Descriptive Statistics Calculator
Free Descriptive statistics Calculator for descriptive & distributions. Enter values to get step-by-step solutions with formulas and graphs.
Formula
Mean = Sum / n | Variance = Sum((xi - mean)^2) / (n-1) | Std Dev = sqrt(Variance)
The mean is the sum of all values divided by the count. Sample variance uses n-1 (Bessel's correction) for an unbiased estimate. Standard deviation is the square root of variance. Quartiles divide the sorted data into four equal parts.
Worked Examples
Example 1: Test Scores Analysis
Problem: A class of 10 students scored: 72, 85, 90, 68, 95, 78, 82, 88, 91, 76. Calculate descriptive statistics.
Solution: Sorted: 68, 72, 76, 78, 82, 85, 88, 90, 91, 95\nMean: 82.5 | Median: 83.5\nStd Dev: 8.79 | Variance: 77.17\nQ1: 76 | Q3: 90 | IQR: 14\nRange: 27 (68 to 95)
Result: Mean: 82.5 | Median: 83.5 | Std Dev: 8.79 | IQR: 14
Example 2: Salary Distribution
Problem: Salaries (in thousands): 45, 50, 55, 55, 60, 65, 70, 75, 80, 120. Note the outlier at 120.
Solution: Mean: 67.5 | Median: 62.5\nThe mean is pulled up by the outlier (120).\nMedian is more representative of the typical salary.\nSkewness is positive, confirming right-skewed distribution.
Result: Mean: 67.5 | Median: 62.5 | Positive skew due to outlier
Frequently Asked Questions
What are descriptive statistics?
Descriptive statistics summarize and describe the main features of a dataset. They include measures of central tendency (mean, median, mode), measures of spread (range, variance, standard deviation, IQR), and measures of shape (skewness, kurtosis). Unlike inferential statistics, descriptive statistics do not draw conclusions beyond the data at hand — they simply describe what is in the data.
What formula does Descriptive Statistics Calculator use?
The formula used is described in the Formula section on this page. It is based on widely accepted standards in the relevant field. If you need a specific reference or citation, the References section provides links to authoritative sources.
Can I share or bookmark my calculation?
You can bookmark the calculator page in your browser. Many calculators also display a shareable result summary you can copy. The page URL stays the same so returning to it will bring you back to the same tool.
Can I use Descriptive Statistics Calculator on a mobile device?
Yes. All calculators on NovaCalculator are fully responsive and work on smartphones, tablets, and desktops. The layout adapts automatically to your screen size.
How do I get the most accurate result?
Enter values as precisely as possible using the correct units for each field. Check that you have selected the right unit (e.g. kilograms vs pounds, meters vs feet) before calculating. Rounding inputs early can reduce output precision.
Is Descriptive Statistics Calculator free to use?
Yes, completely free with no sign-up required. All calculators on NovaCalculator are free to use without registration, subscription, or payment.