Mean: Measure of Central Tendency
The measure of Central Tendency Mean (also know as average or arithmetic mean) is used to describe the data set as a single number (value) which represents the middle (center) of the data, that is average measure (performance, behaviour, etc) of data. This measure of central tendency is also known as measure of central location or measure of center.
Mathematically mean can be defined as the sum of the all values in a given dataset divided by the number of observations in that data set under consideration. The mean is also called arithmetic mean or simply average.
Example: Consider the following data set consists of marks of 15 student in certain examination.
50, 55, 65, 43, 78, 20, 100, 5, 90, 23, 40, 56, 70, 88, 30
The mean of above data values is computed by adding all these values (50 + 55 + 65 + 43 + 78 + 20 + 100 + 5 + 90 + 23 + 40 + 56 + 70 + 88 + 30 = 813) and then dividing by the number of observations added (15) which equals 54.2 marks, that is
$latex \frac{50 + 55 + 65 + 43 + 78 + 20 + 100 + 5 + 90 + 23 + 40 + 56 + 70 + 88 + 30 }{15}=\frac{813}{15}=54.2 $
The above procedure of calculating the mean can be represented mathematically
$latex \mu= \frac{\sum_{i=1}^n X_i}{N} $
The Greek symbol $latex \mu$ (pronounced “mu”) is the representation of population mean in statistics and $latex N$ is the number of observations in the population data set.
The above formula is known as population mean as it is computed for whole population. The sample mean can also be computed in same manner as population mean is computed. Only the difference is in representation of the formula, that is,
$latex \overline{X}= \frac{\sum_{i=1}^n X_i}{n} $.
The $latex \overline{X} $ is representation of sample mean and $latex n$ shows number of observations in the sample.
The mean is used for numeric data only. Statistically the data type for calculating mean should be Quantitative (variables should be measured on either ratio or interval scale), therefore, the numbers in data set can be continuous and/ or discrete in nature.
Note that mean should not be computed for alphabetic or categorical data (data should not belong to nominal or ordinal scale). Mean is influenced by very extreme values in data, i.e. very large or very small values in data changes the mean drastically.
For other measures of central tendencies visit: Measures of Central Tencencies