Statistics
Lessons in this chapter
About Statistics
Statistics is the longest chapter in 6th grade, and it shifts the subject from calculating summaries to describing what a whole data set looks like.
Understand Statistical Questions and Types of Data starts with the distinction that defines the subject. “How tall am I” has one answer; “how tall are the students in this class” has many, and only the second is a statistical question, because only it produces a distribution.
Represent and Interpret Data Using Dot Plots, Stem and Leaf Plots, and Grouped Frequency Tables and Histograms build the toolkit. The histogram is the important new one: it groups values into intervals, so the shape of the data appears but individual values are lost, which is a trade worth naming.
Interpret the Meaning of Center and Interpret the Meaning of Variability are the conceptual core. Center asks what is typical; variability asks how spread out the values are. Two data sets can share a mean and look nothing alike, which is exactly why one number is never a description.
Describe and Summarize Distributions and Represent and Interpret Data using Box and Whisker Plots put it together. A box plot shows the median, the quartiles and the range in one picture, so center and spread are visible at a glance.
Statistics has eight lessons and each one opens as a 6th grade math worksheet in the page. Represent and Interpret Data Using Dot Plots, Interpret the Meaning of Variability and Represent and Interpret Data using Box and Whisker Plots give practice questions worked one at a time and marked as you go. They are free and nothing here needs an account.
Frequently asked questions
Understand Statistical Questions and Types of Data begins with what makes a question statistical, that it expects a spread of answers rather than one. The next three lessons give that spread a picture through dot plots, stem and leaf plots, and grouped frequency tables and histograms, each keeping or losing the individual values in a different way. Interpret the Meaning of Center and Interpret the Meaning of Variability then supply the two numbers that summarize a distribution, what is typical and how spread out it is, and Describe and Summarize Distributions and Represent and Interpret Data using Box and Whisker Plots put both together. The chapter sits in the Common Core domain Statistics and Probability (6.SP); stem and leaf plots are ours, since the Common Core names dot plots, histograms and box plots at this grade.
That it expects many different answers. “How tall am I” is not statistical; “how tall are the students in this class” is, because it produces a distribution.
Center describes what is typical, through the mean or median. Variability describes how spread out the values are, through the range or the interquartile range.
Because two data sets can have the same mean and look completely different. One might be tightly clustered and the other widely spread, which is why variability matters too.
A graph showing how many values fall into each interval. It reveals the shape of the data but loses the individual values, which is the trade it makes.
A diagram showing the minimum, lower quartile, median, upper quartile and maximum. It puts center and spread into a single picture.