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.