Fundamentals of Statistics 1: Basic Concepts :: Percentiles and The Five-Number Summary
The mean and the median describe the center of the distribution when it's roughly normally distributed (the mode describes the most frequent value, which isn't necessarily the center). The minimum and maximum values describe the end points. Two other points of interest which come up a lot are the 25th percentile and the 75th percentile. These are the locations between the middle and minimum and between the middle and maximum respectively.  Any percentile can be identified for a set of data (e.g. the 95th percentile, 5th percentile, 65th percentile).

Data divided into four equal quadrants are called quartiles (just remember quartile sounds like quarter which means .25 or 1/4). The bottom quarter of data, or the 1st 25 percent is called the 1st quartile or Q1. The bottom 75 percent is called the 3rd quartile or Q3.  These give you five numbers to describe your data: the five number summary : min, max, median, Q1 and Q3. For example, if you took a standardized test of vocabulary and were told you scored in the 75th percentile, then you'd know you scored better than 75% of all other test takers. Additionally, you scored lower than 25% of other test takers.  The data that falls between the 25th and 75th percentiles is called the Interquartile range (IQR).  The IQR contains 50 percent of the values in the dataset. The IQR and the quartiles are also one of the best way of describing data that are skewed.

A popular way to show the Q1, Q3, median and IQR is using a graph called a Box-Plot or Box and whisker graph. The box contains the Interquartile range (50 percent of the data) and the whiskers, or asktericks outside the box show outliers in the data. The box-plot can also be configured to have the min and max values displayed, but I don't see that as often.

### How well did you understand this lesson?

Avg. Rating 7.92 (221)

 Not at all Neutral Extremely 0 1 2 3 4 5 6 7 8 9 10