Construction of A Line Plot

Construction of A Line Plot

Sharing Apples

Opening

Sharing Apples

Watch the video. It begins with students discussing how they could share their apples equally. As you watch, think about the mathematics that the students use.

  • Talk to your partner about the method they used.

VIDEO: Sharing Apples

Introduction to the Mean

Opening

Introduction to the Mean

Watch the second video to see how the students decided to share the apples. As you watch, think about the mathematics that the students use.

  • Write an expression for the method they used.

For both methods, the students got the same number of apples. This number is the mean of the total number of apples.

The mean is a measure of center in a set of numerical data, computed by adding the values in a list and then dividing by the number of values in the list.

VIDEO: Sharing Apples 2

Math Mission

Opening

Organize quiz scores in a line plot, and summarize them using the mean.

Represent Math Quiz Data

Work Time

Represent Math Quiz Data

A class took a math quiz in which the highest possible score was 6 points. This data set shows the scores:

{6, 1, 0, 2, 3, 4, 3, 1, 2, 6, 3, 5}

  • Sketch a line plot of the data.

Hint:

  • Start by drawing a horizontal line.
  • Find the extreme values in the data set. Write all of the possible numbers, from the minimum to the maximum, so that they are evenly spaced and under the line.
  • For each value in the data set, place an X or a dot above the line in the appropriate column.
  • Cross off each number in the data set as you go.
  • Label the horizontal line and add a title to your line plot.
  • Check that the number of Xs or dots in your line plot matches the number of values in the data set.

Analyze Math Quiz Data

Work Time

Analyze Math Quiz Data

Using these same data about the math quiz, answer the following questions.

{6, 1, 0, 2, 3, 4, 3, 1, 2, 6, 3, 5}

  • What is the sum of the values in the data set?
  • How many data values are there?
  • Find the mean of the data.
  • Use either the list of values in the data set or your line plot to answer these questions:
    • What is the lowest score? What is the highest score? The difference between the lowest score and highest score is called the range.
    • Which score occurs most often? The score that occurs most often is called the mode.
    • Which score is in the middle of the data? The middle value is called the median.
    • Which score makes up the middle 50 percent of the data?
    • What do you think the typical score is?

Hint:

To find the mean, add up all the data values and divide by the number of data values.

Prepare a Presentation

Work Time

Prepare a Presentation

Prepare a presentation that includes the following information:

  • Explain how you found the mean.
  • Explain how you identified the lowest score and the highest score.
  • Explain how you identified which score occurs most often.
  • Explain how you determined which score is in the middle of the data.
  • Explain how you determined which scores make up the middle 50 percent of the data.

Challenge Problem

If two more students take the quiz, what could their scores be so that the mean does not change?

Make Connections

Performance Task

Ways of Thinking: Make Connections

Take notes as your classmates share how they calculated the mean and identified particular scores.

Hint:

As your classmates present, ask questions such as:

  • How did you find the mean?
  • How did you identify the lowest score?
  • How did you identify the highest score?
  • How did you identify which score occurs most often?
  • How did you determine which score is in the middle of
    the data?
  • How did you determine which scores make up the middle 50 percent of the data?
  • How do the mean, the score in the middle of the data, and the score that appeared most often compare?

The Mean and Describing Data

Formative Assessment

Summary of the Math: The Mean and Describing Data

Read and Discuss

  • Mean: A measure of center in a set of numerical data, computed by adding the values in a list and then dividing by the number of values in the list.
  • Median: A measure of center in a set of numerical data. The median of a list of values is the value appearing at the center of a sorted version of the list, or the mean of the two central values, if the list contains an even number of values.
  • Mode: A measure of center that occurs the most often in a data set. There can be more than one mode, or none at all.
  • Range: The difference between the least and greatest values in a data set.

Hint:

Can you:

  • Describe what the mean is and how to calculate it?
  • Describe what the median is and how to find it?
  • Describe what the mode is and how to find it?

Reflect on Your Work

Work Time

Reflection

Write a reflection about the ideas discussed in class today. Use this sentence starter if you find it to be helpful.

One thing I learned about the mean is …