There's a lot of very useful info already mentioned by both buffalowings and joshtik1. I do agree in many ways that there's a huge gap between a BI/data analyst vs a data scientist just as there is a gap between a financial analyst and a quant.

Many companies don't have enough data, don't have a proper data science team and have no idea what to do when they have the data/insight. Also many leaders forget how important business or cross functional knowledge is in a data science team. We used to collect a lot of production/operational data in the oil and gas industry but we needed deep hydrocarbon/well engineering knowledge to make sense of it.

As mentioned already, you don't need a masters to jump into this. Data science is one of those fields where you can legitimately practice on your own. Download data from NYC open data and start experimenting!