# Statistics for Modern Life: 07 Range and Interquartile Range

Range and Interquartile Range are some of the most useful tools for compiling statistical analysis.

## Interquartile Range: More than another statistical calculation.

Interquartile range is one of the more useful and meaningful terms in statistics, and it offers a better view of your collected data than mean, median, or mode. First off, we need to make a distinction between two terms in statistics so there is no confusion. These are Range and Interquartile Range.
Range by itself is a term that denotes the difference between the lowest data point and the highest data point. For instance, consider the following data points: 2,4,6,7,8,10,11,14. The highest is 14 and the lowest is 2. Therefore, your range would be 14 - 2, giving the range as 12.
The interquartile range, on the other hand, is where the bulk of your data falls. In other words, it is the middle 50%. To find the interquartile range, you must first find the median. Remember that the median is the middle point in a data set. Let's look at the following set of data points:

1,3,4,4,5,7,7,8,9,11,13,14,15,16,17
Now, find the median and separate the set on either side.
1,3,4,4,5,7,7 8 9,11,13,14,15,16,17 As you can see, your median is 8 and there are 7 data points on either side.
Next, you find the median on each set of numbers on each side. In this case, the medians are 4 for the lesser half and 14 for the greater half. Now, you find the range of those two:
14 - 4 = 10, so your interquartile range is 10.

If you have an even set of data points, you simply split the data points into two equal sets and find the median for each set. For instance, if you have the same set of data points as listed above, but without the first number, you would find the interquartile range like this:
3,4,4,5,7,7,8,9,11,13,14,15,16,17
Split evenly, you have:
3,4,4,5,7,7,8 9,11,13,14,15,16,17
The medians for each half are 5 and 14.
The interquartile range is 14 - 5 = 9.

For odd numbered data sets, some statisticians will add the median into both sides, rather than excluding it as demonstrated above. Please remember that statistics is based in theory, unlike other aspects of mathematics. In fact, many universities categorize statistics under psychology, not mathematics. You will frequently come across competing theories for deriving answers, so it is best to adhere to the wishes of your professor or your employer. To illustrate this, in my last article, I wrote about the validity of various methods of collecting data. A reader posted a disagreement with my assessment. Who was right? It all depends on your point of view. Lawyers on either side could make successful arguments for both.

Other Articles on Statistics:
Statistics for Modern Life: 01 An Introduction
Statistics for Modern Life: 02 Beginning Terminology
Statistics for Modern Life: 03 Ratio Scales
Statistics for Modern Life: 04 Learning to Sum
Statistics for Modern Life: 05 Mean, Median, & Mode
Statistics for Modern Life: 06 Common Research Techniques

### Meet the author Robert Ramstetter
Robert Ramstetter is a world traveler and writer of short stories, full length novels, and a vast array of technical articles.