TOKYO, May 31 (Reuters) - Japan’s factory output rose 2.5% in April, government data showed on Monday, compared with a median market forecast for a 4.1% increase. Manufacturers surveyed by the Ministry of Economy, Trade and Industry expect output to fall 1.7% in May and rise 5.0% in June, the data showed. For the poll story click For the full tables on METI"s website: here Reporting by Daniel Leussink Our Standards: The Thomson Reuters Trust Principles.