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7th Grade Math / Lesson 1: Averages

AVERAGES
What will we be learning in this unit?


  • In this lesson you will learn how to find the different types of averages and examine their usefullness.
Vocabulary words are found in this purple color throughout the lesson. Remember to put these in your notebook.


AVERAGES


Another phrase for an average is "measure of central tendency". In other words, it is a way to determine an approximate center of the numbers.

There are three different measures of central tendencies (averages).

  1. MEAN: this is the common form of an average. You add up all of the values that you have and then divide this sum by how many numbers were added together.
  2. MEDIAN: this is the middle value of the numbers. You must first put your numbers in order, then find the one that is in the middle.
  3. MODE: this is the value that appears the most times in your set of numbers. Sometimes there is no mode, if all of the numbers appear once in the list.


AVERAGES

Your grade in math class is the measure of central tendency (average) of your grades during the class. Suppose these were your grades
85, 88, 91, 77, 74, 89, 80, 77, 88

1. Find your mean grade.
85+ 88+ 91+ 77+ 74+ 89+ 80+ 77+ 88 = 749
Now take 749 and divide by 9 because there are 9 grades.
749 / 9 = 83.222222 which rounds to 83.22

2. Find your median grade. Put the numbers in order first.
74, 77, 77, 80, 85, 88, 88, 89, 91
The number in the middle is 85

3. Find the mode.
We see that 77 and 88 both occur twice in the list of grades.
Both 77 and 88 are the modes because they appear the most times.


AVERAGES
The range of a set of numbers is the difference between the largest and the smallest values.
 
Find the range of your grades from the previous problem.
85, 88, 91, 77, 74, 89, 80, 77, 88
Find the highest and the lowest values.
                  Highest:  91
                  Lowest:  74
         Now find the difference between the two.
 
                 91 - 74 = 17
 
The range of the grades is 17.
 

 


 
  • Can you find a mean, median, and mode for a set of data?
  • Can you find the range of a set of data?
  • Go back to the classroom to get to your homework and any other items you need to attend to.