Submitted by: Tuiren Bratina and Janet Bosnick

University of North Florida

Date: June, 1996

BRIEF DESCRIPTION OF THE LESSON:

The students will be able to:

1. State measures which describe central tendency and dispersion of a set of numbers.
2. Find the median, mean, and mode of a set of numbers.
3. Find the range of a set of numbers.
4. Produce sets of numbers whose statistical measures are specified.
5. Use technology to calculate statistics.

Grade Level(s):

5, 6

Subject(s):

• Mathematics/Statistics

BACKGROUND INFORMATION FOR THE TEACHER:

This lesson is intended for students to gain conceptual understanding. The graphing calculator is valuable for checking if the sets of numbers students produce satisfy specifications.

It is beyond the scope of this beginning lesson to illustrate if one of these measures of central tendency provides a better description of a population's characteristics than another measure. That would be a very important follow-up lesson.

CONCEPTS COVERED IN THE LESSON:

• Mean (average)
• Median
• Mode
• Rang

MATERIALS OR EQUIPMENT LIST:

Graphing calculators such as Texas Instruments TI-80

PROCEDURES:

• Median:

  Have an odd number of students stand in the front of the classroom, arrange themselves in terms of ascending heights. The height of the person standing in the middle is the median height.

  Repeat the activity with an even number of students. The median will be halfway between the heights of the two students standing in the middle.

  Have students give the definition of median in their own words.

• Mode:

  For the groups of students standing at the front of the room, if there are some who are the same height, then the height that occurs most frequently is the mode. (It is possible that no two students are the same height. It is also possible to have more than one mode.)

  Have students give the definition of mode in their own words.

• Mean (average):

  Have students compute this by adding up the heights and dividing by the number of students in the sample. For the sake of expediency, convert heights to inches before doing the arithmetic.

  It is important for the teacher to have the students look at their answer in relation to the entire list of numbers.

• Range:

  Have everyone except the tallest and shortest students in that group sit down. Measure the distance from the top of one of their heads to the top of the other person's head. That is the range. Guide students to tell you that subtraction can be used to find this.

USING TECHNOLOGY TO FACILITATE UNDERSTANDING OF STATISTICAL CONCEPTS:

Students need to practice the mathematics operations that are used in finding these statistical indices. There are plenty of problems in the textbook for students to become proficient at the arithmetic.

To solidify understanding of the concepts, students should be able to produce sets of numbers which satisfy certain specifications. Following are types of questions which can be answered with the assistance of a graphing calculator, and students will learn to rely on themselves by checking the "answers" provided by the calculator.

Make a list of ten numbers whose:

(List 1) mean is 75.
(List 2) mean is the same as the mean for List 1, but whose range is bigger than the range of the numbers in List 1.
(List 3) whose median is 6 and whose range is 9.
(List 4) whose mean is bigger than the median.

ASSESSMENT:

The first type of assessment items are just like the ones immediately above. For ease in grading, the number of these will have to be kept small, and in general, the lists should have no more than five numbers.

The standard questions in which a set of numbers is given and students are asked to compute the mean, median, mode, and/or range are good items. Choose the sets of numbers so that the scenarios are interesting and relevant to the students.