Measuring Variability (Lesson 1.7)
Chapter 1 - Day 8
Find the range of a distribution of quantitative data.
Calculate and interpret the standard deviation.
Find and interpret the interquartile range.
To start, let students talk in groups of 4 about which colleges and trade schools they will be applying to and why. Then students will total up the number of schools for their group of 4 and record the value on the board. The reason we decided to group data here is that we don’t want to calculate standard deviation using 30 values…7 or 8 will do just fine.
It might be helpful to calculate the mean as a whole class so that all groups have the correct value for later calculations.
In the activity, students calculate range, interquartile range, and standard deviation without knowing the vocabulary or formula. When you debrief the activity, you will help students by providing them with the vocabulary term for each measure of variability along with helping to build the formulas for each.
The standard deviation that students calculate here will be slightly different than what they see in the applet, because students divided by n instead of n – 1. Anytime your data comes from a sample, divide by n – 1. Anytime your data comes from the whole population, divide by n. The applet automatically assumes that the data is coming from a sample.
The main purpose of having students calculate standard deviation by hand is not the final answer, but for them to gain an understanding of what standard deviation is measuring. It is measuring the typical distance from the mean for all of the values in a data set. It is our strong recommendation that from this point forward, you do not have students calculate standard deviation by hand. It is very easy to use this applet or a graphing calculator to find the standard deviation.
A quick note about notation: s is the standard deviation of a sample, the Greek lowercase symbol σ is the standard deviation of a population.