Data Analysis and Displays
Lessons in this chapter
About Data Analysis and Displays
Data Analysis and Displays closes Algebra 1 with a full toolkit for summarizing and displaying real data.
Measures of Center and Variation reviews mean, median, range, and other spread measures, while Box-and-Whisker Plots introduces the five-number summary (minimum, quartiles, maximum) as a compact way to show a dataset's center and spread in one picture.
Shapes of Distributions has kids describe a dataset as symmetric or skewed, and connect that shape to whether the mean or median better represents the data's center.
Two-Way Tables and Choosing a Data Display close the chapter by organizing two-variable categorical data and deciding which display: among every one covered across this course and earlier grades, best fits a given real dataset.
Each of the five lessons here opens as an Algebra 1 worksheet in the page, including Measures of Center and Variation, Box-and-Whisker Plots and Two-Way Tables. Every question is scored as you answer it, so a median taken from an unsorted list, or a percentage read off the wrong total in a two-way table, is flagged immediately. The practice is free to try, with no login needed for your first 3.
Frequently asked questions
Measures of Center and Variation covers mean, median and mode alongside range and standard deviation, so a data set is described by both where it sits and how spread out it is. Box-and-Whisker Plots shows the five number summary as a picture, Shapes of Distributions reads skew and symmetry and asks which measure of center is honest for each shape, and Two-Way Tables organizes two categorical variables at once. Choosing a Data Display closes by asking which display suits which kind of data. The chapter sits in the high school Statistics and Probability conceptual category (S).
Measures of center (mean, median, mode) describe a single typical value for a dataset; measures of variation (range, interquartile range) describe how spread out the data is around that center.
A box-and-whisker plot displays five key values: minimum, first quartile, median, third quartile, and maximum, with a box spanning the middle half of the data and whiskers extending to the extremes, summarizing an entire dataset’s center and spread in one picture.
A distribution is symmetric if it's roughly balanced on both sides of its center, or skewed if it has a longer tail on one side: the shape affects whether the mean or median better represents a 'typical' value.
A few extreme values pull the mean toward them but barely move the median, so a skewed distribution (with such extreme values) is usually better summarized by its median, while a symmetric distribution can reasonably use either.
A two-way table organizes data on two categorical variables at once, so the count for any specific combination of both categories can be read directly from the table.