Central Tendency

• An important description of a data set is the measure of central tendency. This is the value around which the numbers tend to congregate. There are three ways to describe this. The mean, or average, is the sum of all the values divided by the number of values. The mode is the value that appears most frequently in the data set (note there can be more than one mode). The median is the value that has just as many other values that are less than as greater than it is.
  
  

Variance

• Another important description of a set of numbers is the variance, which is the spread of the values. In a data set with a small variance, the values will be close to one another, whereas the opposite is true for a large variance. Statisticians usually use the standard deviation as a measure of variance. Standard deviation is calculated by a complex formula, but you can think of it as giving an indication of the average distance of all data points from the central data point.
  
  

Percentiles

• Statistics also uses the concept of percentile. The "nth" percentile of a set of numbers is the value which has n percent of the data set below it. So, for example, a student whose score on a test is at the 90th percentile has scored higher than 90 percent of the other students. The most commonly used percentiles are at steps of 25 percent and are thus called quartiles. The most frequently used quartiles are the first quartile, equal to the 25th percentile, and the third quartile, equal to 75 percent.
  
  

Range

• The range of a data set is also important. A statistician can sometimes calculate the range by taking the average plus or minus three times the standard deviation, but this is only true for symmetrical data sets. The most common way to describe the range is simply to give the lowest and highest values in the data set. These values can be helpful in interpreting the other statistics since, for example, the mean of a data set can be skewed by a single very high or very low value.