Finding the Mean, Median & Mode
Lesson
Topic Index | Grade 6 Math | Intermediate Test Prep | StudyZone

  
 


In everyday life it is often important to collect data, perhaps from a survey, or a questionnaire. Once we have collected the data it is then important to arrange it in a way which allows someone to analyze the information, so that conclusions or decisions can be made. 
Mathematicians have named this study of "data" 
Statistics
3 of the most important statistics we use when we analyze data are called:
The mean, the median and the mode.

In this lesson we will define these three terms and demonstrate how to determine these statistics using some basic arithmetic skills.
We will also learn when each measure should be used.
 

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The
Mean


 

The mean of a set of data is the arithmetic average.  To find the mean, add all the data values together and divide by the number of values.

Let's start with an easy example.

In her last 5 games Sara has scored the following number of points respectively:
12, 16, 11, 17, and 18.
What is the mean of these scoring totals?

 To determine the mean all we have to do is add up all of her points and then divide by the number of games she played.

12 + 16 + 11 + 17 + 18 = 74

74/5 = 14.8

Sara's scoring mean was 14.8 points per game!

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The
Median

 

The median is the middle value after the data has been arranged in either ascending (smallest to largest) OR descending (largest to smallest) order.  If the set of data contains an even number of values, then the median is the average (the mean) of the two middle values.

Let's try a couple of these...

  Jake received the following test grades on his last 7 quizzes:
79,88,75,71,89,80,92
What was his median grade?

     First we must arrange the scores in either ascending or descending order:
In ascending order:  71,75,79,80,88,89,92
In descending order:  92,89,88,80,79,75,71 
In this set we have 7 values, and because 7 is an odd number we have a middle value.  The middle value will be the 4th number from either end of the set.
In this case the median would be
71,75,79,80,88,89,92
80!  the median of this set is 80      

 

Now let's do one with an even number of data values

Over an 8 day period Bessy, the cow, produced the following total gallons of milk per day:
16,18,19,15,14,20,17,22
What was the median number of gallons over this period of time?

Again, the first step is to arrange the values in order.
Let's put them in ascending order this time:
14,15,16,17,18,19,20,22
Notice that in this problem the number of data values is even.
There are 8 entries.  That means that there is no value exactly in the middle.  In this case in order to find the median we will need to find the average (the mean) of the
two middle values.
14,15,16,17,18,19,20,22
I have highlighted the 2 middle values.
To average them we simply add them together
and divide by 2.
17 + 18 = 35
35/2 = 17.5
The median of this set is 17.5 gallons!

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The
Mode

The mode is the data value that appears the most in the set.
Because no value may appear more often than any other, it is possible for a set to have no mode.  And because it is possible for a set to contain more than one element which appears the same number of times as another, it is possible for a set to have more than one mode.

Let's look at a couple examples.....

The following is a list of heights (in inches) of a high school basketball team:
68,67,66,70,74,72,68,71,75,68,72,71

 

To determine the mode all we need to do is determine which, if any, of the data values appear the most.
If you look carefully you will see that several of the values appear more than once, but only one of the values appears the most...
There are 2-71's, and 2-72's,
BUT
there are 3-68's!
So, the mode of this set is 68!

Let's look at one more....


This is a list of the grades of a class on a recent math test:
85,78,90,91,88,85,73,84,90,95,67,70
Find the mode for this data.

 


Again, look carefully for data values which appear
more than once.
Rewriting the list in numerical order is helpful because you will clearly see any multiple entries.  It is also helpful because you need to do that to determine the median anyway.
67,70,73,78,84,85,85,88,90,90,91,95
This set has 2 modes, we call this set bimodal.
The modes for this set are 85 and 90.

 

 Now let's practice!

 
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Created by Paul Deritter
Updated by Carol Carroll

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