Statistics Calculator | Free Mean, Median, Mode & Std Dev Tool
Comprehensive descriptive statistics in one place. Compute mean, median, mode, standard deviation, variance, quartiles, and the five-number summary. Analyze frequency tables, detect outliers using IQR or Z-score methods, and generate normally distributed data for practice. Features visual distribution bars and box plots.
📖 Want to understand your results?
Read our complete guide to the Statistics Calculator — with real-world examples, expert insights, and pro tips.
— Advertisement —
Below Result
Responsive
Slot: placeholder-calc-bottom-slot
Calculator Features
Descriptive Statistics
Complete set: mean, median, mode, range, variance (sample & population), standard deviation, quartiles, IQR, and skewness. Includes visual distribution histogram and auto-generated insight about symmetry.
Five-Number Summary & Box Plot
Shows Min, Q1, Median, Q3, and Max with a visual box plot. The box represents the IQR, the line marks the median, and whiskers extend to the extremes.
Frequency Table Analysis
Enter values with their counts for weighted descriptive statistics. Perfect for grouped data, survey results, or any data with repeating values. Includes frequency bars for each value.
Data Generator
Generate normally distributed random data using the Box-Muller transform. Specify count, mean, and standard deviation. Generated data is automatically loaded for analysis.
Outlier Detection
Two methods: IQR (Tukey's Fences) marks values below Q1 - 1.5×IQR or above Q3 + 1.5×IQR. Z-score method flags values with |Z| > threshold (default 2.5). Color-coded results table.
— Advertisement —
Content Mid
Responsive
Slot: placeholder-in-content-slot
Statistics Formulas
Central Tendency
Mean
x̄ = Σx / n
Sum of all values divided by count
Median
Middle value when sorted
If n is odd: value at position (n+1)/2. If even: average of two middle values
Mode
Most frequent value(s)
Value that appears most often in the data set
Dispersion
Range
Max - Min
Difference between largest and smallest values
Variance (Sample)
s² = Σ(x - x̄)² / (n-1)
Average squared deviation from mean, with Bessel's correction
Variance (Population)
σ² = Σ(x - x̄)² / n
Average squared deviation from mean for entire population
Std Deviation
s = √s²
Square root of variance, in same units as original data
IQR
Q3 - Q1
Range of middle 50% of data
Position
Q1 (25th %ile)
Median of lower half
Value below which 25% of data falls
Q3 (75th %ile)
Median of upper half
Value below which 75% of data falls
Z-Score
z = (x - x̄) / s
Number of standard deviations from the mean
Shape & Outliers
Skewness
g = Σ((x-x̄)/s)³ × n / ((n-1)(n-2))
Measures asymmetry: positive = right tail, negative = left tail
IQR Outlier
Outside [Q1 - 1.5×IQR, Q3 + 1.5×IQR]
Tukey's fences: values beyond these bounds are potential outliers
Z-Score Outlier
|z| > 2.5 or 3
Values beyond 2.5 or 3 standard deviations from mean
Reviewed by Emily Watson, M.Ed.
Mathematics EducatorMathematics teacher and curriculum designer with 15+ years of experience.
Statistics Calculator Pros & Cons
Pros
- ✅ Full descriptive statistics suite
- ✅ Outlier detection (IQR & Z-score)
- ✅ Visual box plot & distribution bars
- ✅ Free forever — no subscriptions
- ✅ Works offline after page load
Cons
- ✗ No hypothesis testing (t-test, ANOVA)
- ✗ No CSV data import
Frequently Asked Questions
What is the difference between sample and population standard deviation?
Sample standard deviation (s) divides by n-1 (Bessel's correction) to provide an unbiased estimate of the population parameter. Population standard deviation (σ) divides by n and is used when you have data for the entire population.
How is the median calculated for an even number of values?
For an even number of values, the median is the average of the two middle values after sorting. For example, with values [3, 5, 7, 9], the median is (5 + 7) / 2 = 6.
What does IQR tell me about my data?
The Interquartile Range (IQR) measures the spread of the middle 50% of your data. It is calculated as Q3 - Q1 (75th percentile minus 25th percentile). A larger IQR indicates more variability in the middle portion of your data.
How do I detect outliers in my data?
Our calculator supports two methods. IQR method (Tukey's Fences): values below Q1 - 1.5×IQR or above Q3 + 1.5×IQR are potential outliers. Z-Score method: values where |Z| > 2.5 are flagged.
What is skewness and why does it matter?
Skewness measures the asymmetry of your data distribution. Positive skew means the tail extends to the right (mean > median). Negative skew means the tail extends to the left (mean < median).
What is the five-number summary?
The five-number summary consists of: Minimum (smallest value), Q1 (25th percentile), Median (50th percentile), Q3 (75th percentile), and Maximum (largest value). It is the basis for box plots.
Footer Banner
Responsive
Slot: placeholder-footer-slot