Statistics

Lesson 8

Math

Unit 8

6th Grade

Lesson 8 of 14

Objective


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

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.
  • 6.SP.B.5.D — Relating the choice of measures of center and variability to the shape of the data distribution and the context in which the data were gathered.

Criteria for Success


  1. Understand that the measures of center of a data set vary with the shape and distribution of the data set, and as a result, one measure of center may better represent the data set than others (MP.2).
  2. Determine which measure of center best represents a data set and justify the choice. 
  3. Determine the impact of adding or removing data on the measures of center.

Tips for Teachers


Lesson Materials

  • Calculators (1 per student)
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Anchor Problems

25-30 minutes


Problem 1

Bobbie is a sixth grader who competes in the 100-meter hurdles. In eight track meets during the season, she recorded the following times (to the nearest one hundredth of a second).  

18.11    31.23    17.99    18.25    17.50    35.55    17.44    17.85

a.   What is the mean of Bobbie’s times for these track meets? What does the mean tell you in terms of the context?

b.   What is the median of Bobbie’s times? What does the median tell you in terms of the context?

c.   Explain why the mean is higher than the median.

d.   Which measure of center do you think best represents Bobbie’s 100-meter hurdle time? Explain your reasoning.

e.   The two times that were over 30 seconds were times when Bobbie fell on a hurdle. She decides to take those times out to get a sense of her typical time without falling. What is the new mean? The new median? How do those compare to the original mean and median?

Guiding Questions

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Student Response

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References

Illustrative Mathematics Mean or Median

Mean or Median, accessed on April 3, 2018, 2:10 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 2

At the University of North Carolina (UNC) in the mid-1980's, the average starting salary for a Geography major was over $100,000 (equivalent to almost $300,000 today). 

At that same time, basketball star Michael Jordan was drafted into the NBA with one of the highest salaries in the league. He had just graduated from UNC with a degree in Geography.

a.   Explain why the mean is a misleading measure of center to represent the salary of geography students at UNC.

b.   What measure of center would better represent the salary of geography students at UNC? Explain your reasoning.

Guiding Questions

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Student Response

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References

Minitab Using the Mean in Data Analysis: It's Not Always a Slam-Dunk

Portions of information contained in this publication/book are printed with permission of Minitab Inc. All such material remains the exclusive property and copyright of Minitab Inc. All rights reserved.

Modified by Fishtank Learning, Inc.

Problem 3

The data set below represents the morning commute time of eight colleagues in an office on the same day. The mean of the data set is 32.5 minutes and the median is 38 minutes. 

45           32           38           20           5           40           38           42

There was a typo in the data set, and the input “5” was supposed to be “50.” The typo is corrected and the correct mean and median are found.

Without calculating, explain what impact the typo had on the mean and the median.

Guiding Questions

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Student Response

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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 number of siblings for a group of sixth-grade students is shown below. 

1    0    2    1    6    0    2    0    1    10

a.   Make a dot plot of the data.

b.   Find the mean, median, and mode of the data.

c.   Which measure of center do you think best represents the data? Why?

d.   Eight more students are asked how many siblings they have, and their data is added to the data set. Six of the eight students said they had 1 sibling, and two of the eight said they had 2 siblings. What is the new mean, median, and mode?

Student Response

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References

Illustrative Mathematics Average Number of Siblings

Average Number of Siblings, accessed on March 29, 2018, 1:14 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.

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.

  • MARS Summative Assessment Tasks for Middle School Suzi's Company
  • Inside Mathematics Problems of the Month Pick a Pocket(Note: this requires a data set that is collected from the class. You can either survey the class or provide a hypothetical data set for the students. There are 5 levels to this task, of increasing difficulty, all of which are appropriate for this lesson)

Next

Use the range and interquartile range to understand the spread and variability of a data set.

Lesson 9
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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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