Understanding The Measure of Center

Understanding The Measure of Center

Introduction to the Line Plot

Opening

Introduction to the Line Plot

Look at this line plot.

  • Without making any calculations, what do you think the mode, median, and mean are for the data shown?

Math Mission

Opening

Create line plots that fit given criteria about measures of center.

Explore a Line Plot

Work Time

Explore a Line Plot

Explore the line plot.

Start by entering some data. Explain what you did to reach each of the following goals.

  • Make the median greater than the mean.
  • Make a line plot in which the median is not one of the data points.

(NOTE: To change the starting number, you need to click and drag rather than use you finger.)

INTERACTIVE: Line Plot with Stats

Explore Measures of Center

Work Time

Explore Measures of Center

With a partner, continue working with the line plot, and answer the following questions:

  • What happens to the mean if you add data points above the mean?
  • What happens if you add data points below the mean?
  • Can you add data both above and below the mean so that the mean does not change?
  • What happens to the median if you add data points above the median?
  • What happens if you add data points below the median?
  • Can you add data both below and above the median so that the median does not change?
  • Think about whether the mean would go up or down if you added a data point above the mean.
  • If the mean is 6 and you add a data point at 4, where would you have to add another data point so that the mean does not change?

INTERACTIVE: Line Plot with Stats

Hint:

Think about whether the median would go up or down if you added a data point above the median.

Prepare a Presentation

Work Time

Prepare a Presentation

Prepare a presentation that explains how you changed the measures of center by adjusting the points on the line plot.

Challenge Problem

  • Is it possible for the mode to be greater than the median when the mean is less than the median?

Make Connections

Performance Task

Ways of Thinking: Make Connections

  • Take notes about any interesting discoveries that your classmates made about how adding or removing data points from a line plot affects the measures of center.

Hint:

As your classmates present, ask questions such as:

  • What was your goal when you explored the Line Plot with Stats interactive? How did you reach that goal?
  • What determines whether the mean will change and how it will change when you add data to a data set?
  • What determines whether the median will change and how it will change when you add data to a data set?

Mean, Median, and Mode

Formative Assessment

Summary of the Math: Mean, Median, and Mode

Read and Discuss

  • Measures of Center
    • 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.
  • Measures of Spread
    • Range: The difference between the extreme (least and greatest) values in a data set.
    • Mean Absolute Deviation: A measure of variation in a set of numerical data, computed by adding the distances between each data value and the mean, then dividing by the number of data values.
  • Outlier: A data value that is far from the rest of the data.

Hint:

Can you:

  • Explain how the different measures of center are affected when data values are added or moved?
  • Understand why the median and mean of a data set do not have to be data values, but why the mode, if it exists, will always be a data value?
  • Describe or give an example of a data set for which the median is a better measure of what is typical than the mean?

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.

When I look at a line plot, this is how I find or estimate the measures of center (mean, median, and mode) and spread (range and outlier) ...