Statistical analysis searches for the confidence to report trends or failures to meet trends. Basically, you should ask ... When and how does a change in variable Y correlate with a change in variable X? Now, make variable Y and variable X relatable to real world events. Even as you are saying ... not my area of expertise ... you might already be aware of these "trends" ...
Cold + dry, cold + damp, wet + hot, and hot + dry are associations made about weather conditions. How would you establish whether and when these associations are reasonable statements within statistical confidence levels?
High pressure fronts bring calm weather. Low pressure fronts bring ... Are these statements true? To what confidence level?
Take an umbrella with you, because it certainly "smells" like it is going to rain. How would you prove this advice is statistically valid?
What other weather related insights have you gathered as a layman that could be proven as valid or as gossip by a good go-around with statistical analysis on a large data set?