What is normal distribution?

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The distribution having the below properties is called normal distribution.

  • The mean, mode and median are all equal.
  • The curve is symmetric at the center (i.e. around the mean, μ).
  • Exactly half of the values are to the left of center and exactly half the values are to the right.
  • The total area under the curve is 1.

In a machine learning interview, if you are asked about normal distribution, you can provide the following answer:

A normal distribution, also known as Gaussian distribution, is a symmetric probability distribution that is characterized by its bell-shaped curve. It is defined by two parameters: the mean (μ), which represents the central location of the distribution, and the standard deviation (σ), which measures the spread or variability of the distribution.

In a normal distribution:

  1. The mean, median, and mode are all equal and located at the center of the distribution.
  2. The distribution is symmetric, meaning that the left and right sides of the mean are mirror images of each other.
  3. Approximately 68% of the data falls within one standard deviation of the mean, 95% within two standard deviations, and 99.7% within three standard deviations. This characteristic is known as the 68-95-99.7 rule or the empirical rule.

The normal distribution is essential in statistics and machine learning as many natural phenomena, such as heights of people, IQ scores, and measurement errors, tend to follow this distribution. It is also a fundamental assumption in various statistical methods and models.