Normal distribution is a term commonly used in the field of social sciences. Another name for it is the Gaussian or Gauss distribution. Similarly, it is also a term closely associated with the Central Limit Theorem. The normal distribution represents a probability distribution that symmetric (having positive and negative values) around its mean. It has two ends or tails, known as the right and left tails.
Graphically, it resembles the shape of a bell with an upward curve in the middle. Normal distribution helps describe all possible values that a random variable may take with a given range. It is the most common type of distribution assumed in the technical analysis of the stock market and other statistical analyses.
What are the parameters of Normal Distribution?
There are two main parameters of the normal distribution, namely the mean and standard deviation. These parameters play an important role in shaping the distribution and determining its probabilities. The shape of the distribution depends on the values of these parameters.
Mean
The mean is a measure of the central tendency of the distribution. It helps describe the distribution of variables measured as ratios or intervals. For the normal distribution graph, the mean lies at the location of the peak, and most data points reside near it. Any changes in the value of the mean results in the curve shifting to the left or right along the X-axis.
Standard Deviation
Standard deviation represents a measure of the dispersion of data points with respect to the mean. It shows how far away data points reside from the mean and represents the distance between those points and the mean. The standard deviation is associated with the width of the curve rather than its height, unlike the mean. A small standard deviation can create a steep curve while a large deviation produces a flatter curve in the normal distribution.
What are the characteristics of normal distribution?
The normal distribution has several characteristics. Firstly, it is perfectly symmetric, meaning the distribution curve on both sides is equal. Similarly, the mean, mode, and median of a normal distribution are equal. It is because the point of maximum frequency lies in the middle where all three of these exist. Similarly, in most cases, the distribution exists in the center, while fewer values exist at the tail end.
Furthermore, it represents a family of distribution where the mean and standard deviation dictate the shape of the distribution.
How to calculate or graph Normal Distribution?
The formula to calculate the normal distribution is as follows.
X ~ N (µ, α)
In the above formula, ‘N’ represents the number of observations. ‘µ’ is for the mean of those observations. Lastly, ‘α’ represents the standard deviation.
What are the uses for Normal Distribution?
The normal distribution represents an essential statistical concept that can help in financial analysis as well. It helps investors in constructing their portfolios. For example, it can help them identify overvalued or undervalued stock by tracking the movement of price action from the mean. Overall, investors can use it to devise quantitative and qualitative financial decisions.
Conclusion
The normal distribution is a technique used to show a symmetric probability distribution. It has two parameters, a mean and standard deviation. The normal distribution has several characteristics, some of which are discussed above.
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