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Lesson 16: What Is Normal?

Lesson 16: What Is Normal?

Objective

You will learn what a normal distribution is and how to identify one.

Vocabulary

bell-shaped, normal curve, normal distribution

Essential Concepts

Lesson 16 Essential Concepts

The normal curve, typically called the "normal model", but also referred to as the "Gaussian distribution" or "bell curve," is a model that describes many real-life distributions.

Lesson

  1. Recall that in Unit 1, Lesson 11 (What Shape Are You In?), you sorted histograms into groups based on their shapes.

  2. For the next activity, click on the document name to download a fillable copy of the Normal Plots handout (LMR_2.15).

    The Normal Plots document includes 6 plots (SAT Math, SAT Verb, ACT Mathematics, ACT Reading, ACT English, and ACT Science Reasoning), and contains some of the unimodal bell-shaped distributions from the Sorting Histograms handout from Unit 1, Lesson 11 (Sorting Histograms handout (LMR_1.10).

  3. Observe the group of bell-shaped distributions from the Normal Plots file and answer the following questions in your IDS Journal:

    1. What characteristic does this particular group share?

    2. These types of distributions are often referred to as bell-shaped. Why might this term be used?

  4. Notice the similarities between the shape of a bell and the shape of these distributions.

  5. This shape occurs often in real life. It occurs so often that it’s been given its own name: the normal curve, or normal distribution. Can you think of distributions where you have seen normal curves in previous labs?

  6. Watch the first 41 seconds of the New York Times video, Bunnies, Dragons, and the Normal World by clicking the link below. This video will give you some more background on the normal distribution.

    http://www.nytimes.com/video/science/100000002452709/bunnies-dragons-and-the-normal-world.html

  7. The normal curve has a very precise mathematical definition, which is pretty complex, bu the result is a curve that looks like the one in the “Bunnies” video. In general, the curve looks like the plot shown below.

  8. Normal distributions are good for describing some populations of people. For example, people’s heights are often considered to be normally distributed. Check out the famous Frank Anscombe photograph below. This photo was taken of a group of randomly selected college women who stood in height order.

  9. Why do you think the normal curve is a good fit to the histogram in the above picture? Notice that more people are near the center of the distribution, and fewer are in the outerbedges, or tails. Answer the following questions in your IDS Journal:

    1. Notice that there is a peak in the center of the distribution. What height do you think is at the center?

    2. Why are more people in the center and fewer people in the edges, or tails, of the distribution?

  10. The normal curve is a good description of a distribution when it makes sense that there is a single "typical" value with random deviations above and below that value. Answer the following in your IDS Journal:

    1. Why does this make sense with heights but not with incomes?

    2. Are there more real-life examples, other than height, that you think might follow a normal distribution?

    3. Does it matter that the curve drawn on the photograph does not match exactly to the women’s heights?

  11. During the next few lessons you will be learning more about the normal distribution. In particular, you will learn about a new measure of spread used to describe a normal distribution, how to calculate probabilities from this distribution, and how to randomly sample from this distribution.

  12. Use an index card or a 3 x 5 piece of paper to create a "cheat card" to help you remember information about the normal curve.

Reflection

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