Lesson 9: What is Typical?

Lesson 9: What is Typical?

Objective:

Students will learn about the typical value when looking at a distribution by finding the “center” and determining any point clusters.

Materials:

  1. Nutrition facts dotplot (from lesson 8)

  2. Poster paper

  3. Markers, dot stickers, or sticky notes

Vocabulary:

typical, center, shape, spread

Essential Concepts:

Essential Concepts:

The “center” of a distribution is a deliberately vague term, but it is one way to answer the subjective question "what is a typical value?" The center could be the perceived balancing point or the value that approximately cuts the area of the distribution in half.

Lesson:

  1. Food Habits Campaign Data Collection Monitoring:

    1. Display the IDS Campaign Monitoring Tool, found at https://tools.idsucla.org Click on Campaign Monitor and sign in.

    2. Inform students that you will be monitoring their data collection again today.

      1. See User List and sort by Total. Ask: Who has collected the most data so far?

      2. Click on the pie chart. Ask: How many active users are there? How many inactive users are there?

      3. See Total Responses. How many responses have been submitted?

      4. Using TPS, ask students to think about what they can do to increase their data collection.

  2. Inform students that today they will be learning about a distribution’s typical value.

  3. Ask the class to brainstorm characteristics of the "typical" student. Does the typical 12th grader differ from the typical 9th grader? How so? They may say that everyone is different, and that there's no typical student. Keep pressing them to identify characteristics that are typical. The idea is to get them to recognize that there is variability, and yet we might still have an opinion about what is typical. For instance, not all students walk to school, but this might still be the typical experience.

  4. Give students 3 minutes to write down synonyms to the word “typical” in their DS journals. After time is up, have the students share their responses and keep a record on the board. Some possible synonyms might be: normal, average, usual, standard, representative, regular, ordinary, natural, etc.

  5. Once students share their synonyms, ask students to think about which terms apply best to categorical variables and which terms apply best to numerical variables. Ask volunteers to share out their thoughts and give a brief explanation of why they categorized the term as either applying best to categorical variables or numerical variables. Create a T-chart on the board to keep track of their categories.

  6. Next, display the dotplot created by the class with their nutrition facts labels during the previous class (from lesson 8). Ask: what value might we consider to be the typical value of this distribution? Answers will vary by class. Common answers will be to identify the mode (the value with the most labels) or the value in the center. A common wrong answer will be to confuse the frequency with the value. For example, they will say the most typical number of calories was "3" because, perhaps, 100 calories occurred 3 times, and that was more often than any other value. Students may also identify "clumps” of data: "it's somewhere between 110 and 120." That's ok, but probe them as to why they chose that chunk and not another. The point is to get them to see that chunk as being in the middle or center of the distribution.

    1. Hopefully, at least one student will choose a value close to the center of the distribution. If not, point to a value near the extreme and ask them if they think this is typical. Then move closer to the center until they agree on which values are typical.

    2. It is ok to be vague in the definition of typical for today’s lesson. The discussion needs to be very teacher-driven. Some possible points of discussion might be:

      1. Clustering/clumps of data.

      2. Most of the observations are between          and          .

      3. Overall range of the data.

  7. Ask students to reconsider the typical number of sugar grams. What is the typical amount of sugar (in grams) in our snacks? For example, students may come up with the same answer for different reasons: “The typical amount of sugar grams is 10.” The reasons may include the data points are half below and half above; it’s the mode; it has plurality. Then, tie it back to the synonyms they provided. Ask: Which synonym are you using?

  8. In pairs, ask students to discuss the question:

    1. Which synonyms are associated with “center”? Is this concept of center useful for numerical or categorical variables? Center is useful for numerical variables. The center of the distribution often corresponds to our notion of ‘typical value.’ For example, the typical height of the students in our class might be centered around 5’5.
  9. Inform students that the value at the center of the distribution often matches up with our everyday notion of the typical value of a distribution. The middle observation is not always the typical value. Similarly, the middle person would not always be the center value.

  10. Defining the center of a distribution depends on many things, such as the placement of points in the distribution (known as the shape) and how dense the distribution is at certain values (known as the spread).

  11. Ask the students to write down the number of hours of sleep they got last night. They will be creating a dotplot of this data, so ask them:

    1. What do you think the typical value will be?

    2. What do you think the lowest value will be?

    3. What do you think the highest value will be?

    4. What do you think the shape of the distribution will look like?

  12. One-by-one, have them come up to the board (or poster paper) and put a dot above the correct value on the dotplot. After each student has placed a dot on the board, have a discussion about the distribution. Is the typical value similar to what they originally thought? The shape? The variability? Why or why not?

  13. Next, have the students write down the number of hours of sleep they hope to get this Saturday. How do they think this plot will differ from the first plot? Focus discussion on the shape, center, and spread of the distributions. Repeat steps 8-9 and discuss how this plot is similar and/or different than the first plot.

Class Scribes:

One team of students will give a brief talk to discuss what they think the 3 most important topics of the day were.

Homework

Students should continue to collect nutritional facts data using the Food Habits Participatory Sensing campaign on their smart devices or via web browser.