Mean, Median, Mode, and Range
Data, data, data! Most jobs and businesses rely on analyzed data to perform well in the working world, including the ERB. How else do you think the ERB determines Scaled Scores, Percentile Ranks, and Stanines for your ISEE results? Since the beginning, even your grades in school have been analyzed to show you and your parents how well you have been performing in class. Here are a few ways you can analyze data:
Mean (Average)
You will come across many problems that require you to find the average or mean of a data set. For example, you may want to know the average test score of a class, or the average salary for a certain type of job. The average is the most common way of finding the “middle” of a list of values.
Median
The median is another way of finding the “middle,” but different from the average. The median allows you to find the number that is literally in the middle of the list, when ordered from smallest to largest. This is another useful way of looking at data. You may sometimes find that the average and the median are somewhat different, which happens when the values in the data have more extreme differences.
In the above example, there were an even number of values, so you averaged the two middle numbers to find the median. If there are an odd number of values, you simply take the middle value. For instance, the median of {10, 15, 20, 25, 30} is 20.
Mode
The mode is the value that occurs the most in a list. Rather than just telling you the “middle” of the values, the mode can tell you what is most common. Finding the mode can be confusing though, because a list of values may have one mode, more than one mode, or no mode at all.
In this example there is only one mode. If the set is {1, 5, 5, 6, 7, 7} then there are two modes: 5 and 7. If the set is {1, 3, 5, 7, 9, 11, 13} then there is no mode, since each number appears only once.
Range
The range can demonstrate the extremes of a list of values. If every number in a set were the same, the range would be 0. A larger range means there is a larger variation in the set.
Practice Problems
- Find the mean, median, mode, and range of the following data set: 3, 7, 11, 12, 19, 28.
- Find the mean, median, mode, and range of the following data set: 11, 25, 25, 44, 32.
- Find the mean, median, mode, and range of the following data set: 6, 6, 13, 26, 26, 96, 177.
Answers to Practice Problems
- Mean:13.33, Median:11.5, Mode:No mode, Range:25
- Mean:27.4, Median:25, Mode:25, Range:33
- Mean:50 , Median:26 , Mode:6 and 26 , Range:171
