Median
Example 1: The following set of data shows the heights of the students in Mrs. Rhondi's class.
48 in, 39 in, 40 in, 42 in, 42 in, 36 in, 46 in, 48 in, 37 in, 43 in, 45 in, 45 in, 41 in
Step 1: To determine the median, we will start by ordering the heights from least to greatest.
36 in, 37 in, 39 in, 40 in, 41 in, 42 in, 42 in, 43 in, 45 in, 45 in, 46 in, 48 in, 48 in
Step 2: Determine which number is in the middle.
36 in, 37 in, 39 in, 40 in, 41 in, 42 in, 42 in, 43 in, 45 in, 45 in, 46 in, 48 in, 48 in
The median height in Mrs. Rhondi's class is 42 inches. This means that half the class is 42 in or less and half the class is 42 in or more in height.
In this example, there were an odd number of data values in the set. So the median was the middle number. Let's take a look at the set with an even number of data values.
Example 2: The following set of data shows the scores on the most recent quiz of the students in a small study group.
78%, 88%, 82%, 90%, 95%, 82%, 86%, 94%, 85%, 83%
Step 1: Place the values in order from least to greatest.
78%, 82%, 82%, 83%, 85%, 86%, 88%, 90%, 94%, 95%
Step 2: Determine the middle numbers. Because there are an even amount of values, there will be two numbers in the
78%, 82%, 82%, 83%, 85%, 86%, 88%, 90%, 94%, 95%
Step 3: Find the average of the two middle numbers.
85 + 86 = 171
171 ÷ 2 = 85.5
Therefore, 85.5% is the median score in the class. We can use the median to say that half the class scored below 85.5% and half the class score above 85.5%.
Let's Review:
To find the median we must first order the numbers. If there is an odd number of values, select the middle number and this will be the median. If there are an even number of values, select the two middle numbers, find their average and this will be the median. Then you can use the median to make statements about half of the group or set.
Related Links:
Math
Probability and Statistics
Mean
Mode