Before jumping right in, let me clarify the title: Working the punching bag can provide the best tradeoff between cardio and strength training - This was not meant to imply that working the bag would make you stronger than doing squats with 500 lbs or that it would give you better endurance than running 5 miles a day. Punching bags provide a very effective way to achieve both goals in a very short amount of time.

The Cardio Aspect:
To begin, try standing in one place and throwing one jab a second for a full minute. A jab should be quick and make a popping sound upon bag impact. This should not be a strong punch like the cross; the jab is only meant to stun your opponent and set up future punches. After a full minute of jabs, rest and try it for two minutes, and then try "dancing" around the bag for a minute while jabbing approximately once every second for a minute. You'll notice that you start to sweat pretty quickly and simple normally overlooked actions such as miniscule jabs can be quite taxing and give you quite the workout. Try a 1 minute session standing still for warming up, followed by a 2 minute session with circling the bag. Rest a minute and repeat.

The Strength Aspect:
Throw two jabs, a cross and circle the bag. The cross should be a very strong punch where you use your whole body weight to strike the bag, pivoting off your opposite foot. So if you're a righty, your left foot should pivot. Try two sessions of 3 minutes each, just landing strong solid punches while still remembering to circle the bag. We are after strength so try to really push through all of your punches.

Mix it Up:
To completely exhaust you, try a final 3 minute session that combines cardio and strength methodologies. Throw three, or four jabs followed by a cross, hook, uppercut combination. Really explode on the bag while still being safe; contact the bag aiming for the flat part of your your middle finger and pointer (not your knuckles). Yes, you will get a great workout either way, but it's always better not to break your hand. If you can last a full three minutes, you're in great shape.

So the whole workout is less than 15 minutes and you expend much more energy than you would running. I'm not going to give you numbers here since there is a bit of range depending on the source, but google "calorie burn activity chart" and compare boxing to the other activities. You'll notice that it's towards the highest calorie burn activities, considerably more intensive than running.