What does the distribution of the years found on pennies look like? What does the distribution of the mean year of a sample of pennies look like? The famous jar of pennies makes its appearance every semester in STAT 216: Statistics I to help students answer this question. This semester was no different.
In Prof. Kang‘s class, students sampled pennies from the jar to try to get some intuition about the distribution of dates. What is a typical year for a penny? How much variability is there?
Follow bucknell.math.stat on Instagram!
Students plotted the distribution of the years on their random sample of 25 pennies either using technology (left) or physically by making a histogram of pennies (right). Want a refresher on what a histogram is? Check out this interactive visualization that shows how they are built.
Th penny activity all leads up to learning about one of the most important concepts of the class, the sampling distribution. This is a distribution of a sample statistic (summary of a sample) across multiple samples of the same size. Here we want to know what the distribution of the *mean* year of pennies is for a sample of size 25 (below, left). How does that change if we take smaller samples of size 5 (below, right)?
To visualize the sampling distribution, students create post-it note histograms on the board. Each post-it note has one student’s sample statistic (mean year of their sample of pennies).
What do you notice about the center of both of these sampling distribution? What about the variability? What about the shape? The answers to these questions involve the Central Limit Theorem, another big concept of the course. Students who continue on in statistics and mathematical economics get to prove the Central Limit Theorem later on in their course work (shout out STAT 304: Statistical Inference Theory).
Many sections of Stat I are offered every year, and the class serves students across campus. It is a required class for majors in accounting & finance (or they can take Calculus I), business analytics, biology, economics, mathematical economics, and statistics and is an option for majors in animal behavior, geosciences, and psychology.
The instruction approach for this class follows the American Statistical Association’s Guidelines for Assessment and Instruction in Statistics Education (GAISE guidelines). We emphasize the importance of communicating findings precisely yet accessibility, and use technology to tackle real-world datasets. This class is also a part of Bucknell’s writing across the curriculum program as a writing in the discipline class. Throughout the semester students work both individually and in teams on drafting and revising reports that answer statistical questions on real data.
Connect to Department of Mathematics and Statistics at Bucknell University on LinkedIn.
Are you an alum who took 216? We’d love to hear about what that experience was like for you, so reach out on LinkedIn! Want a chance to be featured in a future blog post? Respond to our question of the week here, and your answer may be chosen for a future post.