To calculate the population standard deviation, we divide the sum by the number of data points (N). But to calculate the sample deviation, the total is divided by the number of data points minus 1 (N-1). Find the square root of the final figure to determine the standard deviation.

### What is the standard deviation σ of the population?

Population Standard Deviation: The population standard deviation of the data a1,a2,⋯,an a 1 , a 2 , ⋯ , a n is defined to be the average of the squared differences between the data values and the mean of a population: σ=(a1−μ)2+(a2−μ)2+⋯+(an−μ)2n.

Is population standard deviation T or Z?

If the population standard deviation is known and the sample size is greater than 30, Z-test is recommended to be used. If the population standard deviation is known, and the size of the sample is less than or equal to 30, T-test is recommended. If the population standard deviation is unknown, T-test is recommended.

How standard deviation is calculated?

The standard deviation is calculated as the square root of variance by determining each data point’s deviation relative to the mean. If the data points are further from the mean, there is a higher deviation within the data set; thus, the more spread out the data, the higher the standard deviation.