Unfortunately, many stereotypes are negative and can produce negative outcomes. Negative stereotypes can lead to prejudice (unjustified, usually negative attitudes toward a group), which can lead to discrimination (unjustified negative behaviors toward a group or its members).
So this topic provides a real-world example of how psychological research can benefit society. People who understand how attitudes are formed (and how they can be influenced by illusory correlations) may be more cautious about relying on stereotypes!