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Statistics Calculator
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Formulas for Statistics
Number of values (Count):
- This represents the count of data points in the dataset.
- Formula: \(\text{Number of values} = n\), where ( n ) is the count of data points.
Sum:
- The sum of all the values in the dataset.
- Formula: \(\text{Sum} = \sum_{i=1}^{n} x_i\), where ( x_i ) represents each individual value in the dataset.
Mean (Average):
- The arithmetic mean or average of the values in the dataset.
- Formula: \(\text{Mean} = \frac{{\text{Sum}}}{{\text{Number of values}}} = \frac{{\sum_{i=1}^{n} x_i}}{n}\).
Sample Variance:
- A measure of the dispersion of a set of values from its mean, calculated from a sample of the population.
- Formula: \(\text{Sample Variance} = \frac{{\sum_{i=1}^{n} (x_i - \text{Mean})^2}}{n-1}\).
Population Variance:
- Similar to sample variance but calculated from the entire population rather than a sample.
- Formula: \(\text{Population Variance} = \frac{{\sum_{i=1}^{n} (x_i - \text{Mean})^2}}{n}\).
Median:
- The median value is the middle value of the dataset when it is sorted in ascending order.
- Formula: For odd \(n\), the median is the value at position \(\frac{{n+1}}{2}\) in the sorted dataset. For even \(n\), the median is the average of the values at positions \(\frac{n}{2}\) and \(\frac{n}{2} + 1\).
Covariance:
- A measure of how much two random variables vary together.
- Formula: \(\text{Covariance} = \frac{{\sum_{i=1}^{n} (x_i - \text{Mean of } x) \times (y_i - \text{Mean of } y)}}{n}\).
Correlation:
- A measure of the strength and direction of the linear relationship between two variables.
- Formula: \(\text{Correlation} = \frac{{\text{Covariance}(x, y)}}{{\text{Standard Deviation}(x) \times \text{Standard Deviation}(y)}}\).