Calculate Standard Deviation
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This learning activity provided by:
Author:
Pamela West
System: Montgomery County School: Montgomery County Board Of Education
General Activity Information
Activity ID:
2919
Title: Calculate Standard Deviation
Digital Tool/Resource: Measuring Spread
Web Address – URL:
Overview: In this learning activity, students will learn to find the standard deviation and be able to find the similarities and differences in 4 data sets. These sets have the same mean but different ranges and standard deviations. Students will discover that the standard deviation increases when points are further away from the mean, even those in the middle. This learning activity is intended to be a During Activity for a standard deviation lesson.
Associated Standards and Objectives
Content Standard(s):
Mathematics 10. Use statistics appropriate to the shape of the data distribution to compare and contrast two or more data sets, utilizing the mean and median for center and the interquartile range and standard deviation for variability.
a. Explain how standard deviation develops from mean absolute deviation.
b. Calculate the standard deviation for a data set, using technology where appropriate.
Unpacked Content
Evidence Of Student Attainment:
Students:
Given two or more different data sets,
Compare the center (median, mean) and the spread (interquartile range, standard deviation) of the data sets to describe differences and similarities of the data sets.
Explain how standard deviation develops from mean absolute deviation.
Calculate the standard deviation for a data set, and use technology where it is appropriate. Teacher Vocabulary:
Center
Median
Mean
Spread
Interquartile range
Standard deviation
Absolute mean deviation Knowledge:
Students know:
Techniques to calculate the center and spread of data sets.
Techniques to calculate the mean absolute deviation and standard deviation.
Methods to compare data sets based on measures of center (median, mean) and spread (interquartile range and standard deviation) of the data sets. Skills:
Students are able to:
Accurately find the center (median and mean) and spread (interquartile range and standard deviation) of data sets.
-Present viable arguments and critique arguments of others from the comparison of the center and spread of multiple data sets.
Explain their reasoning on how standard deviation develops from the mean absolute deviation. Understanding:
Students understand that:
Multiple data sets can be compared by making observations about the center and spread of the data.
The center and spread of multiple data sets are used to justify comparisons of the data.
Both the mean and the median are used to calculate the mean absolute and standard deviations Diverse Learning Needs:
Essential Skills:
Learning Objectives: GEO.10.1: Accurately find the center (median and mean) and spread (interquartile range and standard deviation) of data sets.
GEO.10.2: Present viable arguments and critique arguments of others from the comparison of the center and spread of multiple data sets.
GEO.10.3: Reason how standard deviation develops from the mean absolute deviation.
Prior Knowledge Skills:
Define measure of variability, distribution, and measure of center.
Compare the measure of center and measure of variability of two distributions.
Relate the measure of variation with the concept of range.
Relate the measure of the center with the concept of mean.
Recall how to calculate measure of center and measure of variability.
Alabama Alternate Achievement Standards
AAS Standard:
Learning Objectives: The students will be able to:
Explain the difference between mean absolute deviation and standard deviation.
Compare the center, shape, spread, and unusual features of multiple data sets.
Calculate and learn to interpret the standard deviation of a data set using students’ conceptual understanding of mean absolute deviation.
Use technology to determine the standard deviation.
Strategies, Preparations and Variations
Phase: During/Explore/Explain
Activity:
Students will need to be shown how to calculate the standard deviation using whichever piece of technology they are allowed to use.
The teacher will:
Teach students how to calculate standard deviation using the Measuring Spread Worksheet .
Distribute the Measuring Spread Worksheet .
Show students how to calculate the standard deviation with the calculator, but pose the following question to students first: “Why do we need to find the absolute values of the differences between the mean and each data entry?” (Students should have experienced or should experience with the data in the activity that the sum of these differences is always one.)
Assign groups a certain data set (A, B, C, or D) from the activity on page 1 and have them work problems 1-3 with their group.
Pose all groups this question, “How can we ensure that the sum of the differences doesn’t sum to zero?” (Students will likely not immediately offer the suggestion of squaring the difference.)
After students offer suggestions to the question, have the students calculate the average square difference.
Finally, ask them: “Does the average square distance really tell you a lot about how different the data is from the mean? (No) What could we do to make this more meaningful?”
Have students square root this sum squared difference and compare it with their values calculated with technology.
Next, have students work on the second page of activity problems 4-7. Students will be required to connect their ideas with boxplots and histograms.
As an exit ticket, have students enter the data from problem 7 in their calculator and record the standard deviations in question 8.
Assessment Strategies: The students' responses during class discussions and small group interactions will be assessed as formative assessment.
Advanced Preparation:
The teacher should review the Measuring Spread Worksheet and randomly assign groups, ensuring that at least one member understands deviations.
The teacher will make copies of the Measuring Spread Worksheet .
The teacher should remind the students they are finding the similarities and differences in 4 data sets. However, let them discover that the sets have the same mean but different ranges and standard deviations. Guide the discussion to the point of understanding that the standard deviation increases when points are further away from the mean, even those in the middle.
Variation Tips (optional):
If students are experiencing difficulties, you may consider small group time with the teacher or assign a peer buddy.
Model and demonstrate during whole group instruction during the review phase as needed.
Notes or Recommendations (optional): The teacher should note during the Measuring Spread activity, students find the similarities and differences in 4 data sets. These sets have the same mean but different ranges and standard deviations. The point of the activity is for students to understand that the standard deviation increases when points are further away from the mean, even those in the middle.
This activity could be used as a stand-alone activity or in connection with the following activities:
Keywords and Search Tags
Keywords and Search Tags:
Mean, Mean Absolute Deviation, Range, Spreads, Standard Deviation
