Statistics

Lesson 7

Math

Unit 8

6th Grade

Lesson 7 of 14

Objective


Define and determine the mode of a data set.

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.

Criteria for Success


  1. Understand the mode of a data set is the value(s) or response(s) that appear most often in a data set or with the greatest frequency. 
  2. Understand that there may be more than one mode or no mode of a data set. 
  3. Determine the mode for data sets, including numerical and categorical data.

Tips for Teachers


  • The mode as a measure of center is not specifically called out in the Common Core Standards for Math, but it is mentioned in some state frameworks, such as the Massachusetts 2017 Math Frameworks.
  • This lesson is a good opportunity to continue to practice and build mastery with the other two measures of center.
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Anchor Problems

25-30 minutes


Problem 1

Find the mode of each data set shown below.

Data set A: Width of computer screens in inches
13     13     14.5     13.5     14     13     14.5

Data set B: Female foot length in cm
24    23.5    23.5    21    21    25.2    23    23.3

Data set C: Number of siblings

# of siblings Frequency
0 4
1 5
2 4
3 2
4+ 1

Guiding Questions

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Student Response

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Problem 2

Each of the 20 students in Mr. Anderson’s class timed how long it took them to solve a puzzle. Their times (in minutes) are listed below:

Student 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
Time (min) 3 5 4 6 4 8 5 4 9 5 3 4 7 5 8 6 3 6 5 7

a.   Display the data using a dot plot. 

b.   Find the mean, median, and mode of the data. Did you expect them to be the same values? Why or why not?

Guiding Questions

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Student Response

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References

Illustrative Mathematics Puzzle Times

Puzzle Times, accessed on April 3, 2018, 2:05 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

15-20 minutes


Give your students more opportunities to practice the skills in this lesson with a downloadable problem set aligned to the daily objective.

Target Task

5-10 minutes


The histogram below represents the number of minutes some students studied for a science quiz.

a.   How many students are represented in the histogram?

b.   Determine the median range of minutes that students spent studying for the quiz.

c.   Determine the mode range of minutes that students spent studying for the quiz.

d.   Explain why you cannot determine the mean number of minutes students studied for the quiz.

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.

  • Include examples where students are given data sets for statistical questions and they find the median, mean, and/or mode. Spiral in review of fraction and decimal computation. Avoid giving lists of numbers that don’t have a context or statistical question that accompanies them.
  • MARS Summative Assessment Tasks for Middle School Representing Variability with Mean, Median, Mode, and Range(Note: this includes finding the range of a data set. You can either give students a working definition of range for them to apply to this activity or take that part out of the practice. Students will investigate spread and variability in Lesson 9.)

Next

Determine which measure of center best represents a data set. Determine how measures of center change when data is added or removed.

Lesson 8
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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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