Unit 3, Lesson 4
The Shape of Distributions
Integrated Math 1
Preparation
Lesson Narrative
In this lesson, students describe distributions using appropriate terminology.
- In a symmetric distribution, the mean is equal to the median and there is a vertical line of symmetry in the center of the data display.
- In a skewed distribution, the mean is not usually equal to the median and one side of the distribution has more values farther from the bulk of the data than the other side has.
- A uniform distribution has the data values evenly distributed throughout the range of the data.
- A bimodal distribution has two very common data values seen in a dot plot or histogram as distinct peaks.
- A bell-shaped distribution has a dot plot that takes the form of a bell with most of the data clustered near the center and fewer points farther from the center.
Students practice applying this terminology as they invent reasonable contexts for a described distribution.
The Warm-up activity gives students a reason to begin using language precisely (MP6) and gives the teacher the opportunity to hear how students use terminology and talk about characteristics of the items in comparison to one another. In the Card Sort, as students trade roles, they explain their thinking and they listen to the reasoning of a partner. This provides them with opportunities both to explain their reasoning and to critique the reasoning of others (MP3).
- Describe (orally and in writing) the shape of a distribution, using words such as "symmetric," "skewed," "uniform," "bimodal," and "bell-shaped."
- Interpret a graphical representation to suggest a possible context for the data.
- Let’s explore data and describe distributions.
Required Preparation
None
bell-shaped distribution
In a bell-shaped distribution, most of the data cluster near the center and fewer points are farther from the center. The dot plot or histogram for the data has the form of a bell.
This dot plot shows a bell-shaped distribution.
bimodal distribution
In a bimodal distribution, there are two very common data values. The dot plot or histogram for the data has two distinct peaks.
This dot plot shows a bimodal distribution. The two common data values are 2 and 7.
skewed distribution
In a skewed distribution, one side has more values farther from the bulk of the data than the other side. The mean is usually not equal to the median. The dot plot or histogram for the data shows only one peak leaning to one side.
This dot plot shows a skewed distribution. The data values on the left, such as 1, 2, and 3, are farther from the bulk of the data than the data values on the right.
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