In Module 5, Topic D, students learn to compare two populations with similar variability. They learn to consider sampling variability when deciding if there is evidence that the means or the proportions of two populations are actually different (7.SP.B.3, 7.SP.B.4). The End-of-Module Assessment follows Topic D.

Content Standard(s):

Mathematics MA2019 (2019) Grade: 7

11. 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.

Unpacked Content

Evidence Of Student Attainment:

Students:

Determine which measure of center best represents the typical value in the data set.

Calculate measures of variability (range, interquartile range, and mean absolute deviation), noting how larger values indicate that values are more spread out from the center of the distribution.

Teacher Vocabulary:

Visual overlap

Measure of variability

Data distribution

range

interquartile range

mean absolute deviation

Knowledge:

Students know:

populations can be compared using measures of center and measures of variability

Skills:

Students are able to:

informally assess the degree of visual overlap of two numerical data distributions with similar variabilities.

Measure the difference between the centers by expressing it as a multiple of a measure of variability.

Understanding:

Students understand that:

outliers skew data, which in turn affects the display.

Measures of center give information about the location of mean, median, and mode, whereas measures of variability give information about how spread out the data is.

Diverse Learning Needs:

Essential Skills:

Learning Objectives: M.7.11.1: Define measure of variability, distribution, and measure of center.
M.7.11.2: Analyze the skew of the distributions and recognize the difference in measure of center and variability.
M.7.11.3: Compare the measure of center and measure of variability of two distributions.
M.7.11.4: Relate the measure of variation with the concept of range.
M.7.11.5: Relate the measure of the center with the concept of mean.
M.7.11.6: Recall how to calculate measure of center and measure of variability.
M.7.11.7: Discuss how to read and interpret a graph.

Prior Knowledge Skills:

Describe the center of a set of data in a given distribution.

Compare and contrast the center and variation.

Interpret graphing points in all four quadrants of the coordinate plane in real-world situations.

Alabama Alternate Achievement Standards

AAS Standard: M.AAS.7.11 Make inferences from graphical representations of a data set (e.g. line plot, dot plots, histograms, bar graphs, stem and leaf plots, or line graphs).

Mathematics MA2019 (2019) Grade: 7

12. Make informal comparative inferences about two populations using measures of center and variability and/or mean absolute deviation in context.

Unpacked Content

Evidence Of Student Attainment:

Students:

Use measures of center for numerical data from random samples to draw informal comparative inferences about two populations.

Use measures of variability for numerical data from random samples to draw informal comparative inferences about two populations.

Teacher Vocabulary:

Mean

median

mode

Mean absolute deviation

Range

Interquartile range

Knowledge:

Students know:

measures of center are insufficient to compare populations. measures of variability are necessary to assess if data sets are significantly different or not.

Mean is the sum of the numerical values divided by the number of values.

Median is the number that is the midpoint of an ordered set of numerical data.

Mode is the data value or category occurring with the greatest frequency (there can be no mode, one mode, or several modes).

Mean absolute deviation of a data set is found by the following steps: 1) calculate the mean 2) determine the deviation of each variable from the mean 3) divide the sum of the absolute value of each deviation by the number of data points.

Range is a number found by subtracting the minimum value from the maximum. value.

Skills:

Students are able to:

find the measures of center of a data set.

Find the interquartile range of a data set and use to compare variability between data sets.

Understanding:

Students understand that:

outliers skew data, which in turn affects the display.

Measures of center give information about the location of mean, median and mode, whereas measures of variability give information about how spread out the data is.

The mean absolute deviation of a data set describes the average distance that points within a data set are from the mean of the data set.

Diverse Learning Needs:

Essential Skills:

Learning Objectives: M.7.12.1: Define measure of variability, measure of center, inference and mean absolute deviation.
M.7.12.2: Recall how to calculate measure of center and measure of variability.
M.7.12.3: Recall that center is related to measure of center and measure of variability is related to variation.
M.7.12.4: Compare and contrast the measure of center and measure of variability of two numerical data sets.
M.7.12.5: Calculate the mean absolute deviation of a data set in context.

Prior Knowledge Skills:

Describe the center of a set of data in a given distribution.

Compare and contrast the center and variation.

Alabama Alternate Achievement Standards

AAS Standard: M.AAS.7.12 Compare two sets of data within a single data display such as a picture graph, line plot, or bar graph.

Tags:

center, data, inferences, population, probability, random sample, statistics, variability