Question

14 teachers after you were surveyed about the music listening habits. Here is their data in HOURS:

0,0,0.5,0.5,0.5,1,1,1,1,1,3,4,6,8.5
Use a calculator to calculate the following standard deviation of this data. What is the value? The standard deviation of U is 1.9 hours. Compare the standard deviation you calculated for teachers with that of students. What does that mean about the distribution for teachers vs. students? ​

Answer 1

Using a calculator, you should get a sample standard deviation of approximately 2.5 hours

If you want to find the standard deviation by hand, you need to do the following steps

1. Find the mean mu
2. Subtract each data value from the mean to get (x-mu)
3. Square each result from step 2, so we now have (x-mu)^2
4. Add up each square from the previous step
5. Divide that result over n-1. In this case n = 14 is the sample size. This computes the sample variance.
6. Finally, apply the square root to get the sample standard deviation.

The teacher data set has a sample standard deviation of roughly 2.5 hours; compare this with the sample standard deviation of the students 1.9 hours, and we see that the teacher data set is more spread out. The larger the standard deviation is, the more spread out the data set will be.