Direct Method
In Direct Method, there is no need to determine the deviation from the actual mean to calculate standard deviation. The steps taken to determine standard deviation through the direct method are as follows:
Step 1: First of all, calculate the actual mean (\bar{X}) of the given observations.
Step 2: Now square the observations and determine their total; i.e., ∑X2.
Step 3: Now, apply the following formula:
Or
Where,
σ = Standard Deviation
∑X2 = Sum total of the squares of observations
= Actual Mean
N = Number of Observations
Example:
Calculate the standard deviation from the following data using Direct Method:
Solution:
Standard Deviation (Direct Method)
Arithmetic Mean
Standard Deviation (σ) =
Standard Deviation = 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.