## Statistical Specimens

### Lisa Ove GibsonBay District Schools

#### Description

Students explore sampling techniques that are used to collect data. Students also practice finding mean, median, and mode of a set of data. Finally, students determine appropriate measures of central tendency for a situation.

#### Objectives

The student understands and applies the concepts of range and central tendency (mean, median, and mode).

The student identifies the common uses and misuses of probability or statistical analysis in the everyday world.

The student finds the mean, median, and mode of a set of data using raw data, tables, charts, or graphs.

The student determines appropriate measures of central tendency for a given situation or set of data.

The student identifies and uses different types of sampling techniques (for example, random, systematic, stratified).

The student knows whether a sample is biased.

#### Materials

-Summary Sheet of Instruction for Statistical Specimens (See page 1 of Associated File)
-Finding the Mean, Median, and Mode of a Set of Data (See pages 2-3 of Associated File)
-Answer Key: Finding the Mean, Median, and Mode of a Set of Data (See page 4 of Associated File)
-Determining Appropriate Measures of Central Tendency (See page 3 of Associated File)
-Answer Key: Determining Appropriate Measures of Central Tendency (See pages 4-5 of Associated File)
-Scenarios Using Different Sampling Techniques (See pages 5-6 of Associated File)
-Answer Key: Scenarios Using Different Sampling Techniques (See pages 7-8 of Associated File)
-The following site is a Student Web Lesson found on the Beacon site. This lesson allows students the opportunity to practice finding the mean, median, and mode of a data set. Using it is optional, but highly recommended.
-Student Web Lesson: All That Data! http://www.beaconlearningcenter.com/search/details.asp?item=3105
-All That Data! (Student Web Lesson-printable version) (See pages 1-5 of Associated File)
-Data Detective Diary (used throughout the Unit Plan: Statistical Sleuths)
-Classroom display board (Examples: overhead projector, chart paper, or chalk board)
-Corresponding writing device (example-Vis-à-Vis)
-Blank transparency film for copy machines or printers
-[The American Heritage College Dictionary, Third Edition], Boston, New York: Houghton Mifflin Company, 2000, page 644
-Access to a computer lab or a single computer with presentation capabilities and Internet access

#### Preparations

1. Read the information in Vocabulary for Statistical Sleuths. (See Unit Plan Associated File. Further information is available in Extensions). Prepare a mini-lesson using this Associated File. The lesson will serve as the review for the entire unit. Note to teacher: Here are possible ways to use the concepts from Vocabulary for Statistical Sleuths:
(a) Create a game of Jeopardy for class participation,
(b) Provide a copy of Vocabulary for Statistical Sleuths for each student, and then ask students to create an example for each term. Ask students to illustrate whenever possible,
(c) On the chalkboard write a term from Vocabulary for Statistical Sleuths (example: Mean) and ask students to write their own definition for Mean on the chalkboard next to the term. Continue this process until every term from Vocabulary for Statistical Sleuths has been written on the board. You may want students to record their definition in their detective diaries and when complete ask students to peer assess definitions. Make sure students' definitions are acceptable, or
(d) Assign students to groups of four; ask each group to provide a definition (and illustration when possible) for each word (#1 - 24). When complete, allow each group to share their definitions with the entire class.

2. Review the WebLinks section of this document prior to instruction for a better understanding of the concepts that are used in today’s instruction.

3. Create overhead transparencies of documents from the Associated File:
(a) Finding the Mean, Median, and Mode of a Set of Data. (See Associated File.)
(b) Determining Appropriate Measures of Central Tendency. (See Associated File.)
(c) Optional: Printable Version of the Student Web Lesson: All That Data! (See Associated File.)

4. Prepare a large writing space, preferably an overhead projector, in the front of the classroom to record
(a) Detective diary entries (#9) and
(b) Comments/ideas generated during today's discussion (obtain appropriate writing tools).

5. Set up a presentation cart (with computer/television) and/or a computer lab to accommodate the online Student Web Lessons referenced in the WebLinks or Materials section of this lesson.

6. Using a computer that is Internet accessible, review the Student Web Lesson: All That Data! prior to instruction (see the WebLinks section of this document for the URL address).

