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Definition: Standard deviation is a statistical metric that quantifies the amount of variation or dispersion in a set of data values. It provides insight into how much individual data points deviate from the mean (average) of the dataset.
Mathematical Representation: Standard deviation (c3 for the population or s for a sample) is calculated as the square root of the variance. The variance is the average of the squared differences from the mean.
Formula for Population Standard Deviation (c3):
c3 = \sqrt{\frac{1}{N} \sum_{i=1}^{N} (x_i - bc)^2}
Where:
Formula for Sample Standard Deviation (s):
s=n−11∑i=1n(xi−xˉ)2
Where:
Measure of Spread:
Comparability:
Normal Distribution:
Hypothesis Testing:
Detection of Outliers:
Financial and Risk Analysis:
Standard deviation is a fundamental concept in statistics and data science, providing insights into the variability and distribution of data. Its applications span across various fields, from finance to scientific research, making it an indispensable tool for data analysis.