Basic Statistical Calculator

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: \(\text{Correlation} = \frac{{\text{Covariance}(x, y)}}{{\text{Standard Deviation}(x) \times \text{Standard Deviation}(y)}}\).