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

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:

$\bar{x}=\frac{2+4+6+0+1+10+9+0+6+3+6+8+5+4+6+2}{16}=\frac{72}{16} =4.5$

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

$\therefore Variance = \frac{140}{16}=8.75$