Math 1 · Unit 12 · Lesson 1

Pictures of Data and Their Shapes

One quantity at a time, and the same three questions every time: what shape, where is the center, how spread out? Start with the pictures. A dot plot shows every value, a histogram groups values into bins to show the shape, and a box plot shows the 5-number summary. Then name the shape by its tail: symmetric, skewed right toward the big numbers, or skewed left toward the small ones, and explain the shape from the context.

About 40 minutes The tail tells you the name

The big idea

A data set is a list of values for one quantity, and its distribution is how those values spread along the number line. Ask the same three questions every time, in order: what shape, where is the center, how spread out. Three pictures show the distribution. A dot plot shows every value and suits a small set. A histogram groups values into bins and shows the shape of a big set, and its bin width changes the picture. A box plot draws the 5-number summary, minimum, Q1, median, Q3, and maximum, with the box holding the middle half. Shape is named by the tail: symmetric when the sides match, skewed right when a long tail reaches toward the big numbers, skewed left when it reaches toward the small ones. The context explains the shape: a few stars make incomes skew right, a few low scores make an easy test skew left, and heights pile up in the middle.

The parts of this lesson

Each part is its own short page. Go in order, or pick the one you need.

1The Words We UseThe vocabulary for this lesson, in one place.Start here 2Three pictures, and the three questionsUnit 10 looked at two quantities at once, as scatter plots. 3Shape: find the tailThe first of the three questions is shape . 4Sort the shapesFind the tail. A tail toward the big numbers is skewed right; toward the small numbers, skewed left; two... 5Practice ProblemsTry them, get help one step at a time, then print how it went.

Printables

One page with the three pictures and their uses, the 5-number summary, the three shapes named by the tail, and the context examples. Plus a worksheet with an answer key and a short lesson plan.

Study guide (PDF) Worksheet and answer key (PDF) Lesson plan (PDF)

Where this goes next

Previous lesson: Proving Shapes with CoordinatesThe end of Unit 11. Next lesson: Center, the Mean and the MedianWhere is the center? The mean balances, the median resists. Back to the Math 1 mapEvery Math 1 lesson, in course order. Tell us what you thoughtA few quick questions about this lesson. It takes a minute, and it is how the lesson gets better.

NC Math 1 standards in this lesson: NC.M1.S-ID.1 (represent data with dot plots, histograms, and box plots using technology), NC.M1.S-ID.3 (shape, including skewness, in context).