## Mean Averages

### Michelle Barlow

#### Description

Students find the mean, median, and mode by analyzing numerical data.

#### Objectives

The student identifies the mean, median and mode from a set of data.

#### Materials

-Chalk and Chalkboard
-Paper and Pencils for each student
-One copy of the Mean Averages Quiz for each child (see attached file).

#### Preparations

Make certain that all students have paper and pencil and duplicate a copy of the quiz for each child (see attached file).

#### Procedures

1. Write the following terms on the board: Mean (average), Median, and Mode. Tell the students that they are going be learning how to find each of these terms when analyzing numerical data.

2. Tell students that they will start with learning how to find the mean or average of a set of numbers. Explain that the mean of a set of numbers is the average of those numbers. Demonstrate how to find the mean by writing the following numbers on the board: 70,80,90. Tell the class that in order to find the mean that you must first add all of the numbers together.Once you have a sum, then you must divide the sum by the total number of numbers that you added together (sum divided by total number of addends). Show students how to do this procedure on the board. 70+80+90=240 then divide 240 by 3 which equals 80. Tell the students that 80 is the average of the numbers 70.80,90.

3. Tell the class that they are now going to practice finding the mean of some sets of numbers. Write the following sets of numbers on the board:
a. ( 100, 80, 90) answer 80
b. ( 50,75,100) answer 75
Have the students figure out the mean for both sets.

4. Circulate and check to see if students were able to correctly figure out the mean for each.

5. If students as a whole seem to be able to find the mean without any problems then tell them that they are now going to be looking for the median in a set of numbers. Explain that the median is the middle number when a set of numbers is arranged in numerical order. Have five students stand up and make a line. Ask the class who is in the middle of the line. The class should realize that the third person is in the middle because there are two people on either side of them. State that the same principle works for numbers. Write the following set of numbers on the board: (4,6,7,8,9. ) Ask the class which number is in the middle. They should see that the 7 is the middle or median number. Tell the students that they should always make sure that the numbers are in order from least to greatest when finding the median. Remind students that on tests (FCAT) they will not always be given a set of numbers that are in this order. They should put the numbers in order in these cases.

6. Tell the students that they will now practice finding the median numbers in a couple of sets of numbers. Explain to the students that in order to find the median of a set of numbers the numbers must be arranged in order from least to greatest. Write the following sets on the board:
a. (32,45,67,89,99)
b.(12,16,17,19,21,27,30)
Have students write down the median for each set. Circulate to make certain that they got the correct answers. a. 67, b. 19

7. Tell the class that sometimes a set of numbers will have two middle numbers. Have 8 students make a line in front of the room. Ask the class who is in the middle. Students should see that person number 4 and person number 5 would be the middle because three people are on either side of both of them. Explain to the class that when this happens in a set of numbers you must find the mean of the two middle numbers in order to find the median of the set. Demonstrate by writing the following set on the board: (12,16,18,20,22,24,26,28) Show the students how 20 and 22 are both middle numbers in this set. Show how to find the mean of these two numbers by adding them together 20+22=42 then divide 42 by 2 which equals 21. 21 is the median of the set.

8. Have the students find the median of the following sets where each set has two middle numbers:
a. (10,15,20,25,35,40,45,50) answer 30
b. (20,30,40,60,70,80) answer 50
Circulate to make certain the class understands how to find the median of a set of numbers when there is two middle numbers.

9. Tell the students that the final data they will look for today is the mode in a set of numbers. Explain that the mode is the number that appears more often than the other numbers in the set. Write the following set of numbers on the board (12,15,15,22,29). Ask the class if the see a number that appears more than the other numbers. They should be able to recognize that the number 15 appears more than the others. Tell them that 15 is the mode for this set. Make sure that you tell the students that if a set of numbers does not have any number that appears more often than the other numbers then that set does not have a mode.

10. Have students practice finding the modes in the following sets:
a. (90,90,100,100,75,80,75,75) answer- 75
b. (22,23,27,38,45,46) answer- this set does not have a mode

11. Tell the class that they are now going to help you use what they have learned to help you analyze some data. Write the following information on the board;
Total Pounds of Recycled Paper

Month Class A lbs. Class B lbs.
June 10 lbs. 20 lbs.
July 20 lbs. 40 lbs.
August 30 lbs. 57 lbs

12. Tell the students that they are going to use the information on the board to answer some quesions about mean,median, and mode of numbers. Questions: A.. What was the average pounds of paper for each class? Answer Class A. 20 lbs, Class B .39 lbs
B. Which class had the highest average of paper? Answer Class B
C. What is the median number of pounds for each class? Answer Class A. 20 lbs , Class B. 40 lbs.
D. Look at the data for both teams. Is there a mode in the data when you combine it? If so what is the mode? Answer Yes, 20

13. Tell the class that they are now going to take a quiz on today's lesson to help you determine how well they understand mean, median, and mode. Pass out the quiz to each child (see attached file). Collect when completed to use as an assessment. NOTE: If your class will not be able handle learning mean, median, and mode together, you may want to spend a day on each one separately and use the quiz at the end of the lesson on the third day.

#### Assessments

Formatively assess students as you circulate and check student's work on the practice problems during instruction. The quiz (see attached file) canbe used as a summative assessment when you feel that students are ready. Students should answer 4 out of 5 questions correctly to demonstrate mastery.

#### Extensions

This lesson could be extended by having students plot data on a graph for further comparison. The lesson could also be modified by breaking each section into one lesson a day for 3 days with the quiz on the third day. This would allow students that need it more time to practice each concept.

#### Attached Files

A quiz to be used as a summative assessment for this lesson. An answer key is included.     File Extension: pdf