How to calculate the standard deviation constellation _ how to press the standard deviation

Two formulas of standard deviation: sample standard deviation and population standard deviation.

1, population standard deviation formula:

σ=√(σ(Xi-μ)？ / N)

Where σ stands for population standard deviation, σ stands for summation symbol, xi stands for each data point, μ stands for the average value of data set, and n stands for the total number of data points.

2, sample standard deviation formula:

s =√(σ(Xi-x？ )? / (n - 1))

Where s represents the standard deviation of the sample, σ represents the summation symbol, xi represents each data point, and x? Represents the average value of samples, and n represents the number of samples.

The difference between these two formulas is that the population standard deviation formula is calculated by the average value of the population, and the standard deviation formula of the sample is calculated by the average value of the sample.

Standard deviation is a commonly used index in statistics, which is used to measure the degree of dispersion or variation of a set of data. It represents the degree of deviation between each data in the data set and its average value.

Matters needing attention in using two standard deviation formulas

1, sample standard deviation and population standard deviation are applicable to different scenarios: sample standard deviation is applicable to the case where data samples are known, and population standard deviation is applicable to the case where the whole population is known.

2. The degree of freedom correction should be considered for sample standard deviation: in the calculation of sample standard deviation, the denominator is the sample size minus 1, that is, n- 1. This is because the standard deviation of samples is usually used to estimate population standard deviation. By reducing the denominator, the sample standard deviation can be closer to population standard deviation.

3. Calculation of mean value in formula: When calculating standard deviation, the mean value (sample mean or population mean) needs to be calculated first. The average is the average of all the observations in the data set.