OK
The beta isn't given on a graph, it's a figure inside a range.
They don't vary widely, and they've got better over the years, but each device is different. [There are such things as "matched pairs", more expensive, and matched quads in DIP/IC packages.]
Designers assume maybe the "typical" or work with the specified "minimum", when beta is important. Avoid "beta critical" designs.
Some "rule of thumb" figuring:
Collector current cannot be greater than base current * beta
You can back figure beta by determining where collector current starts to poop as base current is decreased.
With a "common emitter" circuit, base current = (input voltage - V_be) / base resistor).
Collector current (Max) = Vcc / (base current * beta). Your design demand should be less than "max".
A transistor isn't a perfect conductor, that's why it's called a "semiconductor"; there is a voltage drop from collector to emitter (V_ce) - as current increases, V_ce increases. So, be prepared to take that into account. In our "common collector" circuit, V_cc gets divided amongst the LED, the resistor, and across the collector-emitter junction.
Emitter current = base current + collector current
(When collector current is much more than base current, I_c approx = I_e)
So, some transistor has a beta of 50. If it's actually more than that, that's OK.
Let's say the goal is 50 mA collector current.
If everything was ideal we could go with 1mA base current, but anticipate more. With 2mA, then 100 mA collector current is possible, but that's "capacity" kept in reserve, a buffer, it's room to spare.
More base current than necessary should be provided while not over-doing it. That's a "judgement call". 2X? 4X? (V_ce * I_e) < P_d.
That's a presentation in a nutshell, but I think it sheds some light on the matter.