A 6th grade tek

What Is the Mean?

The mean is a measure of central tendency, meaning it represents the "central" or "typical" value of a set of numbers. It is often referred to as the average because it's one of the most common ways to describe a group of numbers with a single value.

Steps to Calculate the Mean

1. Add all the numbers together.
   
   

   • This gives you the total sum of all the values in the set.
     
     

2. Count how many numbers there are.
   
   

   • This tells you the number of values in the set.
     
     

3. Divide the sum by the number of values.
   
   

   • This gives you the mean.
     
     

Example 1: Simple Set of Numbers

Let’s say you have the numbers: 3, 5, 7, and 9.

• Step 1: Add the numbers: 3+5+7+9=243 + 5 + 7 + 9 = 243+5+7+9=24
  
  

• Step 2: Count the numbers (there are 4 numbers).
  
  

• Step 3: Divide the sum by the count: 244=6\frac{24}{4} = 6424​=6
  
  

So, the mean of 3, 5, 7, and 9 is 6.

Example 2: Larger Set of Numbers

Now let’s consider a bigger set of numbers: 10, 20, 30, 40, 50.

• Step 1: Add the numbers: 10+20+30+40+50=150 + 20 + 30 + 40 + 50 = 290+20+30+40+50=430
  
  

• Step 2: Count the numbers (there are 5 numbers).
  
  

• Step 3: Divide the sum by the count: 1505=30\frac{150}{5} = 305150​=30
  
  

So, the mean of 10, 20, 30, 40, and 50 is 30.

What Does the Mean Tell Us?

The mean gives a sense of the "average" value of the set. If most of the numbers are close to the mean, that means the set is balanced. However, if there are numbers far away from the mean (very large or very small), it might indicate that the data is skewed, and the mean may not represent the "typical" value well.

Example of How Outliers Affect the Mean

Suppose we have the following set of numbers: 1, 2, 3, 4, 100.

• Step 1: Add the numbers: 1+2+3+4+100=1101 + 2 + 3 + 4 + 100 = 1101+2+3+4+100=110
  
  

• Step 2: Count the numbers (there are 5 numbers).
  
  

• Step 3: Divide the sum by the count: 1105=22\frac{110}{5} = 225110​=22
  
  

In this case, the mean is 22, but it doesn’t represent most of the numbers, since 100 is far away from the others. The value 100 is an outlier—a number that is much higher or lower than the rest of the data points. The mean is influenced by outliers, and in cases like this, the mean may not reflect the typical or central value of the set.

Summary of Key Points:

• The mean is the sum of the values divided by the number of values.
  
  

• It provides a measure of the "average" value of a data set.
  
  

• The mean can be influenced by outliers, which might make it less representative of the set in some cases.