Math - 2017-18
A.9 - Statistics
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.
Bloom's Level: Evaluate
- I can predict election
winners from polling data, decide the official weight
of a Hershey bar by weighing a fraction of the candy bars coming off a
production line, and determine the risk associated with price-fluctuations of Verizon
- I will understand that deviations are measures used to quantify the amount of variation or scattering in a set of data values.
UNDERSTANDING THE STANDARD
- Descriptive statistics may include measures of
center and dispersion.
- Variance, standard deviation, and mean absolute
deviation measure the dispersion of the
- 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.
- A z-score (standard score) is a measure of
position derived from the mean and standard deviation of data.
- A z-score derived from a particular data value tells
how many standard deviations that data value is above or below the mean of the
data set. It is positive if the data value lies above the mean and negative if
the data value lies below the mean.
The student will use problem solving, mathematical communication, mathematical reasoning, connections, and representations to
A.91 Analyze descriptive statistics to determine the implications for the real-world situations from which the data drive.
A.92 Given data, including data in a real-world context, calculate and interpret the mean absolute deviation of a data set.
A.93 Given data, including data in a real-world context, calculate variance and standard deviation of a data set and interpret the standard deviation.
A.94 Given data, including data in a real-world context, calculate and interpret z-score for a data set.
A.95 Explain ways in which standard deviation addresses dispersion by examining the formula for standard deviation.
A.96 Compare and contrast mean absolute deviation and standard deviation in real-world context.
measures of center, dispersion, Variance,
standard deviation, mean absolute deviation, mean, outliers, z-score (standard