Curriculum / Math / 7th Grade / Unit 7: Statistics / Lesson 4
Math
Unit 7
7th Grade
Lesson 4 of 9
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Analyze data sets using measures of center and measures of variability
The core standards covered in this lesson
7.SP.B.3 — Informally assess the degree of visual overlap of two numerical data distributions with similar variabilities, measuring the difference between the centers by expressing it as a multiple of a measure of variability. For example, the mean height of players on the basketball team is 10 cm greater than the mean height of players on the soccer team, about twice the variability (mean absolute deviation) on either team; on a dot plot, the separation between the two distributions of heights is noticeable.
7.SP.B.4 — Use measures of center and measures of variability for numerical data from random samples to draw informal comparative inferences about two populations. For example, decide whether the words in a chapter of a seventh-grade science book are generally longer than the words in a chapter of a fourth-grade science book.
The foundational 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.A.3 — Recognize that a measure of center for a numerical data set summarizes all of its values with a single number, while a measure of variation describes how its values vary with a single number.
The essential concepts students need to demonstrate or understand to achieve the lesson objective
Suggestions for teachers to help them teach this lesson
This lesson is approaching standards 7.SP.3 and 7.SP.4. It reviews concepts from sixth-grade standards 6.SP.2 and 6.SP.3 in preparation for comparing populations in Topic C.
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Problems designed to teach key points of the lesson and guiding questions to help draw out student understanding
Two dot plots are shown below. One dot plot shows student scores on a recent math quiz. The other dot plot shows the ages of people on a field trip
For each dot plot,
a. Find the mean value.
b. Find the median value.
c. Determine which measure of center best represents the typical value in the data set and explain your reasoning.
The cost of items can vary based on where the items are sold. The table below shows the price of the same loaf of bread that is sold at 6 different stores in a neighborhood.
a. Find the mean absolute deviation of the price of this bread in this neighborhood, based on these six stores.
b. A different neighborhood sells the same loaf of bread at several stores. The MAD of the price of bread is 0.65. Do the prices of the loaf of bread vary more or less in this neighborhood compared to the neighborhood in part A? Explain your reasoning.
A teacher recorded the time, in minutes, it took students in two different classes to complete a recent math test. He represented the data in two dot plots, one for each class.
a. Find the median amount of time, in minutes, it took students from each class to complete the math test.
b. Which class had the least variability in their completion time? Find the interquartile range to support your answer.
A set of suggested resources or problem types that teachers can turn into a problem set
Give your students more opportunities to practice the skills in this lesson with a downloadable problem set aligned to the daily objective.
A task that represents the peak thinking of the lesson - mastery will indicate whether or not objective was achieved
While waiting for their bus to arrive after school one day, 10 students wondered how many baskets from the free-throw line they could each make in 5 minutes. Each student took their turn. The results are shown below:
14, 8, 12, 6, 20, 26, 9, 6, 11, 12
a. Find the mean and median number of baskets made by the students.
b. Which measure of center better represents the typical number of baskets made?
c. Ten players on the co-ed basketball team determined the number of baskets they could make from the free-throw line in 5 minutes. The interquartile range of their data set was 3. Which data set has the greater variability?
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 3
Lesson 5
Topic A: Understanding Populations and Samples
Understand and identify populations and sample populations for statistical questions.
7.SP.A.1
Describe sampling methods that result in representative samples.
Generate a random sample for a statistical question.
7.SP.A.1 7.SP.A.2
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Topic B: Using Sample Data to Draw Inferences About a Population
7.SP.B.3 7.SP.B.4
Determine the impact of sample size on variability and prediction accuracy.
7.SP.A.2
Estimate population proportions using sample data.
Topic C: Using Sample Data to Compare Two or More Populations
Compare different populations by analyzing visual data distributions.
Compare populations by analyzing numerical data.
Identify meaningful differences between populations using the mean and mean absolute deviation (MAD) of samples.
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