Question

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

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

Answer 1

Here we have data:

X	P(X = x)	X * P(X = x)	( x - μ)^2	( x - μ)^2 * P(X = x)
0	0.2	0	6.25	1.25
1	0.2	0.2	2.25	0.45
2	0.1	0.2	0.25	0.025
3	0.1	0.3	0.25	0.025
4	0.2	0.8	2.25	0.45
5	0.2	1	6.25	1.25
SUM		2.5		3.45

Mean:

= 0 + 0.2 + 0.2 + 0.3 + 0.8 + 1

= 2.5

Variance:

= 1.25 + 0.45 + 0.025 + 0.025 + 0.45 + 1.25

= 3.45

Standard deviation:

= SQRT(3.45)

= 1.9