Curriculum / Math / 6th Grade / Unit 8: Statistics / Lesson 4
Math
Unit 8
6th Grade
Lesson 4 of 14
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Describe and analyze the overall shape of dot plots and histograms, including symmetry, skewness, outliers, and clusters.
The core standards covered in this lesson
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.
The foundational standards covered in this lesson
5.MD.B.2 — Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally.
The essential concepts students need to demonstrate or understand to achieve the lesson objective
Suggestions for teachers to help them teach this lesson
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Problems designed to teach key points of the lesson and guiding questions to help draw out student understanding
25-30 minutes
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.
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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.
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.
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.
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15-20 minutes
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A task that represents the peak thinking of the lesson - mastery will indicate whether or not objective was achieved
5-10 minutes
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.
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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Define and determine the mean of a data set.
Topic A: Understanding Statistics & Distributions
Define and identify statistical questions.
Standards
6.SP.A.16.SP.B.5.A
Describe data that is represented in a dot plot. Represent data using dot plots and frequency tables.
6.SP.B.46.SP.B.5.A
Represent data using histograms.
6.SP.B.4
6.SP.A.2
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Topic B: Measurements of Center & Variability
6.SP.A.26.SP.B.5.C
Define and determine the median of a data set.
Define and determine the mode of a data set.
Determine which measure of center best represents a data set. Determine how measures of center change when data is added or removed.
6.SP.A.26.SP.B.5.D
Use the range and interquartile range to understand the spread and variability of a data set.
Understand and determine mean absolute deviation (MAD) as a measure of variability of a data set.
6.SP.B.5.C
Compare measures of center and measures of spread to describe data sets.
6.SP.A.3
Topic C: Box Plots & Circle Graphs
Represent data using box plots.
6.SP.B.46.SP.B.5
Analyze box plots and other representations, and summarize numerical data in context.
Analyze circle graphs in context.
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