Calculate measures of center (mean, median) for a distribution of quantitative data.
Calculate and interpret measures of variability (range, standard deviation) for a distribution of quantitative data.
Explain how outliers and skewness affect measures of center and variability.
Activity: How Many Colleges Are You Applying To?
Today we tackle some of the scariest words in statistics, STANDARD DEVIATION MUAHAHAHAHHAHA!
That is one scary formula. Now to those of us who teach statistics, standard deviation is not scary at all. In fact, we love it! It’s tells us all about how a distribution might look. It’s way better than range. We get to use it to make z-scores and without which we could do very little in this course. It’s not scary to us because we get it. We understand that the very intimidating formula is really just telling us the average distance from the mean. So how do we get students to not run away crying when they see a summation? Well first off, don’t show them the formula! Students need to experience standard deviation before they formalize. So we’re going to have students think through how they would calculate the average distance from the mean.
Begin by having students in groups of 4. Give them a few minutes to figure out a list of all the colleges the group is applying to. They will share the group total with the class. We want a small data set so the calculations don’t get out of control. Once the class data is collected, students should be able to work through the rest of the activity without teacher input but you may want to model the first row for them. At this point you should talk about why we square the distance from the mean. (We want to get rid of the negatives) What would happen if we didn’t square it? (The average would be approx. 0)
After students work through the table and calculate the standard deviation, they should go to stapplet.com to enter the data and find the standard deviation. They’ll see that this is slightly larger than what they calculated. This is because they need to divide by n – 1 instead of by n. Point this out to them and add the formula for standard deviation to the margin, writing it as you think aloud about the process you’ve used for calculating.
Lastly, we need to add in an outlier. We want to see how an outlier affects the mean, median and standard deviation. Tomorrow we will look at IQR as well and will tie this all together.
***You may want to change the name in #6 to your name from Mrs. Gallas. Unless, of course, you’d like to make Mrs. Gallas into a statistics celebrity. That’d be cool too.***
By the way, we know squaring the distance, dividing and then square rooting isn’t technically the same as finding the average distance from the mean, but that’s ok. Students don’t need to know that. What they need is to have a good understanding of what standard deviation is telling them.
Luke's Lesson Notes
Here is a brief video highlighting some key information to help you prepare to teach this lesson.