I am having a hard time finding what is the standard deviation.

Question

A student provided the following probability distribution that shows the distribution of the random variable:

X = The number of pets per household for CBC students

X	P(X)
0	0.47
1	0.25
2	0.18
3	0.06
4	0.02
5	0.02

Calculate the standard deviation of the number of pets for a CBC student. Round your answer to two decimal places.

Answer 1

You need to calculate the mean before you can calculate the std. dev., so first do that, and since you're given a probability distribution, to find the mean you need to multiply each value of "X", by its corresponding P(X), then add them all together.

Then to calculate the std. dev. (and this won't be fun):

1) for each value of X, compute the difference between of X and the mean

2) then square each of the differences you computed in step 1)

3) multiple each squared deviation by it's corresponding probability[P(X)], and then add them all together,

and finally,

4)take the square root, this is the std. dev.

I suggest: You just add columns for the following: X-mean, (x-mean)², P(X), and [(x-mean)²x P(X)], to the table they gave you (helps to keep all you number's straight & go back & check, if needed). Also, add 1 row for the "SUM", so you can just add the last column, and take the square root to get you answer.