Curriculum / Math / 6th Grade / Unit 8: Statistics / Lesson 8
Math
Unit 8
6th Grade
Lesson 8 of 14
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Determine which measure of center best represents a data set. Determine how measures of center change when data is added or removed.
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.
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.
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Problems designed to teach key points of the lesson and guiding questions to help draw out student understanding
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?
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.
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.
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.
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.
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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?
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.
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.
Lesson 7
Lesson 9
Topic A: Understanding Statistics & Distributions
Define and identify statistical questions.
6.SP.A.1 6.SP.B.5.A
Describe data that is represented in a dot plot. Represent data using dot plots and frequency tables.
6.SP.B.4 6.SP.B.5.A
Represent data using histograms.
6.SP.B.4
Describe and analyze the overall shape of dot plots and histograms, including symmetry, skewness, outliers, and clusters.
6.SP.A.2
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Topic B: Measurements of Center & Variability
Define and determine the mean of a data set.
6.SP.A.2 6.SP.B.5.C
Define and determine the median of a data set.
Define and determine the mode of a data set.
6.SP.A.2 6.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.4 6.SP.B.5
Analyze box plots and other representations, and summarize numerical data in context.
Analyze circle graphs in context.
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