Standard Deviation Formula
Standard deviation is used to measure the spread of the statistical data. It tells us about how the statistical data is spread out. Formula to Calculate Standard Deviation is used to find the deviation of all the data sets from its mean position. You may have questions that standard deviation how to calculate or how to calculate a standard deviation. There are two standard deviation formulas that are used to find the Standard Deviation of any given data set. They are,
- Population Standard Deviation Formula
- Standard Deviation Formula Sample
Formula for standard deviation of sample data is,
[Tex] \bold{s = \sqrt{\frac{\sum_{i=1}^n (x_i – x̄)^2}{n-1}}}[/Tex]
where,
- s is Population Standard Deviation
- xi is ith observation
- x̄ is Sample Mean
- N is Number of Observations
Standard Deviation Formula of population data is,
[Tex] \bold{\sigma = \sqrt{\frac{\sum_{i=1}^N (x_i – \mu)^2}{N}}} [/Tex]
where,
- σ is Population Standard Deviation
- xi is ith Observation
- μ is Population Mean
- N is Number of Observations
It is evident to note that both formulas look the same and have only slide changes in their denominator. Denominator in case of the sample is n-1 but in case of the population is N. Initially the denominator in the sample standard deviation formula has “n” in its denominator but the result from this formula was not appropriate. So a correction was made and the n is replaced with n-1 this correction is called Bessel’s correction which in turn produced the most appropriate results.
Formula for Calculating Standard Deviation
Formula used for calculating Standard Deviation is discussed in the image below,
Standard Deviation – Formula, Examples & How to Calculate
Standard Deviation is the measure of the dispersion of statistics. The standard deviation formula is used to find the deviation of the data value from the mean value i.e. it is used to find the dispersion of all the values in a data set to the mean value. There are different standard deviation formulas to calculate the standard deviation of a random variable.
In this article, we will learn about what is standard deviation, the standard deviation formulas, how to calculate standard deviation, and examples of standard deviation in detail.
Table of Content
- What is Standard Deviation?
- Standard Deviation Definition
- Standard Deviation Formula
- Formula for Calculating Standard Deviation
- How to Calculate Standard Deviation?
- What is Variance
- Difference between Variance and Deviation
- Varience Formula
- How to Calculate Variance?
- Standard Deviation of Ungrouped Data
- Standard Deviation of Discrete Grouped Data
- Standard Deviation of Continuous Grouped Data
- Standard Deviation of Probability Distribution
- Standard Deviation of Random Variables
- Standard Deviation Formula Example
- Standard Deviation Formula Excel
- Standard Deviation Formula Statistics