Question

Find the standard deviation of the following data. Round your answer to one decimal place.

x	−5	−4	−3	−2	−1	0
P(X=x)	0.1	0.1	0.2	0.1	0.2	0.3

Answer 1

Solution:

x	P(x)	x * P(x)	x2 * P(x)
-5	0.1	-0.5	2.5
-4	0.1	-0.4	1.6
-3	0.2	-0.6	1.8
-2	0.1	-0.2	0.4
-1	0.2	-0.2	0.2
0	0.3	0	0
Sum	1	-1.9	6.5

Mean = X * P(X)

= -1.9

Standard deviation =

=X 2 * P(X) - 2

=  6.5 - (-1.9)2 = 2.89

Standard deviation = = 1.7