Descriptive Statistics Calculator
Free Descriptive statistics Calculator for descriptive & distributions. Enter values to get step-by-step solutions with formulas and graphs.
Reviewed for accuracy by Daniel Agrici, Founder & Lead Developer
Descriptive Statistics Calculator
Calculator
Adjust values & calculateEnter your values below. Every result is computed in your browser — no data is sent to any server.
Formula: Mean = Sum / n | Variance = Sum((xi - mean)^2) / (n-1) | Std Dev = sqrt(Variance)
Worked example — Mean: 82.5 | Median: 83.5 | Std Dev: 8.79 | IQR: 14
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 Mean: 82.5 | Median: 83.5 Std Dev: 8.79 | Variance: 77.17 Q1: 76 | Q3: 90 | IQR: 14 Range: 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 The mean is pulled up by the outlier (120). Median is more representative of the typical salary. Skewness 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 do skewness and kurtosis tell you?
Skewness measures asymmetry. Positive skew means the right tail is longer (data piled up on the left). Negative skew means the left tail is longer. A skewness near 0 indicates symmetry. Kurtosis (excess) measures tail heaviness compared to a normal distribution. Positive kurtosis (leptokurtic) means heavier tails and more outliers. Negative kurtosis (platykurtic) means lighter tails. The normal distribution has excess kurtosis of 0.
References
Reviewed for accuracy by Daniel Agrici, Founder & Lead Developer · Editorial policy
Related Calculators
🧮Bayesian Posterior Calculator
Calculate bayesian posterior with inputs, formulas, and instant results.
🧮False Discovery Rate Calculator
Calculate false discovery rate with inputs, formulas, and instant results.
🧮Correlation Coefficient Calculator
Calculate correlation coefficient with inputs, formulas, and instant results.
🧮Binomial Distribution Calculator
Calculate binomial distribution with inputs, formulas, and instant results.
🧮Chi Square Test Calculator
Calculate chi square test with inputs, formulas, and instant results.
🧮Ztest Proportions Calculator
Calculate ztest proportions with inputs, formulas, and instant results.
🧮Effect Size Calculator
Calculate effect size with inputs, formulas, and instant results.