How can data be represented and summarized meaningfully?
• Revisit various ways to plot data: dot plots, histograms, and box plots. • Interpret plots of data within the context of the data. • Use the terms “symmetric” and “skewed” as descriptors of distributions.
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.