Curriculum / Math / 9th Grade / Unit 2: Descriptive Statistics / Lesson 7
Math
Unit 2
9th Grade
Lesson 7 of 22
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Interpret the standard deviation and interquartile range.
The core standards covered in this lesson
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-ID.A.4 — Use the mean and standard deviation of a data set to fit it to a normal distribution and to estimate population percentages. Recognize that there are data sets for which such a procedure is not appropriate. Use calculators, spreadsheets, and tables to estimate areas under the normal curve.
The foundational 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 essential concepts students need to demonstrate or understand to achieve the lesson objective
Suggestions for teachers to help them teach this lesson
This GeoGebra tool specifically shows the number of standard deviations and how moving points on the graph alters the mean, standard deviation, and median.
Unlock features to optimize your prep time, plan engaging lessons, and monitor student progress.
Problems designed to teach key points of the lesson and guiding questions to help draw out student understanding
25-30 minutes
Below are the results that show the number of hours 50 babies slept in one night.
How many babies have sleep habits within “one standard deviation” from the mean?
Standard Deviation Visually Represented in a Dotplot by Forest Fisher is made available by GeoGebra under the CC BY-NC-SA 3.0 license. Copyright © International GeoGebra Institute, 2013. Accessed June 21, 2017, 10:18 a.m..
Two teams played 25 games of “cornhole” and charted the number of shots each team got in during a game.
Team A: Team B:
Mean: 8.0 Mean: 6.0 Standard Deviation: 2.0 Standard Deviation: 2.0
Which team is more consistent?
After Team A and Team B were done playing their games, Team C and Team D took over. They altered the rules a bit for higher scoring capability.
Boxplot Grapher is made available by IMathAS under the GNU General Public License. Accessed June 26, 2017, 2:39 p.m..
A set of suggested resources or problem types that teachers can turn into a 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.
A task that represents the peak thinking of the lesson - mastery will indicate whether or not objective was achieved
5-10 minutes
Below are dot plots for three different data sets. The standard deviations for these three data sets are given in the following table. Looking at the dot plots and without calculating the standard deviations, match the data sets to the appropriate standard deviation.
Standard deviation A: 5.9 Standard deviation B: 3.3 Standard deviation C: 2.3
Describe how the standard deviations affect consistency of a data set.
Understanding the Standard Deviation, accessed on June 21, 2017, 10:22 a.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.
The manager at a factory that makes pants is going to award one of the employees Employee of the Month. Below are the number of pants that each of two of the most productive workers have made over a period of 12 days.
Next
Calculate population percentages using the standard deviation.
Topic A: Descriptive Statistics in Univariate Data
Describe statistics. Represent data in frequency graphs and identify the center of a data set.
Standards
HSS-IC.A.1HSS-ID.A.1HSS-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.1HSS-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.2HSS-ID.A.3
Calculate and interpret the spread (variance) of a data set.
HSS-ID.A.3HSS-ID.A.4
Calculate the standard deviation and compare two symmetrical distributions based on the mean and standard deviation.
HSS-ID.A.2HSS-ID.A.4
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.1HSS-ID.A.2HSS-ID.A.3HSS-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.8HSS-ID.C.9
Determine the function of best fit and create a linear equation from least squares regression using technology.
HSS-ID.B.6aHSS-ID.B.6bHSS-ID.C.7
Use residuals to assess the strength of the model for a data set.
HSS-ID.B.6bHSS-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.6aHSS-ID.C.7HSS-ID.C.9
HSS-ID.B.6HSS-ID.C.7HSS-ID.C.8HSS-ID.C.9
HSS-ID.B.6HSS-ID.C.7HSS-ID.C.8HSS-ID.C.9N.Q.A.1
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