A Gaussian, also known as a normal distribution, is a bell-shaped curve that is symmetrical around its mean.
Key Features of a Gaussian:
- Symmetry: The curve is perfectly symmetrical around its mean, meaning both sides are mirror images.
- Peak: The highest point of the curve occurs at the mean, representing the most likely value.
- Spread: The curve's spread is determined by its standard deviation. A larger standard deviation means a wider curve, indicating greater variability in the data.
- Tails: The curve extends infinitely in both directions, gradually approaching zero as it moves further away from the mean.
Examples of Gaussian Distributions:
- Heights of people: The distribution of heights in a population tends to follow a Gaussian curve, with the average height being the most common and heights further from the average becoming less frequent.
- Measurement errors: Errors in scientific measurements often exhibit a Gaussian distribution, with small errors being more common than large errors.
- IQ scores: IQ scores are standardized to follow a normal distribution, with a mean of 100 and a standard deviation of 15.
Visual Representation:
The image above shows a typical Gaussian curve. The x-axis represents the values of a variable, while the y-axis represents the probability density. The curve's peak corresponds to the mean, and the spread is determined by the standard deviation.
