# 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

### 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 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.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.

### KEY VOCABULARY

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

Updated: Jun 08, 2017