Median, Mode, Range, and the Outlaw called the Outlier

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Objective

SWBAT find the median, mode, range, & outlier of a given data set and recognize them as measures of central tendency or measures of variation.

Big Idea

Median, Mode, Range, & Outlier... So... What Are They?

Curriculum Reinforcer

10 minutes

The curriculum reinforcer, is a daily practice piece that is incorporated into almost every lesson to help my students to retain skills and conceptual understanding from earlier lessons. My strategy is to use Spiraled Review to help my students retain what they learned during the earlier part of the year. This will help me to keep mathematical concepts fresh in the students mind so that the knowledge of these concepts become a part of students' long term memories.

Engagement

10 minutes

To open up this lesson, I will teach my students a song. The lyrics to the song is as follows:

 

Mode, Mode, Mode, the most

Range is the distance in between

Median, middle, Median, middle

The average is the mean.

 

These lyrics are to be sung to the tune of Row, Row, Row, your boat and are a way for students to remember which measurement is which. Often times, students get the measurements mixed up… If you ask them to find the mode, they find the median or if you ask them to find the median they find the mean. This song will help with that confusion

Instructon & Teacher Modeling

10 minutes

Today, the students will continue their exploration of mean and will also be introduced to median, mode, range, and outlier. They will focus on being able to find/calculate these measurements when given a set of data.  I will demonstrate to my student how to calculate these different data measures by conducting a survey of how many total siblings each student has. The data gathered by this survey will be used for the purpose of modeling how to use the data items to calculate the different measures of data highlighted in this lesson.

 

The procedure by which we will conduct this survey is as follows:

  1. I will ask each student to write down the number of siblings that they have on a sticky note.
  2. Each student will then bring their sticky note to the board and place the notes in numerical order from least to greatest creating a list of data.
  3. Once we have the data from each student, I will show the students how to calculate the mean, median, mode, range, and check for any outliers. 

The students will follow along and take notes as I demonstrate how to find the mean, median, mode, range, and check for outliers. Then, I will provide my students with the following data set so that they can practice finding the mean, median, mode, range, and outlier.

 

1)      15, 19, 12, 15, 2, 18, 17, 15, 2, 14 

After the students practice finding these measurements of data, then we will discuss what these measurements tell you about the data set as well as what these measurements cannot tell you about the data set

 

Some examples as to questions that I might ask during this time is:

  • Does this measurement give you an indication as to how random your data is?
  • Between what numbers on the number line would this data be located? How do you know?
  • Does the median tell me how spread out the data is?

***Note: These are just a sampling of possible questions. There are many more questions that can be asked during this time that will provide wonderful amount of information about what the students know and understand.

 

Things that I want students to pull form this discussion are:

  • That the median tells you the exact number in the middle of the data set which let’s you know that half of the numbers in your data set are above this measurement and half are below this measurement.
  • The mode gives us an indication as to the randomness of a data set. If one or more numbers show up several times, chances are that the data is pretty consistent.
  • The range also gives us an indication of how random the data is. If the range is a small number that lets us know that the data in the data set are not very far apart from each other. If the range is a larger number than that lets us know that the data is spread further apart and therefore is a bit more random.
  • An outlier will help us to recognize whether or not the measurements of the range and the mean is reliable. Having an outlier can change the mean and range dramatically.
  • Students should remember the significance behind the data measure called mean from the previous lesson. They should remember that his is a measure of central tendency that takes all the items in a data set into consideration in its calculation of center.

 

***Note: Students should know that the most reliable data set should have measurements for mean, median, and mode that are very close if not the same. And, it should also have a small range, and no outliers.

Independent Exploration

20 minutes

To demonstrate their understanding of the concepts taught in today's lesson my students will complete three tasks over a two day period. The tasks are to be completed in the following order:

  1. Suzi's company
  2. The Candy Bar Task
  3. How Am I Doing In Math

Each of these tasks help students to dive into the significance of the different types of data measures in both conventional and non-conventional ways.

Please click on the tasks, which are attached to this section of this lesson so that you may be privy to the details of each of the tasks.

 

As previously stated, the students will complete these tasks over a two day period. They will be placed in groups of no more than four students. The grouped students will collaborate with each other on how to complete each task successfully, as well as the best way to present the tasks.

 

Closing Summary

15 minutes

To close out this lesson, I will have each group place their tasks on the wall. All of the groups will complete a gallery walk while taking note of similarities and differences to the solution approaches in each of the tasks. I will then facilitate a discussion where students will highlight what they have noted during the gallery walk. During this time, the students should be making thoughtful comments, giving critique, asking questions, and defending their work.

 

TOTD:

Answer the following question – Why is it important to have several measures of data?