I've been working as a data-scientist for years without ever hearing it labelled as such. Working as a programmer with a love of R&D I've been able to imagineer data-science strategies to find the solution to most of the challenges involved in decisions/strategy/identified problems. I've engaged in freelance arrangements with marketing companies and agencies for years because I developed my own tools to do data-mining quickly years before it was even common practice to involve in small business. I've been working as primarily a developer of software and websites. Being around such businesses that generate lots of data in a digital market over 16 years, case study examples I can initially think of would include:
I do not have great stage-skills or sales abilities so 90% of the time these data-science ideas and concepts were not understood by the non-technical clients and it was entertained purely on trust I'd established customers from previous work. I might have originally only helped tweak a pay-per-click campaign - It's amazing how much interesting work I've found from a relationship that started taking on some short, low paid very dull work. I've always bumped into clients challenges and problems where I can use data-science approaches by accident. Usually from over-hearing staff chatter or asking why a client doesn't sound as happy as they usually are - I sleep on it and then start firing solutions and ideas to help. Rarely have I been contacted by anyone looking for data-science approaches, skills or solutions to their problems. Now I'm actively re-starting my own freelance business to fund my studies to focus my future in medical research tools - my biggest challenge is figuring out how non-technical people who have never heard of these strategies would actually describe it if they were seeking such assistance? None of the freelancer market places have entertained my request to buy search data from them on the freelancer searches they see, or which searches do not find any matches - these are the gold nuggets we both need!
I hope that helps with your request for examples! feel free to PM me, I am always looking for freelancers to collaborate on ideas with potential.