Understand that a set of data collected to answer a statistical question has a distribution which can be described by its center, spread, and overall shape.
Official wording from the Common Core State Standards for Mathematics (Β© 2010 National Governors Association Center for Best Practices and Council of Chief State School Officers). View on thecorestandards.org
When you collect data to answer a statistical question, the values form a distribution: a picture of which values occur and how often. Sixth graders learn to describe a distribution using three features. Center is where the data tend to be, a typical value. Spread is how much the values vary, from tightly bunched to widely scattered. Shape is the overall pattern: symmetric, skewed to one side, with one peak or several.
Looking at a dot plot of the number of books read over summer by a class, a student might say the center is around 6 books, the values spread from 1 to 15, most students cluster between 4 and 8, and one student who read 15 is an outlier, so the distribution is skewed right. That kind of description is the goal. It uses everyday language first; precise measures like the median and interquartile range come in 6.SP.A.3 and 6.SP.B.5. Students also start to notice clusters, gaps and peaks, and to explain them using the context of the data.
Saying 'the data go from 2 to 20' gives the range but says nothing about where most values are or the shape.
Data with a long tail to the right are skewed right, even though most values are on the left. The tail names the direction.
The mode is one feature. A full description also includes spread and overall shape.
Twelve students recorded the number of hours they spent outdoors on Saturday: 1, 2, 2, 3, 3, 3, 3, 4, 4, 5, 5, 11. Describe the distribution.
Answer: Center about 3 hours, most values from 2 to 5, range 10, skewed right because of an outlier at 11 hours.
Show several dot plots with the same center but different spreads, and others with the same spread but different shapes. Asking students to write a three-part description (center, spread, shape) builds the habit.
Assessment items commonly display a plot and ask students to describe it, identify an outlier, or choose which of two data sets has more variability.
Original questions written for this standard. Choose an option or type your answer, then press Check. Every question has a worked explanation.
Answer: A) Center, spread and shape
A distribution is described by its center, its spread and its overall shape.
Answer: D) Skewed right
The long tail stretches toward the high values on the right, so it is skewed right.
Answer: 18
18 is far from the cluster of values between 4 and 7, so it is an outlier.
Answer: 19
Range = maximum - minimum = 31 - 12 = 19 cm. The range is one simple measure of spread.
Answer: A) Plot B has more variability
Plot B's values are much more spread out, so it has more variability, even though the centers are the same.
A full lesson with slides, activities and an exit ticket on distributions: center, spread and shape, pitched to grade 6 and editable in PowerPoint or Google Slides.
Make a lesson βA printable, differentiated worksheet on 6.SP.A.2 with an answer key, ready in about a minute.
Make a worksheet βTurn distributions: center, spread and shape into a quiz students answer online that marks itself, with a class summary for you.
Build a test βIt is the overall pattern of a data set: which values occur and how often. It is usually shown in a dot plot, histogram or box plot.
Mostly they describe features in words. Calculating measures of center and variability is the focus of 6.SP.A.3 and 6.SP.B.5.