Median

The median is the middle number of a data set when the data set is arranged in numerical order. Unlike the mean, it will always be one of the actual data points in the set itself. The set can be arranged as ascending or descending order: the median will still always be in the middle.

When a student wants to find the middle/median number in a data set, they must take the number of values in a data set (n = 23 for example) and divide it by two.

Median of Odd-Numbered Data Sets

In the example listed above, n= 23/2 = 11.5. Because there is an odd number of values in the data set, dividing this number by two results in a nonwhole number. For an odd-numbered data set, we will take this partial number and round it up, in this example to 12. This tells us that the middle number, in other words, the median, is the 12th number in the data set.

Median of Even-Numbered Data Sets

For even-numbered data sets, there is not one number in the middle of the data set. Instead, there are two middle values, and the median is the average (mean) of those two numbers. This is why if there was a sample of 24 data points (instead of the 23 from above), the same operation from above leads to a whole number: 24/2 = 12. The 12th data point is the first of the two median numbers. To get the 2nd number, round up to the next whole number, which tells us that the 13th data point is the second of the two median numbers. The median is then the average of the 12th and 13th numbers.

Remember, for this trick the product of the equations is not equal to the value of the median itself, but merely its “place in line” in the data set. It says where to look, but not what the median is.

How It Appears on the Test

Median questions are similar to average/mean questions. Students will normally be asked to do one of two things. Either they will be asked to calculate the median of a given data set (displayed through a table or graph) or they will be asked to describe how a change in the data set will or won’t change the median (or what change(s) would need to be made to the data set to lead to a certain change in the median).