What tool to find expected and hidden patterns in data? I have no background AT ALL in data science/stats/mathematics. However, I've always been interested in what data shows.

I have a huge dataset right now - daily attendance figures for a factory of ~300 for the past 10 years. I'm interested in finding out answers to questions like is there a pattern of leaves correlated with public holidays? For example, around which holiday (+/- 2 days) are workers most likely to take a leave? This is an expected pattern. Or, was there a significant increase (+10%) in on-time reporting after bonuses were issued. Maybe there are hidden patterns which an algorithm can find.

Is there a tool I can plug this data in which can help me find these patterns? Google tells me there's a tool http://www.i-programmer.info/news/84-database/3501-mine-finding-patterns-in-big-data.html but I'm not sure if this is the right direction for me.

I'd appreciate any advice!
You are unlikely to find a tool that will truly do this for you. Various bits of software may produce some nice graphs. However we're not at a stage where tools can generate interesting questions to ask, ask them, and then explain the results to you.

If this is commercial, your best bet is to hire someone with an appropriate background and set them some questions. Tell them what your biggest goals and costs are, explain the data to them, and see what happens.  So the answer is a contractor.