Losing weight can be a bit more complicated than calories in versus calories out and making sure expenditure is more than intake. This is because you must consider other factors besides food and consumption, and calorie burn and exercise. There are several genetic factors that play into your resting metabolic rate. For the same people who are the same height and same starting weight who follow the exact same diet and exercise routine, one might lose more weight than another because of genetics and their metabolism.
Still, the fact remains that there are 3500 calories in a pound of fat. So then, for all intents and purposes, you must be burning 3500 calories more than you are taking in, to lose a pound. To break this down over the course of a week (or 7 days), you would need to cut your daily intake by 500 calories (because 500 x 7 days equals 3500 calories) to lose a pound in a week. But if you are running, then you will be burning even more calories, meaning you will not have to slash your intake as much!
On average, you will burn roughly 100 to 120 calories per mile ran. However, again this depends on several factors- mainly, your pace (how fast you are running) and level of exertion and effort, and your own genetics and metabolism. You might have a very fast metabolism and a body that responds very well to exercise, burning closer to 130 calories per mile. Without having to go through scientific analyses and tests, though, you can estimate that you are burning 100 calories per mile, and then factor that into your 500-calorie decrease (if you are aiming to burn one pound per week). Adjust your intake and calorie decrease based on how fast you are looking to lose a pound (making sure that you are not trying to lose it TOO fast so that your body does not go into starvation mode or slow down your metabolism).