Actual Mean Method
In actual mean method, standard deviation is calculated by taking deviations from the actual mean. The steps taken to determine standard deviation through the actual mean method are as follows:
Step 1: Determine the actual mean of the given observation.
Step 2: Now, calculate the deviation of each item of the given series from the mean calculated in the first step; i.e., calculate . Denote the deviations with x.
Step 3: After finding out the deviation, square them and determine its total; i.e., ∑x2
Step 4: Apply the following formula:
Where,
σ = Standard Deviation
∑x2 = Sum total of the squares of deviations from the actual mean
N = Number of pairs of observations
Example:
Calculate the standard deviation from the following data:
Solution:
Standard Deviation (Actual Mean Method)
Arithmetic Mean
Standard Deviation (σ) =
Standard Deviation = 2.9 or 3
Standard Deviation in Individual Series
A scientific measure of dispersion that is widely used in statistical analysis of a given set of data is known as Standard Deviation. Another name for standard deviation is Root Mean Square Deviation. Standard Deviation is denoted by a Greek Symbol σ (sigma). Under this method, the deviation of values is taken from the arithmetic mean of the given set of data. Standard Deviation can be calculated in three different series; viz., Individual, Discrete, and Frequency Distribution or Continuous Series.