There is often a need to describe a collection of data (a data set). One way to do this to find the middle value. This is called the average or sometimes the measure of central tendency. Below are examples of three types of average; arithmetic mean, median, and mode.
The examples below will show how to calculate the arithmetic mean, the median, and the mode for the following set of values showing the heights of students in a 6th Grade class.
Student Heights (cm) 

135  154  154  152  144 
145  157  152  153  142 
149  151  146  138  152 
147  156  140  146  159 
149  162  140  148  152 
Sometimes just the term "mean" is used. There are other types of "mean" so, to be precise, we should say "arithmetic" mean. The arithmetic mean is calculated by taking the sum of all values and dividing by the number of values. The examples below show this.
Example 1: The Arithmetic Mean
Solution:
arithmetic mean 
=  sum of the values  
number of values  
=  (135 + 154 + 154 + 152 ....)  
25  
= 

3723  
25  
arithmetic mean 
=  148.9 cm 
Note: Arithmetic Mean does not always provide the best description of the middle of a set of data. For example, in a sports team, if one or two superstars are paid much more than the rest of their team mates, then they will "skew" the data.
The Median is the value that separates the lower half from the upper half of a data set. In other words, if the values are sorted in order, the median will be the value in the middle. If there are an odd number of values the median is obvious. If there an even number of values, the median is calculated by taking the arithmetic mean of the two middle values.
Example 2: The Median
Solution:
First, order the data from smallest to largest.
Student Heights (cm) 

135  138  140  140  142 
144  145  146  146  147 
148  149  149  151  152 
152  152  152  153  154 
154  156  157  159  162 
There are 25 values. The median is therefore the 13th value. There are 12 lower values and 12 higher values.
The median of the data is 149 cm
The Mode is the value that appears most often in a data set
Example 3: The Mode
Solution:
It is often easier to find the most occurring value after sorting and ordering the data (which you have to do anyway if you are also looking for the median).
There are four occurrences of the height measurement of 152cm. The next most common values are 140, 146, 149, and 154 which all occur two times.
The mode is 152 cm.
Try the worksheets below with your children to help them practice calculating arithmetic mean, median, and mode for different sets of data.
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