# What Does the Data Tell Us? Describing Data

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## Objective

The students will be able to 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.

#### Big Idea

Understanding how to interpet data by its shape, spread, and center helps students to understand statistics.

## DO NOW

15 minutes

The beginning part of the lesson reviews the concept of mean, median mode and range.  It’s a fun scenario about a town called Whateverville.  The students will be investigating the temperatures of the town to find the mean, median, mode and range.  They will also be looking at the affects of outliers on the mean. (see shape of distribution power point, slide 2)

## Describing Data Attributes

55 minutes

The bulk of the lesson begins with the vocabulary.  It will be very important to discuss each vocabulary word and make sense of what it is saying.  It may be helpful to draw a sketch of what each word means.  There is a website  I used to assist me in making the vocabulary meaningful.  They have great graphics too. After working through the vocabulary, I like to have students work in pairs to go over the vocab.  For example, one student can describe the definition in as many ways as they can.  They may not use the definition in front of them.  They may use gestures.  Their partner must guess the word they are describing.  The partners will switch turns.  To make this more challenging, you could set a timer (similar to catchphrase)

Once the vocabulary has been defined, the next slides show graphs.  This will allow the students to apply the vocabulary word to a visual representation.  I’ve used several different data sets and representations so the students can apply their knowledge to more than one graph.

After students have had the direct/guided instruction, they can do a short activity called Find someone who.(I chose this activity because it allows students a movement break after sitting for so long and it only allows them to work with one other person at a time which should allow for some in depth conversation.. Additionally, the students can have the advantage of working with a partner if they are still struggling with the concept)  When students answer questions on someone else’s paper, remind them they will need to use mathematical terms to explain their answers (SMP 6)

Find someone who.

• Students will find a partner and exchange papers.
• Each partner will solve a problem on the other person’s paper.
• Once both partners are done finding the center, spread,  and shape of the data they will explain what they found to their partner. Upon agreement of their findings, they initial their work and find another partner.
• The process then starts all over again
• (SMP 1,3,7)

## Closure

10 minutes

Before giving students the exit slip, have the following discussion with them by using the lesson objective.

• In your own words, describe a data sets “center”.?
• In your own words, describe the “shape”: of a data set?
• In your own words, describe the “spread” of a data set?

Although there are only 3 questions to wrap up the learning, the questions can be broken down in to more specifics to allow more students to participate.  For example,  you could ask what a wide spread data means or a small data spread means.  You could talk about skewness and more specifically left skewed or right skewed.  How will you determine the center of a data set?  If you wanted more students involved you could allow them to partner share their responses before moving to whole group discussion.  Just remind students to apply the ELA speaking and listening standard while working in pairs.

Allow students time to work on one problem on their own.  Collect this to assess student understanding.