Curriculum / Math / 9th Grade / Unit 2: Descriptive Statistics / Lesson 1
Math
Unit 2
9th Grade
Lesson 1 of 22
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Describe statistics. Represent data in frequency graphs and identify the center of a data set.
The core standards covered in this lesson
HSS-ID.A.1 — Represent data with plots on the real number line (dot plots, histograms, and box plots).
HSS-ID.A.2 — Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets.
HSS-IC.A.1 — Understand statistics as a process for making inferences about population parameters based on a random sample from that population.
The foundational standards covered in this lesson
7.SP.A.1 — Understand that statistics can be used to gain information about a population by examining a sample of the population; generalizations about a population from a sample are valid only if the sample is representative of that population. Understand that random sampling tends to produce representative samples and support valid inferences.
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 essential concepts students need to demonstrate or understand to achieve the lesson objective
Suggestions for teachers to help them teach this lesson
Students will need notes that allow them to organize their thinking around shape, center, and spread. Over this set of lessons, up through lesson 9, students will be using the terms shape, center and spread, and will need to parse how the two different measures of center (mean and median) relate to the two main measures of spread (standard deviation and interquartile range), through analysis of the shape (skew left, symmetrical, skew right). Students will also need to think about how the graphical representations of histograms and box plots relate to these concepts. Start the work to organize their thinking in this lesson and continue this through lesson 9.
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Problems designed to teach key points of the lesson and guiding questions to help draw out student understanding
After watching Why Statistics from the U.S. Census Bureau and Why You Need to Study Statistics from This is Statistics, what is statistics and how can it be applied?
Below are two data representations. How are these representations similar? Different?
Aaron wanted to answer the question “How old are people in Boston?” He accessed this data from the US Census Bureau:
Aaron looked at the data and was unsure of how to answer his question. He summarized the data from the table above into the histogram below.
How would you answer Aaron’s question based on the histogram of data?
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
Sam said that young people from the ages of 0 to 10 make up nearly one-third of the Kenyan population. Do you agree? Why or why not?Â
How does this compare with the same age group in Boston?Â
Algebra I > Module 2 > Topic A > Lesson 1 of the New York State Common Core Mathematics Curriculum from EngageNY and Great Minds. © 2015 Great Minds. Licensed by EngageNY of the New York State Education Department under the CC BY-NC-SA 3.0 US license. Accessed Dec. 2, 2016, 5:15 p.m..
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 2
Topic A: Descriptive Statistics in Univariate Data
HSS-IC.A.1 HSS-ID.A.1 HSS-ID.A.2
Describe center and spread. Represent data in a box plot (box-and-whisker plot) and calculate the center and spread.
HSS-ID.A.1 HSS-ID.A.2
Represent data in a histogram and calculate the center. Identify when the median and mean are not the same value.
HSS-ID.A.1
Describe the shape of the data in box plots and histograms. Choose an appropriate measure of center (or an appropriate shape) based on the shape and the relationship between the mean and the median.
HSS-ID.A.2 HSS-ID.A.3
Calculate and interpret the spread (variance) of a data set.
HSS-ID.A.3 HSS-ID.A.4
Calculate the standard deviation and compare two symmetrical distributions based on the mean and standard deviation.
HSS-ID.A.2 HSS-ID.A.4
Interpret the standard deviation and interquartile range.
Calculate population percentages using the standard deviation.
HSS-ID.A.4
Given summary statistics, describe the best measures of center and spread. Describe reasoning.
HSS-ID.A.2
Develop and answer statistical questions through data analysis of existing data using appropriate statistical measures and displays. (Part 1/3)
HSS-ID.A.1 HSS-ID.A.2 HSS-ID.A.3 HSS-ID.A.4
Develop and answer statistical questions through data analysis of existing data using appropriate statistical measures and displays. (Part 2/3)
Develop and answer statistical questions through data analysis of existing data using appropriate statistical measures and displays. (Part 3/3)
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Topic B: Descriptive Statistics in Bivariate Data
Define categorical and numerical data. Create two-way tables to organize bivariate categorical data.
HSS-ID.B.5
Describe relative and relative conditional frequencies of two-way tables.
Create scatterplots and identify function shapes in scatterplots.
HSS-ID.B.6
Calculate, with technology, the correlation coefficient for a data set. Explain why correlation does not determine causation.
HSS-ID.C.8 HSS-ID.C.9
Determine the function of best fit and create a linear equation from least squares regression using technology.
HSS-ID.B.6a HSS-ID.B.6b HSS-ID.C.7
Use residuals to assess the strength of the model for a data set.
HSS-ID.B.6b HSS-ID.B.6c
Describe the relationship between two quantitative variables in a contextual situation represented in a scatterplot using the correlation coefficient, least squares regression, and residuals as evidence.
HSS-ID.B.6a HSS-ID.C.7 HSS-ID.C.9
HSS-ID.B.6 HSS-ID.C.7 HSS-ID.C.8 HSS-ID.C.9
HSS-ID.B.6 HSS-ID.C.7 HSS-ID.C.8 HSS-ID.C.9 N.Q.A.1
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