Standard Deviation Formula
Formula for Calculating Standard Deviation
The population standard deviation formula is given as:
Here,
Similarly, the sample standard deviation formula is:
Here,
Standard Deviation of Ungrouped Data
The calculations for standard deviation differ for different data. Distribution measures the deviation of data from its mean or average position. There are two methods to find the standard deviation.
Standard Deviation by The Actual Mean Method
Standard deviation by Assumed Mean Method
Standard Deviation of Grouped Data
Standard Deviation of Grouped Discrete Frequency Distribution
For n number of observtions, x1,x2,....x_{n}, and the frequency,
f_{1}, f_{2}, f_{3}, . . . f_{n} the standard deviation is:
Example: Let's calculate the standard deviation for the data given below:
Calculate mean (): (6+8 +10+12+ 14)/5 = 10
= 1/18 × 128 = 7.1
Calculate SD: σ = √Variance = √ 7.1 = 2.66
Standard Deviation of Grouped Continuous Frequency Distribution
Standard Deviation of Random Variables
The experimental probability consists of many trials. When the difference between the theoretical probability of an event and its relative frequency get closer to each other, we tend to know the average outcome. This mean is known as the expected value of the experiment denoted by 𝜇.
Standard Deviation Tips:
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