Statistics

Lesson 4

Math

Unit 8

6th Grade

Lesson 4 of 14

Objective


Describe and analyze the overall shape of dot plots and histograms, including symmetry, skewness, outliers, and clusters.

Common Core Standards


Core Standards

  • 6.SP.A.2 — Understand that a set of data collected to answer a statistical question has a distribution which can be described by its center, spread, and overall shape.

Foundational Standards

  • 5.MD.B.2

Criteria for Success


  1. Understand that some distributions are symmetrical around a center, and some distributions show skewness toward higher or lower values.
  2. Understand that distributions can also congregate or cluster around certain values or they may contain outliers, which stand far from the rest of the data set.
  3. Describe the overall shape of data representations.
  4. Identify outliers and/or clusters in distributions of data.

Tips for Teachers


  • When it comes to skewness, it is less important for students to memorize the definitions of skewed left versus skewed right than it is for students to understand what skewness means about a data set. It is also a common misconception that skewed left means the “peak” of the mound sits to the left, when it is actually the “tail” that creates the skewness. 
  • Shodor Interactive has a Histogram tool that has some interesting data sets and histograms (such as NBA salaries and College SAT Math scores). You can change elements of the histogram as well, such as the interval range, in order to see how the graph changes. This could be useful to have students look at and analyze the shape of the graph.
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Anchor Problems


Problem 1

Three histograms are shown below.

a.   Describe the shape of each distribution and explain what it means about the data set. Which graph is skewed left? Skewed right? Symmetrical?

b.   If these histograms represented the wages that people at a company earned, which company would you want to work at? Why? (Assume the same scale in each graph.

Guiding Questions

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Problem 2

Many elections for public office are determined based on the results of a popular vote (the candidate who earns the most votes in the election wins). But, the election for the President of the United States is not determined by the popular vote. Instead, a process called the Electoral College is used, where each state receives a certain number of electoral votes, depending on the population of the state. 

The following table shows the number of electoral votes for each state. A dot plot graphically represents this information.

Table showing each state and the number of electoral votes it holds.

a.   Which state has the most electoral votes? How many votes does it have?

b.   Based on the given information, which state has the second highest population of citizens?

c.   What is the shape of the distribution shown in the dot plot: skewed left, symmetric, or skewed right? Explain your reasoning.

d.   Do you see any outliers or clusters in the data? Explain your reasoning and identify any states that represent outliers.

Guiding Questions

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References

Illustrative Mathematics Electoral College

Electoral College, accessed on April 3, 2018, 1:44 p.m., is licensed by Illustrative Mathematics under either the CC BY 4.0 or CC BY-NC-SA 4.0. For further information, contact Illustrative Mathematics.

Modified by Fishtank Learning, Inc.

Problem Set

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Target Task


Isabelle is interested in buying a new microwave. She narrows down her options to two different microwaves and looks at customer review scores of each one. The two histograms below show the distribution of review scores for each microwave, where 0 is the lowest score and 10 is the highest score.

a.   Describe the shape of the distribution for each microwave.

b.   Which microwave should Isabelle buy? Explain your reasoning using information from the histograms.

Student Response

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Additional Practice


The following resources include problems and activities aligned to the objective of the lesson that can be used for additional practice or to create your own problem set.

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Lesson 3

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Lesson 5

Lesson Map

A7CB09C2-D12F-4F55-80DB-37298FF0A765

Topic A: Understanding Statistics & Distributions

Topic B: Measurements of Center & Variability

Topic C: Box Plots & Circle Graphs

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