Standard Deviation

About Standard Deviation

The positive square root of the variance is the standard deviation. One of the most basic statistical tools is standard deviation. The standard deviation, abbreviated as SD and represented by the letter ", indicates how far a value has varied from the mean value. A low standard deviation indicates that the values are close to the mean, whereas a large standard deviation indicates that the values are significantly different from the mean.

What do you mean by Standard Deviation?

In descriptive statistics, standard deviation is the degree of dispersion or scatter of data points relative to the mean. It describes how the values are distributed over the data sample and is a measure of the data points' deviation from the mean. The square root of the variance is the standard deviation of a sample, statistical population, random variable, data collection, or probability distribution.

When there are n observations and the observations are x₁,x₂,.....x_n the mean deviation of the value from the mean is. The sum of squares of departures from the mean, on the other hand, does not appear to be a good measure of dispersion. The observations x_ix_i are near to the mean xx if the average of the squared differences from the mean is modest. This level of dispersion is lower. If this number is large, it means that the observations are more dispersed from the mean xx. As a result, we infer that is a good predictor of dispersion or scatter.

We take as a proper measure of dispersion and this is called the variance(σ²). The square root of the variance is the standard deviation.

Steps to Calculate Standard Deviation

1. Determine the mean or the arithmetic average of the observations.
2. Calculate the squared deviations from the mean. (the data value - mean)²
3. Calculate the mean of the squared differences. (Variance = sum of squared differences divided by the number of observations)
4. Calculate the square root of the variance. (√Variance = Standard deviation)

Standard Deviation Formula

Population	Sample
X - The value in the data distribution μ - The population Mean N - Total Number of Observations	X - The value in the data distribution   x? - The Sample Mean n - Total Number of Observations

To get the list of Maths formulas check out the main page.

Download free pdf of Standard Deviation Formula Its Use And Solved Examples