Normal Distribution
Gaussian Distribution
The Normal distribution is one of the most important distributions, and is often referred as Gaussian or Bell Curve. These distributions are symmetric around the mean, and the datapoints near the centre appear more frequently than the ones further. The bell curve applies in many situations, such as distributing blood pressure results, heights of people, and university exam scores.
The name, Bell Curve, comes from the shape (bell-shaped curve) of the distribution. Similarly, Gaussian, is named after the mathematician Carl Friedrich Gauss.
The following is an example of a normal distribution. This instance uses random generated numbers through the use of Python (NumPy & Matplotlib) and not actual figures.
Features of Normal Distribution
There are some important properties (features) associated with Gaussian distributions. These are measures such as mean, mode, median, and standard deviation. In addition, there are observational rules as well as skewness and kurtosis.
Measures
Mean refers to the average, median to the middle datapoint, and mode to the most frequent datapoint. In Gaussian distributions, all three point to the same point (the highest observational point). Standard deviation measures the variability of the data. Both mean and standard deviation define a Bell Curve.
For more on the above statistical measurements, basic statistics and variance & standard deviation.
Observational rules
After the standard deviation calculation, there is a rule of thumb regarding how spread the datapoints are – in other words, the proportion of the numbers falling within a particular distance of the standard deviation and the mean. 68% of the observations are within 1 standard deviation of the mean, 95% are within 2 standard deviations of the mean, and 99.7% are within 3 standard deviations.
Kurtosis & Skewness
Kurtosis is a measure of tailedness – representation of how thick the tails of the distributions are. Gaussian distribution has a kurtosis of 3. A kurtosis of less than 3 (negative excess) produces thinner tails and flattens the overall structure. And kurtosis of more than 3 (positive excess) has thicker tails and creates a shape with more pointy peak.
Skewness is a measure of symmetry. A skewness of less than 0 (negative) produces a longer left tail and tilts the structure to the right. And skewness of more than 0 (positive) has a longer right tail and tilts the shape to the left. As a symmetric distribution, normal distribution has a skewness of 0.
Next: Uniform Distribution
