#### 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

*Adopted: 2009*

### BIG IDEAS

- 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
stock.

- 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
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.
- 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.

### ESSENTIALS

**The student will use
problem solving, mathematical communication, mathematical reasoning,
connections, and representations to**

A.9_{1} **Analyze** descriptive statistics to determine
the implications for the real-world situations from which the data drive.

A.9_{2} Given data, including data in a real-world
context, **calculate** and **interpret** the mean absolute deviation of a data set.

A.9_{3} Given data, including data in a real-world
context, **calculate** variance and standard deviation of a data set and interpret
the standard deviation.

A.9_{4} Given data, including data in a real-world
context, **calculate** and **interpret** z-score for a data set.

A.9_{5} **Explain** ways in which standard deviation
addresses dispersion by examining the formula for standard deviation.

A.9_{6} **Compare** and **contrast** mean absolute deviation
and standard deviation in real-world context.

### KEY VOCABULARY

measures of center, dispersion, Variance,
standard deviation, mean absolute deviation, mean, outliers, z-score (standard
score)

*Updated: Jun 08, 2017*