math

Standard Deviation

A measure of the spread or dispersion of a data set from its mean (average).

Standard deviation (Οƒ) quantifies how spread out data points are from the average. A low standard deviation means data points cluster near the mean; a high standard deviation means they are spread out.

Steps to Calculate

  1. Find the mean (average)
  2. Subtract the mean from each data point and square the result
  3. Average those squared differences (variance)
  4. Take the square root of the variance

Example

Data: 4, 8, 6, 5, 3. Mean = 5.2. Squared differences: 1.44, 7.84, 0.64, 0.04, 4.84. Variance = 2.96. SD = √2.96 = 1.72.

The 68-95-99.7 Rule

In a normal distribution: 68% of data falls within 1 SD, 95% within 2 SD, 99.7% within 3 SD of the mean.

Related Calculators

πŸ“Š Standard Deviation CalculatorπŸ“Š Average Calculator

Related Articles

πŸ“ Standard Deviation Explained

Related Terms

Percentage

A number expressed as a fraction of 100, used to describe proportions and rates of change.

Mean, Median, and Mode

Three measures of central tendency used to describe the center of a data set.

Pythagorean Theorem

A fundamental relation in geometry: the square of the hypotenuse equals the sum of squares of the other two sides.

Area and Perimeter

Area measures the surface inside a shape (in square units); perimeter measures the distance around it.

Fractions

A number representing a part of a whole, written as a numerator over a denominator.

Logarithm

The inverse of exponentiation β€” the logarithm of a number tells you the exponent needed to produce that number from a given base.