I want to know the average cost of living including house rent, food etc. per month in Finland particularly in Helisinki.

Statistics Finland compiles the official statistics concerning whole Finland.
Their main page: http://www.tilastokeskus.fi/index_en.html

Income and Consumption (includes household expenditures): http://www.tilastokeskus.fi/tk/tp/tasku/taskue_tulot.html

Housing (includes average rents of rented dwellings): http://www.tilastokeskus.fi/tk/tp/tasku/taskue_asuminen.html

Prices and costs (includes selected food prices):
http://www.tilastokeskus.fi/tk/tp/tasku/taskue_hinnat.html

Finland in figures, all kinds of statistics about everyday life in Finland: http://www.tilastokeskus.fi/tk/tp/tasku/suomilukuina_en.html

The pages above give information on the whole Finland. Statistics concerning Helsinki are compiled by Tietokeskus (http://www.hel.fi/tietokeskus).

General statistics-based information on Helsinki: http://www.hel.fi/tietokeskus/en/tilastoja/seutu.htm

More specific report on the economy of households in Helsinki, not quite what you asked for, though:
http://www.hel.fi/tietokeskus/en/tutkimuksia/resea999.html

Specific statistics on expenditure per household are not to be found on the Internet, but in Helsinki City Library you can get the figures in a printed book: Helsingin kaupungin tilastollinen vuosikirja 2000 = Statistical yearbook of the City of Helsinki 2000, p. 240. If you are not in Helsinki, you can obtain the figures as an inter-library loan, so please turn to your local library.