What is the first big female detective in literature or on television?

Mis Marple 

                Miss Marple and Honey West.

The first big female detective in literature is widely considered to be Miss Marple, created by Agatha Christie. Miss Marple first appeared in a short story in 1927 and later in her first full-length novel, "The Murder at the Vicarage" in 1930. Miss Marple is an elderly amateur detective who solves crimes using her extensive knowledge of human nature and her observation skills.

As for the first big female detective on television, that would be Honey West, portrayed by Anne Francis in the 1960s TV series of the same name. Honey West was a private detective who solved crimes with the help of her pet ocelot and a variety of gadgets. The show only lasted for one season, but it was notable for being the first television series with a female detective as the main character !