Standard Deviation Calculator

Understanding Standard Deviation

Standard deviation is a statistical measure that quantifies the amount of variation or dispersion in a set of values. A low standard deviation indicates that the values tend to be close to the mean, while a high standard deviation indicates that the values are spread out over a wider range.

Interesting Facts

• The concept of standard deviation was introduced by Karl Pearson in the late 19th century.
• In a normal distribution, approximately 68% of the data points lie within one standard deviation of the mean.
• Standard deviation is widely used in finance to measure market volatility.

How to Calculate Standard Deviation

The formula for standard deviation (σ) is:

σ = √(Σ(xi – μ)² / N)

Where:

• Σ is the sum of
• xi represents each value in the dataset
• μ is the mean of the dataset
• N is the number of values in the dataset

Example Calculations

$$\sigma = \sqrt{\frac{(5 – 5.8)^2 + (7 – 5.8)^2 + (3 – 5.8)^2 + (10 – 5.8)^2 + (4 – 5.8)^2}{5}}$$
$$\sigma = \sqrt{\frac{(-0.8)^2 + (1.2)^2 + (-2.8)^2 + (4.2)^2 + (-1.8)^2}{5}}$$
$$\sigma = \sqrt{\frac{0.64 + 1.44 + 7.84 + 17.64 + 3.24}{5}}$$
$$\sigma = \sqrt{\frac{30.8}{5}}$$
$$\sigma = \sqrt{6.16} \approx 2.48$$

Using the Standard Deviation Calculator

To use the standard deviation calculator, simply input your dataset into the provided field. The calculator will automatically compute the mean and standard deviation for you, allowing for quick analysis of your data.