# The following data show the number of hours of sleep attained during a recent night for a sample of 20 workers: 6,5,10,5,6,9,9,5,9,5,8,7,8,6,9,8,9,6,10,8. What is the mean? What is the variance? What is the standard deviation?

##### 1 Answer

Mean = 7.4

Standard Deviation

Variance = 2.94

#### Explanation:

The **mean** is the sum of all the data points divided by number of data points. In this case, we have

The **variance** is *"the average of the squared distances from the mean."* http://www.mathsisfun.com/data/standard-deviation.html

What this means is you subtract every data point from the mean, square the answers, then add them all together and divide them by the number of data points. In this question, it looks like this:

We add a 4 in front of the brackets because there are four 5's in this data set. We then do this to the rest of the numbers:

The last step is to add them all together and then divide them by how many there are, which looks like this:

The **standard deviation** is easy, it is simply the square root of the variation, which is

I hope I helped!