7. Collect and provide formative feedback to students regarding their answers to All That Data! before using the Student Web Lesson for full class instruction.

8. Make sure that students' detective diaries are available for today’s assignment.

9. Create copies of Scenarios Using Different Sampling Techniques for each student. (See Associated File.)

10. Review each of the following documents from the Associated File before assessing student work:
(a) Answer Key to Finding the Mean, Median, and Mode of a Set of Data. (See Associated File.)
(b) Answer Key to Determining Appropriate Measures of Central Tendency. (See Associated File.)
(c) Answer Key to Scenarios Using Different Sampling Techniques. (See Associated File.)

#### Procedures

Prerequisite: The student understands fractions (parts to the whole) and how to convert a fraction to a percentage. These concepts will be utilized in the construction of a circle graph.

Part I:
1. REVIEW: Review misconceptions from activities, such as Data Display Practice in the lesson, The Guise of a Graph Gumshoe. Return assessed Data Display Practice worksheets to students. Remind students that they will take the summative assessment in three days.

2. NEW MATERIAL: Use overhead transparency of Finding the Mean, Median, and Mode of a Set of Data. (See pages 2-3 of the Associated File.) For whole class instruction, write the correct responses for a, b, and c. Model how to find the mean, median, and mode for students. Most students have successfully found the mean, median, and mode for several years. Use your own discretion and/or the diagnostic assessment to determine your students' needs. This serves as formative assessment.

3. Option #1: Provide a copy of All That Data! (a Student Web Lesson, printable version) for each student. (See pages 1-5 of the Associated File.) Instruct students to write their responses on their copy of All That Data! (Student Web Lesson, printable version) before using the Student Web Lesson as an instructional model. Option #2: Create a transparency of All That Data! (a Student Web Lesson, printable version) to use for a whole class discussion. This serves as formative assessment.

4. After all students complete All That Data! (Student Web Lesson, printable version), either Option #1 or #2, use the actual online Student Web Lesson All That Data! as an instructional model. (See the Weblinks section of this document for the specific Web address.) Demonstrate the use of the Web lesson page by page on an Internet accessible computer/TV presentation cart. In this lesson, students review a group of committee members' survey results and how they displayed their data in order to identify the range, mean, median, and mode of their individual and collective data results.

5. Provide a class discussion at the end of each Web page. Come to a consensus about the best answer for each field during the discussion. Type in the most popular answers from the class discussion in each field of the Web lesson and further discuss the computer's responses as a whole class. The program will offer hints if the answer is not correct, and it will offer congratulations if you are right. If you have a computer lab or access to several computers, you may choose to allow students to complete the Student Web Lesson, All That Data! individually or in groups of two students.

6. If using Option #1, when complete, ask students to turn in their answers for All That Data! (Student Web Lesson, printable version). Provide formative feedback for each student and offer more instruction to students who had difficulty with any part of this lesson.

Part II:
7. Special Note: Review misconceptions that students may have had from Part I of this lesson. Remind students the summative assessment is in two days. Use overhead transparency of Determining Appropriate Measures of Central Tendency. (See page 15 of the Associated File.) For whole class instruction, model how to find the mean, median, and mode for students. After discussing each response with students, write the correct responses for 1a, b, and c. Also, show students how to respond to #2. (See Answer Key to Determining Appropriate Measures of Central Tendency on page 16 of the Associated File.) If students need additional practice, create other problems like this one for students. This serves as formative assessment.

8. Write this entry in an area that all students can see, Detective Diary Entry #9: Define each of the following sampling techniques: random, systematic, and stratified. Also define when a sample can be biased. Ask students to include as much specific information as possible. This serves as formative assessment. This activity serves as a review for students. They were already taught these techniques in the lesson, Sampling Snoops. If you have not used this lesson, then you can acquire Sampling Snoops at http://www.beaconlearningcenter.com/search/
details.asp?item=1564. The definitions for each of these sampling techniques is in Vocabulary for Statistical Sleuths. (See Unit Plan Associated File. Further information is available in Extensions.)

