Shanma is correct but I think may be of some use in helping you make your question clearer.
1) What is hate speech? What you may think is I or others may not. Just as what I may feel is hate speech you and others may not. Please define so reader can know what it is you are looking for.
2) Limit your question! What media source? It will be impossible to monitor every television channel, radio station, news papers,magazines, ect. You may want to focus in on one but more than that you would need a team.
3) Methodology approach. In your study it may just be watching, listening, or reading and counting the number of times statements met your defined requirements for statement to be considered hate speech. Or listening to prime time shows and comparing them to one another. Many such methodologies are a valid approach to your question.
4) Have a statistical method or approach can be done much the same as #3.
I hope this helps and I look forward to your reply,
Dear Nazia, I've studied the media discourse about fear of violent crime in Brazil. First of all, of course you need to define what you are calling hate speech, but I think you must do it in your research, not here. However you set your concept, I think you can combine two methodologies: discourse analysis and quantitative analysis. For it, you can use a program called "n-vivo", which was reviewed to Portuguese by professor Alex Niche Teixeira, but it is originally in English. It's a kind of program like SPSS, but it's suitable to apply in qualitative researches, mainly in narratives and writings.
To define what you are calling hate speech you can read some books and papers I am listing below. Actually, they deal with the topic of fear, but you can build the connection between fear and hate speech to prepare your own concept. I am pointing some texts about discourse analysis too. Unfortunately, some of them are in portuguese, because I am from Brazil.
ALEXANDER, Jeffrey C. On the Social Construction of Moral Universals: the “Holocaust” From War Crime to Trauma Drama. European Journal of Social Theory, 5, 1: 5-85, 2002b. (Periódicos CAPES).
ALEXANDER, Jeffrey C. & GAO, Rui. Remembrance of Things Past: Cultural Trauma, the “Nanking Massacre” and Chinese Identity. Disponível em: research. yale.edu/ccs/workshop/0506/gao_nanking.pdf, 2005. Acesso em: 18 abr. 2006.
BENETTI, Márcia. Análise do discurso em jornalismo: estudo de vozes e sentidos. In: LAGO, Cláudia & BENETTI, Márcia. Metodologia de pesquisa em jornalismo. Petrópolis: Vozes, 2007, pp. 107-122.
BUCCI, Eugênio. Como a violência na TV alimenta a violência real – da polícia. In: BUCCI, Eugênio & KEHL, Maria Rita. Videologias. São Paulo: Boitempo, 2004a, pp. 107-116.
CALDEIRA, Teresa Pires do Rio. Cidade de muros: crime, segregação e cidadania em São Paulo. São Paulo: Editora 34/Edusp, 2000.
CERQUEIRA, Rafael Torres de & NORONHA, Ceci Vilar. Escrito em vermelho: a construção do discurso sobre criminalidade e linchamento no jornal. In: Dossiê: violência, criminalidade e justiça. Salvador: Caderno CRH/UFBa, vol. 19, n. 47, maio/ago 2006, pp. 247-258.
CHERMAK, Steven. Crime in the News Media: a Refined Understanding of How Crimes become News. In: BARAK, Gregg. Media, process, and the social construction of crime: studies in newsmaking criminology. New York, London: Garland, 1994, pp. 95-129.
CUNHA, Isabel Ferin. O SPSS e os estudos sobre os media e o jornalismo. In: LAGO, Cláudia & BENETTI, Márcia. Metodologia de pesquisa em jornalismo. Petrópolis: Vozes, 2007, pp. 168-196.
EYERMAN, Ron. Art and Assassination as Public Performance. Disponível em: research.yale.edu/ccs/research/working-papers/eyerman_vanGogh.pdf, 2005.
GILL, Rosalind. Análise do Discurso. In: GASKELL, George & BAUER, Martin (eds.). Pesquisa qualitativa com texto, imagem e som: um manual prático. Petrópolis: Vozes, 2002, pp. 244-270.
GLASSNER, Barry. Criminalidade no noticiário: histórias inacreditáveis e estatísticas exageradas. In: GLASSNER, Barry. Cultura do Medo. São Paulo: Francis, 2003, pp. 73-111.
GUSFIELD, Joseph R. The Culture of Public Problems: drinking-driving and the symbolic order. Chicago: University of Chicago Press, 1984.
