Standard deviation
• Describe variability by calculating deviations from the mean. • Compare two data sets with the same means but different variabilities, and contrast them by calculating the deviation of each data point from the mean. • Interpret sets with greater deviations as having greater variability. • Calculate a standard deviation by hand for a small data set, and understand standard deviation as an indicator of a typical deviation from the mean of an element of the data set.
Instead of creating representations of data, the emphasis in high school is on interpreting representations and judiciously interpreting measures of center and spread. Students describe the shape of a data distribution in more detail (symmetric, skewed, flat, or bell-shaped). Students develop a more precise understanding of measures of center and understand relationships between mean and median for symmetrical and skewed data distributions. They learn that outliers affect the mean of a data set but not the median. They recognize outliers when they exist and learn to investigate their source. Students learn that standard deviation is a measure of spread, that a larger standard deviation means the data are more spread out, and to understand standard deviation as “typical distance from the mean” for a symmetrical distribution. They also understand that interquartile range is a description of variability better-suited to a skewed distribution. Finally, students are introduced to two-way frequency tables and understand how to interpret relative frequencies in the context of the data represented in the tables.