How do I get started in producing mathematical models from data?

Question

Lets say I have a system where user-defined questionnaires are displayed and a number of respondents submit their answers. Below is a sample JSON object of an answer:

{
  "fullname": "Some guy"
  "gender": male,
  "q1": true,
  "q2": false,
  "q3": true,
  "q4": false,
  "q5": true,
  "qualifications": ["Diploma","Degree"]
}

Now most developers could query results like this and be able to produce answer questions like

• What percentage of respondents answered TRUE to question 1?
• How many diploma holders are female?

I want to produce these answers without a developer being involved. Sure, I could just supply the raw data and let the users start making their own pivot tables in Excel, but even an Excel pivot table is describing the relationship of data. That is respondents where "qualifications" includes "Diploma", give a breakdown of gender.

I know I'm dipping into data science and mathematical models, but I'm not sure where's the best place to start.

How do I describe these relationships in software? What standards and tools exist? If I have the schema of data available, can I have the machine figure out the relationships (like making suggestions)?