# Describing Single-Variable Data Sets

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## Objective

SWBAT describe the shape, center and variability of a one-variable data sets.

#### Big Idea

In order to make sense of a data set, we must know about the shape of the distribution, where its center is located, and how far the values tend to stray from the center.

## Opening Activity

30 minutes

When my students enter the classroom, I ask them to take a card from a deck that I have prepared in advance.  This deck has the ace through 8 of three suits.  After the bell rings, I ask students to get together with the students who have the same cards (different suit) as them.  These will be the groups for today's warm-up, which is a matching game.

Matching Histogram, Boxplot, Summary is a set of cards that should be printed on cardstock before using the first time.  The set contains a histogram, box plot and set of summary statistics for 8 different distributions.  The goal of the activity is to match up the 8 sets of cards and record the match on the Matching Record Sheet recording sheet.  The goal of the activity is for students to refine their conceptual understanding of the standard deviation as a measure of variability.

## Foldable Notes

30 minutes

I want my students to remember that the most important features of a one-variable data distribution are Shape, Outliers, Center and Spread. To help them remember this, I use the mnemonic SOCS:

• S = the shape of the distribution
• O = whether or not there are outliers in the data set
• C = the location of the center
• S = a measure of how far the values tend to be from the center

In this lesson, we make a Foldable Resource for their notes that details best practices for describing these four characteristics of a univariate data set.

## Practice Describing Data Sets

20 minutes

Using their Foldable notes, students will describe the three data sets in Data to Describe.  I send this data to my students as a TI Nspire file so that they do not spend time entering the data.  I remind them that their descriptions should be paragraphs, not lists, and they they must refer to the summary statistics (mean, median, standard deviation, IQR) that they obtained using the calculator.

## Wrap-Up Discussion

10 minutes

I invite volunteers to the board to share their written description of the three distributions in Data to Describe.  I emphasize the importance of describing the distribution in a paragraph rather than a list.  This is an important skill that they will need for more advanced study in statistics so I help them hone it early on [MP3].  As a class, we review each of the volunteers' answers and work to improve it if necessary.