Objectives
In this activity, you will describe the distribution of a statistic by observing its average value and variability between samples. Compare to the distribution of the variable in the population.
Assignment
Arrange yourselves into groups of 3 or 4. on the following activity. Write your answers in your own notes and add your data to the histogram at the front of the class.
Background
A standard deck of 52 playing cards consists of four copies each of the numbers 2 through 10, along with Jacks, Queens, Kings and Aces. In many games, it is important to track the point value of a hand of cards. Face cards (Jacks, Queens, and Kings) are usually treated as 10 points, while Aces are treated as 1 point. Number cards (2 - 10) are treated as the number shown.
Below is a distribution of the point values for standard deck of cards:

Activity
Each person should do the following:
- Thoroughly shuffle one of your group’s deck of cards.
- Draw 10 cards from the deck (without replacement) to form a sample.
- Compute the mean value of your cards (counting Aces as 1 and Faces as 10)
- Write the value of the mean on a sticky note and add it to the appropriate interval on the front chalkboard.
- Repeat steps 1 - 4 an additional four times. After you’ve used physical cards at least once, you may complete remaining shuffles using the random card shuffler at https://www.random.org/playing-cards/
Discussion
As a group, answer the following questions:
- What is the theoretical mean value for the data set of card values?
- How does the distribution of sample means compare to the distribution of card values?
- What is the relationship between the centers of the two distributions?
- Which distribution appears to have more variability?
- How do the shapes of the two distributions compare?
- What does the variability of sample means suggest about the means in repeated samples?