Set A {3,3,3,4,5,5,5} has a standard deviation of 1.

Variance = (sum of (squares of difference of each number from mean )) / total number of numbers
Standard deviation = sqrt Variance

When we multiply all the numbers by something then while calculating the standard deviation we can take out that thing common and new standard deviation will be equal to value by which we multiplied all the number* old standard deviation.

Ex:
Suppose we have 4 entries a,b,c,d and suppose the mean is m
Then standard deviation = sqrt { { (a-m)^2 + (b-m)^2 + (c-m)^2 + (d-m)^2 } / 4 }

Now we multiply all the number by 4
so the new set will be 4a, 4b, 4c, 4d the new mean will be 4a + 4b+ 4c+ 4d /4 = 4 *( (a+b+c+d) /4 ) = 4m

Standard Deviation = sqrt { { (4a-4m)^2 + (4b-4m)^2 + (4c-4m)^2 + (4d-4m)^2 } / 4 }
sqrt {4^2} *sqrt { { (a-m)^2 + (b-m)^2 + (c-m)^2 + (d-m)^2 } / 4 }

= 4 * old standard deviation

So, Answer will be C
Hope it helps!

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