Is there any way to solve this problem without calculation?

You can deduce three of the four options just by some common sense.

But what about the 4th one?

Do I need to calculate the SD?

Think about the “spread” of the numbers. Does the mean also give a clue?

spread is 30 though!

And the mean?

55

Does that give you a hint on what the standard deviation could be? Think about how it works from the formula.

Do I try to average out the 2 values ?

Which two values?

the average and the standard deviations?

I still don’t get any hint

OK. The mean is 55. If you take a look at what the formula is, it’s

\sqrt{\frac{(-20 - 55)^2 + (10 - 55)^2 + (40 - 55)^2 + (70 - 55)^2 + (100 - 55)^2 + (130 - 55)^2}{7}}

=\sqrt{\frac{75^2 + 45^2 + 15^2 + 15^2 + 45^2 + 75^2}{7}}

Show that this must be less than 75.

But at this point we can just calculate the SD I guess.

You can, but the point is to show that you don’t have to. That’s why the question suggested looking at the average instead.