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)	0.2	0.1	0.1	0.2	0.2	0.2

Answer 1

Solution:

X	P(X)	X*P(X)	X^2*P(X)
0	0.2	0	0
1	0.1	0.1	0.1
2	0.1	0.2	0.4
3	0.2	0.6	1.8
4	0.2	0.8	3.2
5	0.2	1.7	5.5
Sum =	1	3.4	11

Mean :

$\mu$ = $\sum$ X * P(X)

= 3.4

Standard deviation:

$\sigma$ = $\sqrt{}$ $\sum$ X² * P(X) - ($\mu$)²

= $\sqrt{}$ 11 - ( 3.4 )²

= $\sqrt{}$ -0.56

= 0.7