This may be a silly question but I am not really a math/statistics person and we are working on this assignment at work. So my job is to figure out what is the trend of the data from the last 30 days. So basically I get around 30 values, each is an average value from one day. And using this data I draw a linear graph. Now the difficult part for me, how do I know that mathematically that on average the trend is upward or downward? I can see it from the graph but how do I figure this out matematically?
Fit a smoother and obtain an estimate of the derivative. If this is negative over a certain range (30 days in your case), the trend is downward.
Look at Trend shifts in timeseries and pick up some pointers. Detecting trend is not accomplished by specifying a model or a derivative but by allowing the data to suggest the underlying model and then drawing inference. Auto-correlation , level shifts , error variance heterogeneity , outliers etc can easily thwart any simple strategy.