Algebra 1 Online!
Henrico County Public Schools, Virginia
 Home Pacing - Middle School Pacing - High School SOL Tracker Algebra 1 Standards Virginia Department of Education Return to HCPS Math Courses
 Expressions and Operations Equations and Inequalities Functions Statistics SOL Review Materials Frequently Asked Questions
A.9
The student, given a set of data, will interpret variation in real-world contexts and calculate and interpret mean absolute deviation, standard deviation, and z-scores.
 Essential Knowledge and Skills Analyze descriptive statistics to determine the implications for the real-world situations from which the data derive. Given data, including data in a real-world context, calculate and interpret the mean absolute deviation of a data set. Given data, including data in a real-world context, calculate variance and standard deviation of a data set and interpret the standard deviation. Given data, including data in a real-world context, calculate and interpret z-scores for a data set. Explain ways in which standard deviation addresses dispersion by examining the formula for standard deviation. Compare and contrast mean absolute deviation and standard deviation in a real-world context. Essential Understandings Descriptive statistics may include measures of center and dispersion. Variance, standard deviation, and mean absolute deviation  measure the dispersion of the data. The sum of the deviations of data points from the mean of a data set is 0. Standard deviation is expressed in the original units of measurement of the data. Standard deviation addresses the dispersion of data about the mean. Standard deviation is calculated by taking the square root of the variance. The greater the value of the standard deviation, the further the data tend to be dispersed from the mean. For a data distribution with outliers, the mean absolute deviation may be a better measure of dispersion than the standard deviation or variance.
Vertical Articulation
1. SOL 5.16 - a) describe mean/median/mode; b) describe mean as fair share; c) find the mean/median/mode/ range; d) describe range as measure of variation.
2. SOL 6.15 - a) describe mean as balance point; b) decide which measure of center is appropriate
3. SOL AFDA.7 - analyze norm distribution - a) characteristics of normally distribution of data; b) percentiles; c) normalizing data, using z- scores; d) area under standard norm curve/ probability
4. SOL AII.11 - ID properties of norm distribution/apply properties to determine probabilities associated with areas under the standard normal curve
Instructional Materials
1. VDOE ESS Lesson: Analyzing and Interpreting Statistics - Statistics (PDF) - Analyzing and interpreting descriptive statistics (Word)
2. VDOE ESS Lesson: Exploring Statistics - Statistics (PDF) - Calculating mean absolute deviation, variance, standard deviation, and z-scores (Word)
3. VDOE ESS Lesson: z-Scores - Statistics (PDF) - Calculating and interpreting z-scores (Word)
4. VDOE Technical Assistance documentation (pdf)
5. Activity: Standard Deviation Student Worksheet (doc) | Student Excel file (xls) | Solutions (doc)
6. Notes: Z-scores (ppt)
7. Notes: Standard Deviation and z-scores (ppt)
8. Notes: Student Notes Outline for Standard Deviation and z-score ppt (doc)|(pdf)
9. Notes: Z-Scores (doc) | Answer Key (pdf)
10. Guided Notes: Statistics (doc)
11. Guided Notes: Statistics Review (doc)
12. Variance and Standard Deviation Calculator (xlsx)
Real World Lessons
Practice
Self-Assessments
Skills
Videos
Explore Learning
1. Real-Time Histogram - Try to click your mouse once every 2 seconds. The time interval between each click is recorded, as well as the error and percent error. Data can be displayed in a table, histogram, or scatter plot. Observe and measure the characteristics of the resulting distribution when large amounts of data are collected.
Websites