Statistics

The measure of Central Tendency: Mean

Mean is the average of a data set. It is one of the most common methods to identify the central position.

To calculate the Mean,

  1. Need to sum of all the values in the data set.
  2. Divide the sum by the number of values in the data set.

Formula of Mean

Sample Mean: $$\overline{x} = {{\sum{x}}\over{n}}$$
Population Mean: $$μ ={{\sum{x}}\over{n}}$$

Here,

  • The lower-case Greek letter μ (mu) denotes the population mean, while x̄ (“x bar”) denotes the sample mean.
  • The greek capital letter sigma (means “sum of”) “ΣXi” is the sum of all data X, which is same as \({x_1 + x_2 + \dots + x_n}\)
  • N or n is the total number of data points in a data set

Mean Example

$$\overline{x} = {{5 + 10 + 8 + 5}\over{4}}= {{28}\over{4}}= {7}$$

Do not use Mean

  1. If outliers exist in the data set, then mean should not be the method to measure the central tendency.
  2. When data is skewed, media is better than mean to get the central position.