9. Option #1: Provide each student with a copy of the activity, Scenarios Using Different Sampling Techniques. (See Associated File.) Students complete this activity. Use Answer Key to Scenarios Using Different Sampling Techniques to assess the best choice for each question. (See Associated File.) Also, assess students' responses based on completeness using the criteria in the Long-Answer Question Rubric. (See Unit Plan Associated File. Further information is available in Extensions.)
Option #2: Read the sampling Scenarios aloud and discuss the answers as a class. As a more individual assessment, have students verbally create an example of one type of sampling and pose it to a partner to see if they agreed that it was a good example. This serves as formative assessment.

Part III:
10. Special Note: Remind students that the summative assessment is tomorrow. Review all concepts from the Unit Plan: Statistical Sleuths. Use Vocabulary for Statistical Sleuths as your guide during review. (See Unit Plan Associated File. Further information is available in Extensions.) One reason this file is helpful for review is because the summative assessment will use the same terminology. See the Teacher Preparation section of this document for suggestions on how to conduct the review.

11. Offer as many practice opportunities as possible for students before administering the summative assessment for the Unit Plan: Statistical Sleuths.

#### Assessments

Formative assessments: Students find the mean, median, and mode in the activity, Finding the Mean, Median, and Mode of a Set of Data. (See Associated File.) Students also successfully complete All That Data! (a Student Web Lesson, printable version). (See Associated File.) Use Answer Key to Finding the Mean, Median, and Mode of a Set of Data and the answers collected by the teacher after completing the Student Web Lesson, All That Data! (See Associated File.)

Formative assessment: Students determine the appropriate measure of central tendency for a given situation in the activity, Determining Appropriate Measures of Central Tendency. (See Associated File.) The Answer Key for Determining Appropriate Measures of Central Tendency shows the best response for each question in the activity. (See Associated File.)

Formative assessment: Students identify different types of sampling techniques being used; however, they will not use these sampling techniques.

Formative assessment: Students define systematic, stratified, and random sampling techniques, as well as identify when a sample can become biased. Students also successfully complete the worksheet, Scenarios Using Different Sampling Techniques. (See Associated File.) Students' answers may vary. The Answer Key to Scenarios Using Different Sampling Techniques offers the best choice for each sampling technique being demonstrated. Assess students' responses based on completeness using the criteria in the Long-Answer Question Rubric. (See Unit Plan Associated File. For more information, see the Extensions section.)

#### Extensions

1. Here are optional standards that could be integrated into this activity:
-Determines the mean, median, and mode and range of a set of real-world data using appropriate technology.
-Organizes, creates graphs, and analyzes a set of real-world data using appropriate technology.

2. The Beacon Unit Plan associated with this lesson can be viewed by clicking on the link located at the top of this page or by using the following URL: http://www.beaconlearningcenter.com/search/details.asp?item=2958. Once you select the unit’s link, scroll to the bottom of the unit plan page to find the section, Associated Files. This section contains links to the Unit Plan Overview, Diagnostic and Summative Assessments, and other associated files (if any).

3. This lesson plan was written as part of the Unit Plan: Statistical Sleuths. It is the fourth and final lesson plan in the series.

4. Allow students to peer–assess each other’s diary entries if they are at a point where they can assess the content accurately enough to provide effective feedback.

This site offers interactive information and an opportunity for students to practice finding and using the median of a set of data.
The Party Comedian

This site offers interactive information and an opportunity for students to practice finding and using the mean, median, and mode of a set of data.
All That Data!

This site offers additional practice for students to practice finding the mean, median, and mode of a set of data.
Florida Comprehensive Assessment Test (FCAT) - FCAT Test Item and Performance Task Specifications (2001) (See pages 231-233)

This site offers information about how to collect reliable data.
Collecting Data

This site offers use of different sampling techniques in a real-world context and offers a section titled, Sampling Techniques and Terminology.
Sampling Techniques and Terminology

This site offers comparisons and contrasts between histograms and bar graphs.
Histograms vs. Bar Graphs Discussion

This site offers an excellent program that randomly generates numbers for population sampling.
Research Randomizer

This site offers a more extensive definition and an example for mean, median, and mode.
Range, Mean, Median, and Mode

#### Attached Files

Statistical Specimens Associated File     File Extension: pdf