Algebra 1 Online!
Henrico County Public Schools, Virginia
Expressions and Operations

Equations and Inequalities

Functions

Statistics

SOL Review Materials
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: Calculating Measures of Dispersion - Statistics (PDF) - Calculating mean absolute deviation, variance, and standard deviation (Word)
  3. VDOE ESS Lesson: Exploring Statistics - Statistics (PDF) - Calculating mean absolute deviation, variance, standard deviation, and z-scores (Word)
  4. VDOE Technical Assistance documentation (pdf)
  5. Activity: Standard Deviation Student Worksheet (doc) | Student Excel file (xls) | Solutions (doc)
  6. Notes: Mean Absolute Deviation (ppt)
  7. Notes: Standard Deviation (ppt)
  8. Notes: Sigma Notation and Mean Absolute Deviation (ppt)
  9. Notes Outline: Summation Notation and Mean Absolute Deviation (doc)|(pdf)
  10. Notes: Standard Deviation and z-scores (ppt)
  11. Notes: Student Notes Outline for Standard Deviation and z-score ppt (doc)|(pdf)
  12. Notes: Standard Deviation and Mean Absolute Deviation (doc) | Answer Key (pdf)
  13. Notes: Statistics (ppt)
  14. Guided Notes: Statistics (doc)
Real World Lessons
Practice
  1. VDOE ESS: Interpreting Descriptive Statistics Worksheet (pdf)
  2. VDOE ESS: Data Collection and Exploring Statistics (pdf)
  3. VDOE ESS: Heights of Basketball Players (pdf)
  4. Worksheet: Standard Deviation and Z-Scores (doc)
  5. ExamView Quiz: Deviation and Z-Scores
  6. Standard Deviation (pdf) | Solution (pdf)
  7. Mean Absolute Deviation (pdf) | Solution (pdf)
  8. Standard Deviation graphs (pdf) | Solution (pdf)
Self-Assessments
  1. SOL Mini Quiz
Skills
  1. JMU Pivotal Question: Mean Absolute Deviation (doc)
Videos
  1. Video: PH Finding Standard Deviation
  2. Video: PH Using Standard Deviation
  3. What is a "Standard Deviation?" and where does that formula come from? - YouTube video
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
Old Website Links
Common Core Standards
6.SP.5c
7.SP.1
7.SP.2
7.SP.3
S-ID.2
S-ID.3