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# Median

The median is used when locating the middle value in a numerical data set. To illustrate how to find the median, consider the following example. Data Set: 23, 8, 11, 10, 31 The first step in trying to locate the median value is to re-order the data set from the smallest value to the greatest value. Therefore, the new order of this data set is: 8, 10, 11, 23, 31. The median value is simply the middle number of this set of values, which in this case is 11. This case provides a simple example of how to find the median since the data set consists of an odd number of points. However, if the data set consisted of an even number of values, there would be an extra step in distinguishing the median value. For example, consider this new data set consisting of 8 values: 4, 7, 3, 9, 12, 3, 8, 5. So the first step again is to order the values from smallest to largest. Therefore, the new order is: 3, 3, 4, 5, 7, 8, 9, 12. Now in this case, there is no one single middle value. Instead, you need to take the fourth and fifth largest values and find the mean of these two numbers. The fourth and fifth numbers in this data set represent the two middle values in this set of 8 data points. Therefore, the mean of 5 and 7 = (5+7)/2 = 6. Thus, the median value is 6. Â© BrainMass Inc. brainmass.com April 16, 2024, 12:01 pm ad1c9bdddf

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