Question

Consider the following data:

x	5	6	7	8	9
P(X=x)P(X=x)	0.30.3	0.1	0.1	0.3	0.2

Copy Data

Step 2 of 5 :

Find the variance. Round your answer to one decimal place.

Answer 1

Solution:
For variance, first, we will calculate the mean of the distribution as follows
Mean = xi*P(xi) = 5*0.3 + 6*0.1 + 7*0.1 + 8*0.3 + 9*0.2 = 1.5+0.6+0.7+2.4+1.8 = 7

X	P(X)	X*P(X)
5	0.3	1.5
6	0.1	0.6
7	0.1	0.7
8	0.3	2.4
9	0.2	1.8

The variance of the distribution is given as follows:
Variance = (Xi-mean)^2 * P(Xi) = (5-7)^2*0.3 + (6-7)^2*0.1 + (7-7)^2*0.1 + (8-7)^2*0.3 + (9-7)^2*0.2 = 1.2+0.1+0+0.3+0.8 = 2.4
Variance = 2.4

X	P(X)	X*P(X)	Xi-mean	(Xi-mean)^2	(Xi-mean)^2 *P(Xi)
5	0.3	1.5	-2	4	1.2
6	0.1	0.6	-1	1	0.1
7	0.1	0.7	0	0	0
8	0.3	2.4	1	1	0.3
9	0.2	1.8	2	4	0.8