Distributions and Their Shapes

Examples, videos, and solutions to help Algebra I students learn how to use informal language to describe the shape, center, and variability of a distribution based on a dot plot, histogram, or box plot.

New York State Common Core Math Algebra I, Module 2, Lesson 1

Worksheets for Algebra 1

Lesson 1 Student Outcomes

• Students learn how to use informal language to describe the shape, center, and variability of a distribution based on a dot plot, histogram, or box plot.
  
• Students recognize that a first step in interpreting data is making sense of the context.
  
• Students make meaningful conjectures to connect data distributions to their contexts and the questions that could be answered by studying the distributions.

What is Statistics?

Statistics is all about data. Without data to talk about or to analyze or to question, statistics would not exist. There is a story to be uncovered behind all data - a story that has characters, plots, and problems in the data. The questions or problems addressed by the data and their story can be disappointing, exciting, or just plain ordinary! This module is about stories that begin with data.

Lesson 1 Summary

Statistics is about data. Graphs provide a representation of the data distribution and are used to understand the data and to answer questions about the distribution.

Example 1: Graphs

Data are often summarized by graphs; the graphs are the first indicator of variability in the data.

Dot plots: A plot of each data value on a scale or number line.

Histograms: A graph of data that groups the data based on intervals and represents the data in each interval by a bar.

Box plots: A graph that provides a picture of the data ordered and divided into four intervals that each contains approximately 25% of the data.

The data may be symmetric or skewed.

Exit Ticket

1. Sam said that a typical flight delay for the sixty BigAir flights was approximately one hour. Do you agree? Why or why not?
2. Sam said that 50% of the twenty-two juniors at River City High School who participated in the walkathon walked at least ten miles. Do you agree? Why or why not?
3. Sam said that young people from the ages of 0 to 10 years old make up nearly one-third of the Kenyan population. Do you agree? Why or why not?

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