Curriculum / Math / 6th Grade / Unit 8: Statistics / Lesson 5
Math
Unit 8
6th Grade
Lesson 5 of 14
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Define and determine the mean of a data set.
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.C — Giving quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered.
The foundational standards covered in this lesson
6.NS.B.2 — Fluently divide multi-digit numbers using the standard algorithm.
6.NS.B.3 — Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation.
The essential concepts students need to demonstrate or understand to achieve the lesson objective
Suggestions for teachers to help them teach this lesson
In Lessons 5–7, students will learn about three measures of center: mean, median, and mode. In Lesson 8, students will determine which measure of center best represents a data set given various circumstances.
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Problems designed to teach key points of the lesson and guiding questions to help draw out student understanding
A company hires five people for the same job for one week. The amount that each person is paid for the week is shown in the table below.
Person D states that the payments are not fair since each person is doing the same job and brings the same set of skills to the job. Everyone agrees that they should all get paid the same amount.
How much should each person get paid so that everyone gets the same amount? Assume that the company will spend the same amount as it currently is.
After finding the average or fair share payment for each person, Person E decides to not take the job because they would be making less money.
a. If Person E leaves, then what is the new average payment of persons A–D?
b. What impact did Person E leaving have on the average payment?
The company asks the five people how many hours each person worked that week to complete the job. The results are shown in the table below.
What is the mean, or average, number of hours worked by a person last week?
A task that represents the peak thinking of the lesson - mastery will indicate whether or not objective was achieved
The dot plot below shows the numbers of miles that sixth grade students live from their school.
What is the average number of miles that this group of sixth graders live from school?
An example response to the Target Task at the level of detail expected of the students.
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 4
Lesson 6
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
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.
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.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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