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Henrico County Public Schools, Virginia
Algebra and Functions

Data Analysis

SOL Review Materials
The student will analyze the normal distribution. Key concepts include:
a)   characteristics of normally distributed data;
b)   percentiles;
c)   normalizing data using z-scores; and
d)   area under the standard normal curve and probability.
Essential Knowledge and Skills 
  • Interpret mean, median, mode, range, interquartile range, variance, and standard deviation of a univariate data set in terms of the problem’s context.
  • Explain the influence of outliers on a univariate data set.
  • Explain ways in which standard deviation addresses dispersion by examining the formula for standard deviation.
  • Identify the properties of a normal probability distribution.
  • Describe how the standard deviation and the mean affect the graph of the normal distribution.
  • Determine the probability of a given event, using the normal distribution.
Essential Understandings
  • Analysis of the descriptive statistical information generated by a univariate data set includes the relationships between central tendency, dispersion, and position. 
  • The normal distribution curve is a family of symmetrical curves defined by the mean and the standard deviation.
  • Areas under the curve represent probabilities associated with continuous distributions.
  • The normal curve is a probability distribution and the total area under the curve is 1.
  • The mean of the data in a standard normal density function is 0 and the standard deviation is 1.  This allows for the comparison of unlike data.
  • The amount of data that falls within 1, 2, or 3 standard deviations of the mean is constant and the basis of z-score data normalization.
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 a measure of variation.
  2. SOL 6.15 - a) describe mean as balance point; b) decide which measure of center is appropriate
  3. SOL A.9 - given a set of data, interpret variation in real‐world contexts/calculate/interpret mean absolute deviation/stand dev/z‐scores.
  4. SOL AII.11 - identify properties of normal distribution, apply properties to determine probabilities associated with areas under the standard normal curve.
Instructional Materials
  1. AFDA.7ab - Notes: Normal Curve (ppt)
  2. AFDA.7c - Notes: Z-scores (ppt)
  3. AFDA.7d - Area Under the Curve (ppt)
Frederick County Resources
Real World Lessons
Explore Learning
Common Core Standards