Question

Sixteen college freshmen were asked to record the number of alcoholic drinks they typically consume in a week. Here are their data: 2, 4, 6, 0, 1, 10, 9, 0, 6, 3, 6, 8, 5, 4, 6, 2. What is the variance of the number of alcoholic drinks consumed per week?

a.3.26
b.2.96
c.12.25
d.8.75

Answer 1

Solution: The correct option is d. 8.75

Step-by-step explanation:

The formula for variance is:

`Variance =\frac{\sum(x-\bar{x})^(2)}{n}`

First we need to find the mean
`\bar{x}` of the given data:

`\bar{x}=(2+4+6+0+1+10+9+0+6+3+6+8+5+4+6+2)/(16)=(72)/(16) =4.5`

Now let's find
`\sum(x-\bar{x})^(2)`, please have a look at the attached picture:

`\therefore Variance = (140)/(16)=8.75`