Weekly sales snapshot
Summarize store sales over seven days to see average performance and variability.
Data: 120, 135, 140, 128, 132, 145, 138
Find the mean, median, range, and standard deviation in one calculation.
Statistics Calculator
Analyze a dataset quickly with this statistics calculator. Enter your values to calculate central tendency, spread, extrema, and sample versus population measures from one set of inputs.
Enter a series of numbers separated by commas, spaces, semicolons, or line breaks
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
- Enter your dataset using commas, spaces, semicolons, or line breaks.
- Click the calculate button to generate summary statistics instantly.
- Review the results for mean, median, mode, range, variance, and standard deviations.
- Use the sorted data and mode output to inspect the distribution more closely.
Geometric mean is only defined for positive values. If your dataset contains zero or negative numbers, that field will show as unavailable.
Statistics Calculator Examples
Exam score review
Compare how spread out student scores are around the class average.
Data: 72, 75, 78, 80, 85, 90
Use the standard deviation and sample variance to assess score dispersion.
Product measurement checks
Inspect measurement consistency during quality control.
Data: 10.01, 10.02, 9.99, 10.00, 10.01
Low range and low variance indicate a stable process.
Growth factor analysis
Use geometric mean for positive growth multipliers or ratios.
Data: 1.02, 1.05, 1.01, 1.03
Geometric mean shows the compounded average growth factor.
Statistics Calculator FAQ
What statistics does this calculator compute?
It calculates count, sum, mean, median, mode, range, smallest and largest values, population variance, population standard deviation, sample variance, sample standard deviation, geometric mean, and sorted data.
Why are population and sample variance different?
Population variance divides by the full number of values. Sample variance divides by n-1 to estimate variability for a larger population from a sample.
Why does the geometric mean show as unavailable?
Geometric mean requires all values to be positive. If your dataset includes zero or a negative number, the calculator cannot produce a valid geometric mean.
How does the calculator determine the mode?
It counts how often each value appears and returns the value or values with the highest frequency. If every number appears once, it reports that there is no mode.