Shape Up Your Data: Exploring Distributions

Mathematics Grades 7th Grade 5:06 Video
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Lesson Description

Learn about the shapes of data distributions: symmetrical, right-tailed (skewed right), and left-tailed (skewed left). Discover how these shapes tell us about the data's central tendency and spread.

Video Resource

Thinking about shapes of distributions | Data and statistics | 6th grade | Khan Academy

Khan Academy

Duration: 5:06
Watch on YouTube

Key Concepts

  • Data Distribution
  • Symmetrical Distribution
  • Skewed Distribution (Right-tailed and Left-tailed)

Learning Objectives

  • Students will be able to identify symmetrical, right-tailed, and left-tailed distributions from histograms and box plots.
  • Students will be able to describe the characteristics of each type of distribution.
  • Students will be able to relate the shape of a distribution to potential real-world scenarios.

Educator Instructions

  • Introduction (5 mins)
    Begin by asking students what they already know about data representation. Show a simple bar graph and ask them to describe what they see. Introduce the idea that data can have different 'shapes' and that these shapes can tell us something about the data.
  • Video Viewing (10 mins)
    Play the Khan Academy video "Thinking about shapes of distributions | Data and statistics | 6th grade | Khan Academy." Instruct students to take notes on the key vocabulary (symmetrical, right-tailed, left-tailed, skewed) and the examples given.
  • Discussion and Examples (15 mins)
    After the video, review the key vocabulary and concepts. Discuss the examples from the video and work through a few additional examples as a class. Show histograms and box plots and have students identify the shape of the distribution.
  • Independent Practice (15 mins)
    Provide students with a worksheet containing several histograms and box plots. Have them individually identify the shape of each distribution and explain their reasoning. Encourage them to think about real-world scenarios that might create these types of distributions.

Interactive Exercises

  • Distribution Shape Sort
    Provide students with cards showing different histograms and box plots. Have them sort the cards into three categories: Symmetrical, Right-tailed, and Left-tailed. Students can work in small groups to complete the sort.
  • Create-a-Distribution
    Give students a scenario (e.g., test scores, height of students, waiting times at a restaurant). Ask them to create a data set and a corresponding histogram that represents the scenario. Have them identify the shape of the distribution they created.

Discussion Questions

  • What does it mean for a distribution to be symmetrical?
  • How can you tell if a distribution is right-tailed or left-tailed?
  • Can you think of a real-world example of data that might have a right-tailed distribution? What about a left-tailed distribution?
  • How can understanding data distribution help us with analyzing data?

Skills Developed

  • Data Interpretation
  • Critical Thinking
  • Visual Literacy

Multiple Choice Questions

Question 1:

Which of the following describes a symmetrical distribution?

Correct Answer: Data is evenly distributed around the mean.

Question 2:

What is another name for a right-tailed distribution?

Correct Answer: Skewed Right

Question 3:

In a box plot, which part represents the middle 50% of the data?

Correct Answer: The box

Question 4:

If a distribution has a tail on the left side, it is said to be:

Correct Answer: Left-tailed

Question 5:

Which of the following data displays is used in the video to describe data distributions?

Correct Answer: Histogram and Box Plot

Question 6:

What can the shape of a data distribution tell us?

Correct Answer: The time the data was collected

Question 7:

In a symmetrical distribution, where is the median likely to be?

Correct Answer: Close to the center

Question 8:

Which of the following would likely result in a skewed-right distribution?

Correct Answer: The test scores on a very easy test

Question 9:

Skewness helps us understand the location of the _____ in relation to the median and mode.

Correct Answer: mean

Question 10:

If a box plot's median is significantly to the left within the box, the data can be described as _____.

Correct Answer: right-skewed

Fill in the Blank Questions

Question 1:

A distribution that is roughly the same on both sides is called ________.

Correct Answer: symmetrical

Question 2:

A distribution with a long tail extending to the right is said to be ________.

Correct Answer: right-tailed

Question 3:

In a box plot, the ________ represents the middle value of the data.

Correct Answer: median

Question 4:

When a distribution is skewed, the ________, median and mode are not all the same.

Correct Answer: mean

Question 5:

Another name for a left-tailed distribution is ________.

Correct Answer: skewed left

Question 6:

Histograms and box plots are used to describe the ______ of data.

Correct Answer: shape

Question 7:

The 'meat' of the distribution is represented by the _______ in the box plot.

Correct Answer: box

Question 8:

When the mean of a distribution is to the left of its median and mode, the distribution is typically ________ skewed.

Correct Answer: left

Question 9:

The ends of the box plot are known as the _______.

Correct Answer: whiskers

Question 10:

If the data is symmetric, folding the histogram across the _______ of symmetry allows for the sides to meet.

Correct Answer: line

Educational Standards

7.D.1:Interpret and analyze data, creating the most appropriate display, using a variety of tools. 7.D.1.1:Design simple experiments, collect data, and calculate measures of center (mean, median, and mode) and spread (range and interquartile range). Use these quantities to draw conclusions about the data collected and make predictions. 7.D.1.3:Use technology to create and analyze box plots.

Teaching Materials

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