**Learning Targets**

**Describe the effect of adding or subtracting a constant or multiplying or dividing by a constant on the probability distribution of a random variable.**

Quick Lesson Plan |
Time |

Activity | 20 minutes |

Debrief Activity | 10 minutes |

Big Ideas | 10 minutes |

Check Your Understanding | 10 minutes |

**Activity: Time for a Raise**

**Download Word | pdf | Answer Key **

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).

**Teaching Tips **

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.

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