Bell-shaped curve

Bell-shaped curve or normal distribution is a term used in statistics to describe a type of continuous probability distribution for a real-valued random variable. The graph of the normal distribution is characterized by its bell shape, hence the name.

Overview

The bell-shaped curve is symmetric, centered around its mean, and its shape is determined by its mean and standard deviation. The curve is highest at the mean and its height decreases symmetrically on either side, creating a bell shape. The area under the curve represents the total probability of all possible outcomes, which is equal to 1.

Properties

The bell-shaped curve has several important properties:

• Symmetry: The curve is symmetric around the mean. This means that the probability of getting a value less than the mean is the same as the probability of getting a value greater than the mean.

• Mean, Median, Mode: In a normal distribution, the mean, median, and mode are all equal and located at the center of the distribution.

• Standard Deviation: The standard deviation measures the spread of the distribution. About 68% of values drawn from a normal distribution are within one standard deviation away from the mean; about 95% are within two standard deviations; and about 99.7% lie within three standard deviations.

Applications

The bell-shaped curve is widely used in statistics, natural sciences, social sciences, and engineering because many random variables are either approximately or exactly normally distributed. It is also used in quality control and risk management.

See also

• Standard deviation
• Mean
• Probability distribution
• Statistics