## Learning Math: Data Analysis, Statistics, and Probability

# Min, Max and the Five-Number Summary

## Investigate various approaches for summarizing variation in data, and learn how dividing data into groups can help provide other types of answers to statistical questions. Understand numerical and graphic representations of the minimum, the maximum, the median, and quartiles. Learn how to create a box plot.

Sessions 2 and 3 explored different ways to organize data in order to draw out patterns in the variation. In these sessions, we investigated a variety of approaches to organizing data in graphs and tables and examined some of the different ways we can answer statistical questions, based on these representations.

**In This Session**

**Part A:**Min, Max, and the Two-Number Summary

**Part B:**The Median and the Three-Number Summary

**Part C:**Quartiles and the Five-Number Summary

**Part D:**The Box Plot

**Finding the Five-Number Summary Numerically**

Part E:

Part E:

**Homework**

In this session, we will explore how dividing data into groups can give us yet another way to answer statistical questions. See Note 1 below.

**Learning Objectives**

The goal of this session is to learn how dividing data into groups can help us provide other types of answers to statistical questions. In this session, you will learn how to do the following:

- Understand the median as the value that divides the ordered data into two groups, with the same number of data values (approximately one-half) in each group
- Understand quartiles as the values that divide the ordered data into four groups, with the same number of data values (approximately one-fourth) in each group
- Investigate the concept of quartiles using several different representations
- Summarize an entire data set with a Five-Number Summary
- Summarize an entire data set with a box plot

### Key Terms

**Previously Introduced:**

**New in This Session:**

box plot

Five-Number Summary

interquartile range

midrange

quartiles

summary measures

Three-Number Summary

Two-Number Summary

### Notes

**Note 1
**This session relies on a hands-on activity using spaghetti noodles. Gather the necessary materials before beginning the session.