Explanation:
the standard deviation is the square root of the sum divided by the number of data points of the squares of the individual differences to the mean value.
so, first we need the mean value.
that is the sum of all data points divided by the number of data points :
(4+7+10+12+16+17)/6 = 66/6 = 11
the sum of the squares of all individual differences to the mean value is
(4-11)²+(7-11)²+(10-11)²+(12-11)²+(16-11)²+(17-11)² =
= (-7)²+ (-4)² + (-1)² + 1² + 5² + 6² =
= 49 + 16 + 1 + 1 + 25 + 36 =
= 128
that divided by the number of data points is
128/6 = 21.333333333...
and the square root of that is the standard deviation
4.618802154... ≈ 4.62