remember very clearly what conditions had been like before the Rebellion.
(Orwell, Animal Farm, george-orwell.org)
Since no one is taking notes or trying to keep tabs on the actual food production, there is no reason to doubt Squealer, even though the animals feel that they are working harder for fewer benefits. By confusing the animals with facts and figures -- most of which are entirely invented -- Squealer convinces them that the pigs are working for their benefit without having to actually work or prove real production.
In Animal Farm, Squealer represents the Russian propaganda under Stalin. Under Stalin, propaganda was shown to the Russian people and to other countries to create the false sense of securiy and the belief that everything had improved in Russia after he took power.
In chapter eight