Parameters of Normal Distribution
The parameters of the Normal Distribution, also known as the Gaussian Distribution, are the mean and the standard deviation. The mean represents the average or central value of the data, while the standard deviation measures the spread or variability of the data points. Together, these parameters describe the shape and characteristics of the bell-shaped curve that is typical of the Normal Distribution. The mean determines the center of the curve, and the standard deviation controls how wide or narrow it is. These parameters are essential for understanding and analysing data in various fields, including statistics, science, and finance.
I. Mean of Normal Distribution
In a normal distribution, the mean represents the central value where most data clusters. It determines the peak of the bell-shaped curve on a graph. If you change the mean, the whole curve shifts left or right on the horizontal axis. Essentially, the mean is the average value in the dataset, indicating where the data tends to center around, and it is a key factor for understanding the central tendency of the data. The mean in a normal distribution is denoted by the symbol μ (mu).
II. Standard Deviation of Normal Distribution
The normal distribution typically has a positive standard deviation. The mean indicates where the graph is balanced, while the standard deviation shows how much the data is spread out. A smaller standard deviation means the data is closer together, resulting in a narrower graph. Conversely, a larger standard deviation means the data is more spread out, resulting in a wider graph. Standard deviations help divide the area under the normal curve, with each division representing a percentage of data within a particular part of the graph. The formula for the standard deviation (σ) in a normal distribution is given as follows:
σ = √Variance = √σ²
Where,
- σ represents the standard deviation.
- σ² represents the variance.
- X represents individual data points.
- μ represents the mean (average) of the data.
- N represents the total number of data points.
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