Lesson 6.2 – Sampling Distributions: Center and Variability
- Determine whether or not a statistic is an unbiased estimator of a population parameter.
- Describe the relationship between sample size and the variability of a statistic.
Activity: How many sticks are in the bag?
We begin our lesson by showing students a bag containing an unknown number of sticks. The sticks are numbered starting at 1. Take 5 sticks out of the bag and show students the numbers. In groups, the students should brainstorm different ways of estimating the total number of sticks in the bag. They should share out these ideas for statistics but then assign half of the class to use the statistic of 2 times the median or the maximum. Give each of the groups a bag with the same number of labeled sticks. Each group will take samples of 5 and calculate their assigned statistic. They will write the statistic on a sticker and add it to the dotplot at the board.
The goal of the lesson is to understand that there are different types of statistics and that some are good estimators and others are not. The notion that there are statistics other than mean, median and mode is itself a difficult concept for students to grasp. You’ll want to make sure to really hammer home the definition of a statistic as a number that describes a population. When students share out their ideas for estimating the number of sticks in the bag, continue to point out that they are all statistics. The dotplot is a great visual for students to understand that a biased estimator consistently under- or over-estimates a parameter.
Today’s activity is modeled after the German Tank Problem which is discussed in the application problem of the textbook. If you prefer to use the German tanks as the context for the activity there are lots of versions out there. This activity on the StatsMonkey is excellent.