Statistics Calculator
Enter a series of numbers separated by commas
What is Statistical Analysis?
Statistical analysis involves collecting and interpreting numerical data to identify patterns and trends. The key measures include: \[\bar{x} = \frac{\sum_{i=1}^{n} x_i}{n}\] for mean calculation, and \[\sigma = \sqrt{\frac{\sum_{i=1}^{n} (x_i - \bar{x})^2}{n}}\] for standard deviation. These measures help us understand the central tendency and spread of data.
Geometric Mean
The geometric mean is a type of average that uses the product of values rather than their sum. It is calculated as: \[\sqrt[n]{x_1x_2...x_n}\] This is particularly useful when dealing with ratios, rates of growth, or when values vary by orders of magnitude.
Population vs Sample Statistics
When working with data, we distinguish between population and sample statistics: \[\text{Population Variance: } \sigma^2 = \frac{\sum(x_i - \mu)^2}{N}\] \[\text{Sample Variance: } s^2 = \frac{\sum(x_i - \bar{x})^2}{n-1}\] The sample variance uses n-1 (degrees of freedom) to provide an unbiased estimate of the population variance.
How to Use This Calculator
1. Enter your numbers separated by commas (e.g., 1, 2, 3, 4, 5)
2. Click the Calculate button
3. View comprehensive statistical results including:
- Basic measures (count, sum, mean, median)
- Spread measures (range, variance, standard deviation)
- Additional statistics (geometric mean, sample statistics)
4. The calculator will also show sorted data and identify any modes in your dataset