Normal Distribution

Understanding Normal Distribution

  • Normal Distribution, also known as the Gaussian Distribution, is a type of probability distribution that is symmetric about the mean, displaying where the values of a variable are most likely to occur.
  • This distribution is “bell-shaped”, where the highest point signifies the highest probability event(s), typically the mean value.
  • The mean (μ), median, and mode of a normal distribution are all equal and are at the peak of the bell curve.
  • The bell shape signifies that the data is balanced on each side of the mean.

Understanding Standard Deviation in Normal Distribution

  • The spread of distribution is determined by the standard deviation (σ), representing the average distance that the observed values fall from the mean.
  • Generally, if the standard deviation is small, the values tend to be close to the mean, forming a narrow bell-shaped curve. A large standard deviation tends to result in a wide bell-shaped curve, indicating that data is spread over a wider range of values.

The Empirical Rule

  • This rule, also known as the 68-95-99.7 rule describes how data behaves in a normal distribution.
  • About 68% of the data falls within one standard deviation from the mean, approximately 95% falls within two standard deviations, and about 99.7% lies within three standard deviations.
  • This rule provides a quick estimate of the probability associated with data within a given standard deviation range.

Z-Score in Normal Distribution

  • The z-score, also referred to as a standard score, indicates how many standard deviations an element is from the mean.
  • A positive z-score signifies the raw score is greater than the mean, while a negative z-score implies it is less.
  • Z-scores are used to determine the probability that a value from a Normal Distribution is within a certain range.

Normal Distribution and Probability Calculation

  • Normal distribution can be used in probability calculations. For example, if you know the mean and standard deviation, you can determine what proportion of values lie above, below or between certain values.
  • Understanding the properties of normal distribution can be helpful in interpreting data and predicting the likelihood of future events.