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Lesson 11: What Shape Are You In?

Lesson 11: What Shape Are You In?

Objective

You will learn to classify distributions in terms of shape, and to suggest theories for why a distribution might be one shape or another.

Vocabulary

symmetric, right-skewed, left-skewed, unimodal, bimodal

Essential Concepts

Lesson 11 Essential Concepts

Identifying the shape of a histogram is part of the Interpret step of the Data Cycle.

Lesson

  1. For this lesson you will be sorting 18 histograms into groups according to their shapes.

  2. In a histogram, the type of data being measured is represented on the horizontal axis, and the vertical axis represents how many observations are in each bar.

  3. Histograms that have similar shapes should be placed together in one of the six boxes. This activity has been formatted so that you can place the histograms directly on top of each other to verify whether or not their shapes are similar.

    Directions: Copy the Histogram Sort PowerPoint slide to your Google Slides. Find View on the menu option, then go to Zoom and choose 50% to view the 18 histograms that need to be sorted.

  4. Once you have sorted the histograms into groups, answer the following questions in your IDS Journal:

    1. Describe what’s similar about the plots in each group.

    2. Pick the best example of a graph from each group.

    3. Give the group a name that you think describes the general shape.

    4. If there are graphs that do not fit into any group, try to determine why it was difficult to place them. What is different or confusing about them?

  5. After writing down your observations, think about how your classmates may have grouped their histograms. Do you think their groupings and general shapes would be similar to yours?

  6. In statistics we use specific terminology when discussing the shapes of distributions, such as symmetric, right-skewed, left-skewed, unimodal, bimodal, etc. A symmetric distribution looks like a bell with a peak at the center and the "tails" on each side nearly identical. A right-skewed distribution has a peak near the left and a "tail" on the right. A left-skewed distribution has a peak near the right and a "tail" on the left. A unimodal distribution has only one peak, also known as a "mode". A bimodal distribution has two peaks.

    Note: Another type of distribution is a "uniform distribution", which has no peak and looks almost like a rectangle.

    Did you use any of these terms? If not, identify which of your histograms could be classified as each shape.

  7. Let's practice looking at a scenario and determining what a corresponding histogram might look like:

    Scenario: What would the distribution of grades on an easy test look like?

    Answer: The distribution of grades on an easy test would be left-skewed and unimodal. Since the test was easy, a lot of students will score high, so most scores will be in the 80s and 90s with a single peak around 90. There will only be a few students that have low scores like 60s and 70s, so there will be a tail on the left.

  8. Read the following scenarios and try to determine what a corresponding histogram might look like. In your IDS Journal, use statistical terms to describe your answer and provide a justification.

    1. The grades on a difficult test.

    2. The number of times IDS students study during the first week of class.

    3. The age of cars on a used car lot.

    4. The amount of time spent by students on a difficult test (max time allowed is 50 mins).

    5. The heights of students in your high school band.

    6. The salaries of all persons employed at a school district.

Reflection

What are the essential learnings you are taking away from this lesson?

Homework

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