Descriptive Statistics Calculator
Free Descriptive statistics Calculator for descriptive & distributions. Enter values to get step-by-step solutions with formulas and graphs.
Reviewed by Daniel Agrici, Founder & Lead Developer
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.
References
Reviewed by Daniel Agrici, Founder & Lead Developer · Editorial policy