Handbook of Descriptive Statistics/Measures of Statistical Variability/Standard Deviation

Descriptive Statistics

Descriptive Statistics is statistical measures that are used to describe numerical data; this numerical data can be in form of a table, number list, frequency distribution etc.

Common Statistical measures are arithmetic mean (AM) (or average or simply the mean), median, mode and standard deviation.

Arithmetic Mean (or average or mean)

Arithmetic Mean (AM) of a list of n numbers is defined as the sum of n numbers divided by n. This is a kind of center of the number list or simply the average of the number list. The order of numbers in the list is not important.

For example, the AM of the number list 3, 8, 7, 3, 5, 10, and 2 is

${\frac {3+9+7+3+6+10+4}{7}}=6$

Median

Median is another type of central tendency of list of numbers. To calculate the median of list of n numbers, first the numbers should be arrange in ascending order i.e. from smallest to greatest. If n is odd then the median is defined as the middle number, if n is even then the median is defined as the average of two middle numbers. The order of the numbers is important for this tendency.