How to read/determine trend from a line graph?

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? • To address your specific question: you regress your variable of interest against time and check if the slope is positive or negative. But that's frequently not the best way to analyse time series data, especially if you have unusual trends like those in the plot above. – mkt Aug 30 '17 at 14:36
• (1) The plot is extremely deceptive because it compresses most of the month in the left half and uses the right half to show just five days. (2) It doesn't look like a good idea to describe this behavior as a "trend" when there basically was no change for 29 days and then a sudden drop in the last day. Why not describe exactly what happened? – whuber Aug 30 '17 at 17:23
• whuber's observations are spot on. The first thing I would want to know is whether the collapse of the series in the last day is a real value or an error in recording and, thus, should be dropped. If the former and assuming you have additional information or features about this data, then consider decomposing the series into two components: 1) an analyzable trend component for the first 29 days where a simple regression model or spearman correlation would help define its directionality and 2), a second model predicting the probability of collapse given the previous history. – Mike Hunter Aug 30 '17 at 17:49
• Wrt the second model and assuming the collapse is real, there could be something cyclical going on. In that case, having more data going back more a single month would not only be useful but necessary as a single month won't be the least bit informative. – Mike Hunter Aug 30 '17 at 17:50
• In agreement with others: the simple but crucial question that must be answered first is what happened at the end of the series. If there isn't independent evidence explaining that, then it's hard to know how to describe the data except by showing the graph and declaring a mystery. Fitting a complicated model to 30 values would be a real stretch here: either it quantifies the obvious, or it is dubious. – Nick Cox Aug 30 '17 at 18:01