Once we collect data, our first step is to consolidate and describe it by using simple indexes. The simplest way to accomplish this is through calculating an average. In statistics, we often call averages measures of central tendency. They are utilized in an assortment of contexts and form the foundation of statistics.
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The mean is the most common type of average that is calculated.
The mean is the most common type of average that is calculated.
The mean is simply the sum of all the values in a data set, divided by the number of values in that set.
The mean is simply the sum of all the values in a data set, divided by the number of values in that set.
Example: An English Language Arts teacher gives her students an SGO (Student Growth Objective) exam early in the school year. A few of the test results of this exam are: 71, 61, 69, 51 and 61.
Step 1: Add the values in your data set.
71 + 61 + 69 + 51 + 61 = 313
Step 2: Divide the numbers by the number of values. In this case, we have 5 values.
313 ÷ 5 = 62.6
The mean or class average of the SGO test is 62.6.
STATS FACT: The μ symbol represents represents the mean of population values.
The mean can also be written with the Latin letter M.
The median is another type of average. The median is identified as the middle value in a data set.
The median is another type of average. The median is identified as the middle value in a data set.
There is no standard formula for computing the median in a data set.
Step 1:
Reorder the values in your data set from lowest to highest.
Data set: 71, 61, 69, 51, 61 =
Reordered data set: 51, 61, 61, 69, 71
Our data set has an odd number (5) of values listed. The middle-most value is 61.
The median is 61.
If the data set included an even number of values, such as
71, 61, 69, 51, 61, 80
The median would have to be calculated.
First, reorder the values in your data set from lowest to highest.
51, 61, 61, 69, 71, 80
The middle two values are 61 and 69.
Add the two values and divide them by 2.
61 + 69 = 130
130 ÷ 2 = 65
The median is 65.
STATS FACT: If the number of values is odd, then the median is the component in the middle of the data set.
If the number of values is even, then the median is the average of the two middle values.
A second measure of central tendency is the mode.
A second measure of central tendency is the mode.
The mode is the value that occurs most repeatedly in a data set.
The mode is the value that occurs most repeatedly in a data set.
Step 1: List the values in your data set.
71, 61, 69, 51, 61
Step 2: Look for the value that repeats most often.
71, 61, 69, 51, 61
The value, 61, occurs twice in the data set.
The mode is 61.
STATS FACT: Sometimes a data set might have more than one mode. If there are two repeating values in a data set, the mode is called bimodal. If there are three repeating values in a data set, the mode is called trimodal. If a data set does not contain a repeating value, the set of data has no mode.
Explanation & Examples of Mean, Median & Mode
Using SPSS to Calculate Mean, Median & Mode
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