**Standard Deviation Calculator** is a measure of variability or dispersion. It is denoted σ and calculated as the square root of the variance. Determined the difference between each data point from the mean.

Use the standard deviation:

It is a useful tool in building an investment strategy and trading because it measures the volatility and predicts investment efficiency.

In addition to expressing population variability, the standard deviation is used to measure statistical results as the margin of error. When used in this manner, the standard deviation is often called the standard error of the mean or standard error of the estimate concerning the mean. The calculator above computes population standard deviation and sample standard deviation, as well as confidence interval approximations.

Variance is a typical data form representing the dispersion of values compared to the mean of the dataset. A large variance indicates more variation in data set values. There may be more gaps between the values of observations. If all of the observations were to stand close together, the variance would be smaller.

*Population Standard Deviation*:

σ = ([Σ (x - u) 2] / N) 1⁄2

σ is the population standard deviation

Σ shows the sum of the values or the sum between 1 and N

x is an individual value

u is the average of the population

N is the total population

*For example*:

You grow 20 crystals from a solution and measure the lengths of each crystal in millimeters. Here is your data:

9, 2, 5, 4, 12, 7, 8, 11, 9, 3, 7, 4, 12, 5, 4, 10, 9, 6, 9, 4

Calculate the population standard deviation of the lengths of the crystals.

Calculate the average of the data: add all the numbers and divide by the total number of data points. (9 + 2 + 5 + 4 + 12 + 7 + 8 + 11 + 9 + 3 + 7 + 4 + 12 + 5 + 4 + 10 + 9 + 6 + 9 + 4) / 20 = 140⁄20 = 7

Subtract the mean from each data point (or vice versa, if you like, you will be squaring this number)

Calculate the mean in the square differences. (4 + 25 + 4 + 9 + 25 + 0 + 1 + 16 + 4 + 16 + 0 + 9 + 25 + 4 + 9 + 9 + 4 + 1 + 4 + 9) / 20 = 178⁄20 = 8.9

Variance is 8.9

The population standard deviation is the square root of the variance. Use a calculator to get this number.

The population standard deviation is 2,983

Applications of the standard deviation:

Standard deviation is used in the weather to measure climate, to determine regional differences. It is widely used in mathematics, experimental facilities, and industry to test models.

*For example* :

1. Standard deviation of average height for adult men

2. Finance

3. Geometric interpretation