How to quantify increasing nature of dataset

There is a call center which records the number of complaints against a service on daily basis.

For example, the values below show the number of complaints in a month

01,02,03,04,05,06,07,08,09,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30

05,06,07,05,05,04,05,04,07,08,07,08,06,07,07,06,08,08,09,11,12,11,07,13,13,15,16,18,19,21


I am not trying to estimate anything here. By looking at the graph i can see that the overall values are increasing from right to left. I don't know much statistics other than mean, median, mode so i phrased it as "increasing nature". I want a single numeric value (e.g. standard deviation) which would let me know if it is a straight horizontal line or going downwards or going upwards from left to right.

For example, suppose there is a function XYZ (which i am looking for) which receives this dataset and returns a numeric value from 0 to 100. 0 means the highly decreasing nature, 50 means straight line and 100 means highly increasing nature. If the graph is increasing and decreasing symmetrically across a horizontal line then the result would be 50 (as an average of increasing and decreasing natures). If the graph has more increasing nature then decreasing then the result would be > 50 and vice versa. Following are some sample graphs

Question: How can I quantify increasing nature of this given data?

• "quantify it's increasing nature" is incredibly vague. What do you mean by that? Are you trying to answer "is this increasing or could it just be ephemeral noise?" or are you trying to estimate the overall rate at which it's increasing or decreasing? or are you trying to get a smooth trend? Or are you trying to model it more generally (so you can answer questions like "is it higher on Mondays?)? – Glen_b Sep 19 '17 at 6:19
• @Glen_b I am not trying to estimate. If you look at the graph the overall values are increasing from start to end. I don't know much statistics other than mean, median, mode so i phrased it as "increasing nature". I want a single numeric value (e.g. standard deviation) which would let me know if it is a horizontal line or increasing from left to right. You are most welcome to edit the question and phrase it correctly or tell me how should i phrase it – bjan Sep 19 '17 at 6:30
• It looks like you really do want to estimate a trend. You could do this with linear regression, estimating its slope and testing that it is statistically greater than 0. To my eye it looks like it has curvature and so you could fit the regression as a quadratic function of months and test the significance of the linear and quadrartic terms. – Michael Chernick Sep 19 '17 at 6:56
• "which would let me know if it is a horizontal line or increasing from left to right" ... but you already stated it "was increasing from start to end"... it's not clear what more than that you need -- if you can see that, why would a number make a difference? What about the possibility that (a different set of data) is neither increasing from left to right nor a horizontal line; perhaps it decreases a bit then increases for example - what should it tell you then? Some additional clarity on the kind of information you seek would help. ... ctd – Glen_b Sep 19 '17 at 6:57
• ctd... You don't need to know statistics (indeed it would be preferable if you avoided trying to couch anything in statistical terms) -- just describe in plain English the question(s) you're trying to answer. – Glen_b Sep 19 '17 at 6:59