## Lesson 1.7 – Measuring Variability

• Find the range of a distribution of quantitative data.
• Find and interpret the interquartile range.
• Calculate and interpret standard deviation.

Activity: How many colleges are you applying to?

For this activity we did not want 30 pieces of data since we wanted to model the process for calculating standard deviation.  So each group of four created a list of
all the colleges they were applying to and reported the total.  This gave us 7 or 8 pieces of data per class.  Students used the class data to find quartiles in their groups.  Everything went fairly smoothly.

Calculating Standard Deviation

We tried going through the standard deviation portion two different ways.  Luke had his students work through calculating the standard deviation in their groups and he gave added guidance when needed.  Students struggled with this.  The directions need to be more scaffolded for this to work.  Lindsey used modeling and the think aloud strategy to use the definition to work through the calculations in front of the class.  Students did not complete this in groups, they just followed along with her work.  This was fairly successful but students still had quite a few questions on the steps.  They were really focused on being able to replicate the process instead of understanding what a standard deviation tells us.

Using the text

We also had students begin annotating the text in their groups.  Each person was assigned two pages of the section to read and annotate.  After their members finished, they shared with the rest of the group what they had learned.  Some really good discussions happened during this time.  The students took the task really seriously.  Using the document camera we showed the class what we had highlighted and annotated in our text so they could compare what they had done.  As we go through the year, we will be putting more of this responsibility on the students.

Application 1.7: Have we found the beef?

Overall, this application is pretty straight forward.  The only common mistake students made was trying to decide whether or not to include the middle number in each half of the data when they were looking for the quartiles without the applet.  Students used the iPads and the SPA applet to calculate standard deviation since we will not be requiring them to calculate this by hand.