Transforming Random Variables
Day 55 - Lesson 6.2
Describe the effect of adding or subtracting a constant or multiplying or dividing by a constant on the probability distribution of a random variable.
Activity: Time for a Raise
We are using the same “hourly wage” context that we used in yesterday’s lesson. You will need the hourly wage distribution data from yesterday. Today, the students will get a raise. They have to decide whether they would rather have their hourly wage increased by $10 or doubled (more importantly, what happens to the hourly wage distribution in each scenario).
The rules for means from this lesson are fairly intuitive. If we add 10 to every value in a distribution, we add 10 to the mean. If we double every value in a distribution, we double the mean.
The rules for standard deviation require a bit more reasoning. If we add 10 to every value in a distribution, the standard deviation does not change. If we double every value in a distribution, the standard deviation doubles (what happens to the variance?) A nice easy way to help students understand the rules for standard deviation is to look at a much simpler measure of variability: the range. When we add 10 to every value, the range stays the same: 25-1=24 to 35-11=24. When we double every value, the range doubles: 25-1=24 to 50-2=48.
You may also want to remind students that we have already talked about transforming data back in Lesson 2.1. The only difference here is that we have a discrete probability distribution rather than a list of numbers.