Normal Distribution

What is the Normal Distribution?

The normal distribution, also known as the Gaussian distribution or bell curve, is one of the most important probability distributions in statistics. It describes a continuous probability distribution for a random variable where the data tends to cluster around the mean, with symmetrical tails on either side.

Most important things to know about the Normal Distribution:

• Symmetry: The normal distribution is symmetric around its mean, which is also its median and mode. The mean, median, and mode all coincide at the center of the distribution, creating a bell-shaped curve.
• Bell-shaped Curve: The shape of the normal distribution resembles a bell, with the majority of the data concentrated near the mean and gradually tapering off towards the tails. The curve is smooth and unimodal, indicating a single peak.
• Parameters: The normal distribution is defined by two parameters: the mean (μ) and the standard deviation (σ). The mean determines the central location of the distribution, while the standard deviation controls the spread or dispersion of the data.
• Empirical Rule: The normal distribution follows the empirical rule, also known as the 68-95-99.7 rule. It states that approximately 68% of the data falls within one standard deviation of the mean, about 95% within two standard deviations, and approximately 99.7% within three standard deviations

As a final note, the standard normal distribution is a specific form of the normal distribution with a mean of 0 and a standard deviation of 1. It serves as a reference distribution and is often used in statistical calculations and hypothesis testing.