HALL, Stuart, CHRITCHER, Chas, JEFFERSON, Tony, CLARKE, John & ROBERTS, Brian. A produção social das notícias: o mugging nos media. In: TRAQUINA, Nelson (org.). Jornalismo: questões, teorias e “estórias”. Lisboa: Vega, 1993, pp. 224-248.
HAMM, Bradley J., SHAW, Donald L. & TERRY, Thomas C. Vertical versus horizontal media: using agenda-setting and audience agenda-melding to create public information strategies in the Emerging Papyrus Society. Disponível em: HighBeam Encyclopedia. Acesso em: 23 nov. 2007.
JEWKES, Yvonne. Media and crime. London: Sage Publications, 2006.
KATZ, Jack. Seductions of crime: moral and sensual attractions in doing evil. New York: BasicBooks, 1988.
LANIER, Mark M. & HENRY, Stuart. What is crime? Defining and measuring the crime problem. In: LANIER, Mark M. & HENRY, Stuart. Essential Criminology. Boulder: Westview, 2004, pp. 18-65.
MOLOTCH, Harvey & LESTER, Marilyn. As notícias como procedimento intencional: acerca do uso estratégico de acontecimentos de rotina, acidentes e escândalos. In: TRAQUINA, Nelson (org.). Jornalismo: questões, teorias e “estórias”. Lisboa: Vega, 1993, pp. 34-51.
MYTHEN, Gabe & WALKLATE, Sandra. Communicating the terrorist risk: Harnessing a culture of fear? Disponível em: http://cmc.sagepub.com/cgi/content/abstract/2/2/123. Acesso em: 15 mai. 2008.
REINER, Robert. Media made criminality: the representation of crime in the mass media. In: MAGUIRE, Myke, MORGAN, Rod & REINER, Robert (eds.). The Oxford Handbook of Criminology. New York: Oxford University Press, third edition, 2002, pp. 376-416.
ROSHCO, Bernard. Newsmaking. Chicago: The University of Chicago Press, 1975.
SARTRE, Jean-Paul. Esboço para uma teoria das emoções. Porto Alegre: L&PM, 2009. (it can help you to think about what is hate. It is available in English, I suppose it's as "sociology of emotions")
SMITH, Philip. Narrating the guilhotine: punishment technology as myth and symbol. Theory, Culture & Society, 20, 5: 27-51, 2003. (Periódicos CAPES).
TEIXEIRA, Alex Niche & BECKER, Fernando. Novas possibilidades da pesquisa qualitativa via sistemas CAQDAS. Porto Alegre: Sociologias, n. 5, jun. 2001. Disponível em: http://www.scielo.br/scielo.php?script=sci_arttext&pid=S1517-45222001000100006&lng=pt&nrm=iso. Acesso em: 1º mai. 2009.
TONRY, Michael. Thinking about crime: sense and sensibility in American penal culture. New York: Oxford University Press, 2004.
WILSON, James Q. & HERRNSTEIN, Richard J. Television and the mass media. In: Crime and Human Nature. New York: First Touchstone Edition, 1986b, pp. 337-354.
Sounds like interesting research, though I agree with the previous responses that a clear operational definition of 'hate speech' would be important. Assuming that you might be interested in something beyond the incidence of 'hate speech' reported in the media, I would recommend a non-statistical approach to address this type of research question. A qualitative analytic method such as discursive psychology or conversation analysis would be well equipped to explore the positioning of hate speech actors and their targets by the media. Depending on what you were most interested in you could focus on the broader discourses involved in media reporting (discourse analysis) or the fine grain detail of reports (e.g., conversation analysis). There are good introductory chapters concerning discourse analysis in: Willig, C. (2013). Introducing qualitative research in psychology. McGraw-Hill International. (link below)
I hope this is helpful - best wishes with your research.
I think that some form of sentiment analysis could be of use here. Maybe you would find the strategy I used in my paper on YouTube tutorial videos helpful:
Article ‘It took me about half an hour, but I did it!’ Media circuit...
David Yanagizawa has done some empirical research Propaganda and Conflict: Theory and Evidence from the Rwandan Genocide (2014). As you may be aware, the role of the media and hate speech/incitement was a central feature of the conflict arising from radio broadcasts. The research examines the effect of that hate speech on the level and extent of the violence perpetrated. He has used quantitative data to assess it. The criminal prosecution was heard at the ICTR in the case of Nahimana. Hope that helps.