Question

find the standard deviation of the following data. Round your answer to one decimal place. x −3 − 3 −2 − 2 −1 − 1 0 0 1 1 2 2 P(X=x) P ( X = x ) 0.1 0.1 0.1 0.1 0.1 0.1 0.2 0.2 0.3 0.3 0.2 0.2 Copy Data

Answer 1

Solution:

The formula for the standard deviation for the probability distribution is given as below:

Standard deviation = Sqrt[∑[P(X)*(X - mean)^2]]

Where, mean = ∑XP(X)

The calculation table is given as below:

X	P(X)	XP(X)	P(X)*(X - mean)^2
-3	0.1	-0.3	0.961
-2	0.1	-0.2	0.441
-1	0.1	-0.1	0.121
0	0.2	0	0.002
1	0.3	0.3	0.243
2	0.2	0.4	0.722
Total	1	0.1	2.49

Mean = ∑XP(X) = 0.1

Standard deviation = Sqrt[∑[P(X)*(X - mean)^2]]

Standard deviation = Sqrt(2.49)

Standard deviation = 1.577973384

Standard deviation = 1.6