Expressions and Operations 

Equations and Inequalities 

Functions 

Statistics 

SOL Review Materials 




A.9 
The student, given a set of data, will interpret variation in realworld contexts and calculate and interpret mean absolute deviation, standard deviation, and zscores. 

Essential Knowledge and Skills 
 Analyze descriptive statistics to determine the implications for the realworld situations from which the data derive.
 Given data, including data in a realworld context, calculate and interpret the mean absolute deviation of a data set.
 Given data, including data in a realworld context, calculate variance and standard deviation of a data set and interpret the standard deviation.
 Given data, including data in a realworld context, calculate and interpret zscores 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 realworld 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 
 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.
 SOL 6.15  a) describe mean as balance point; b) decide which measure of center is appropriate
 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
 SOL AII.11  ID properties of norm distribution/apply properties to determine probabilities associated with areas under the standard normal curve

Instructional Materials 
 VDOE ESS Lesson: Analyzing and Interpreting Statistics  Statistics (PDF)  Analyzing and interpreting descriptive statistics (Word)
 VDOE ESS Lesson: Calculating Measures of Dispersion  Statistics (PDF)  Calculating mean absolute deviation, variance, and standard deviation (Word)
 VDOE ESS Lesson: Exploring Statistics  Statistics (PDF)  Calculating mean absolute deviation, variance, standard deviation, and zscores (Word)
 VDOE Technical Assistance documentation (pdf)
 Activity: Standard Deviation Student Worksheet (doc)  Student Excel file (xls)  Solutions (doc)
 Notes: Mean Absolute Deviation (ppt)
 Notes: Standard Deviation (ppt)
 Notes: Sigma Notation and Mean Absolute Deviation (ppt)
 Notes Outline: Summation Notation and Mean Absolute Deviation (doc)(pdf)
 Notes: Standard Deviation and zscores (ppt)
 Notes: Student Notes Outline for Standard Deviation and zscore ppt (doc)(pdf)
 Notes: Standard Deviation and Mean Absolute Deviation (doc)  Answer Key (pdf)
 Notes: Statistics (ppt)
 Guided Notes: Statistics (doc)

Real World Lessons 

Practice 
 VDOE ESS: Interpreting Descriptive Statistics Worksheet (pdf)
 VDOE ESS: Data Collection and Exploring Statistics (pdf)
 VDOE ESS: Heights of Basketball Players (pdf)
 Worksheet: Standard Deviation and ZScores (doc)
 ExamView Quiz: Deviation and ZScores
 Standard Deviation (pdf)  Solution (pdf)
 Mean Absolute Deviation (pdf)  Solution (pdf)
 Standard Deviation graphs (pdf)  Solution (pdf)

SelfAssessments 
 SOL Mini Quiz

Skills 
 JMU Pivotal Question: Mean Absolute Deviation (doc)

Videos 
 Video: PH Finding Standard Deviation
 Video: PH Using Standard Deviation
 What is a "Standard Deviation?" and where does that formula come from?  YouTube video

Explore
Learning 
 RealTime 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 
SID.2 
SID.3 

