Free Calculator · Mean · Median · Mode · Std Dev · Quartiles
Statistics Calculator
Calculate mean, median, mode, standard deviation, variance, quartiles, skewness, kurtosis and detect outliers. Supports sample and population modes with histogram visualisation.
How to Use the Statistics Calculator
Enter your numbers in the input field separated by commas, spaces or new lines. Furthermore, you can paste an entire column from Excel or Google Sheets directly. Additionally, select whether your data represents a sample or an entire population, then click Calculate to see all descriptive statistics instantly.
- Enter your dataType numbers separated by commas, spaces or new lines. Paste from spreadsheets works too.
- Select sample or populationSample uses n-1 (Bessel correction) for variance. Population uses N. Choose sample if your data is a subset.
- Click Calculate StatisticsAll results appear instantly: central tendency, spread, quartiles, shape and outliers.
- Review the breakdownResults are organised into sections: central tendency, spread, distribution shape and five-number summary.
- Copy or downloadCopy the full summary to clipboard or download as CSV for use in reports and presentations.
What Is a Statistics Calculator?
A statistics calculator computes descriptive statistics that summarise a dataset. Furthermore, descriptive statistics condense large amounts of data into meaningful numbers that reveal central tendency, spread and distribution shape. Additionally, this calculator provides over 20 statistical measures in a single computation.
Descriptive statistics answer three fundamental questions about data. First, what is the typical value (mean, median, mode)? Second, how spread out are the values (range, variance, standard deviation)? Third, what shape does the distribution have (skewness, kurtosis)? These measures together paint a complete picture of any numerical dataset.
Measures of Central Tendency
The mean is the arithmetic average: sum all values and divide by the count. Furthermore, the mean is sensitive to outliers — a single extreme value can shift it significantly. Additionally, use the mean when data is roughly symmetric without extreme outliers.
The median is the middle value in sorted data. Furthermore, for even-count datasets, it is the average of the two middle values. Additionally, the median is resistant to outliers and better represents the typical value when data is skewed.
The mode is the most frequently occurring value. Furthermore, a dataset can be unimodal (one mode), bimodal (two modes) or multimodal. Additionally, the mode is the only central tendency measure applicable to categorical data.
Measures of Spread and Dispersion
Standard deviation measures how far values typically sit from the mean. Furthermore, a small standard deviation indicates values cluster tightly around the mean, while a large one shows wide dispersion. Additionally, approximately 68% of data falls within one standard deviation of the mean in a normal distribution.
Variance is the square of the standard deviation. Furthermore, sample variance divides the sum of squared deviations by n-1 (Bessel correction) to produce an unbiased estimate. Additionally, population variance divides by N. The choice between sample and population affects both variance and standard deviation values.
| Measure | Formula | Use case |
|---|---|---|
| Range | Max - Min | Quick spread estimate |
| Variance | Sum of squared deviations / (n-1 or N) | Statistical tests, ANOVA |
| Std Deviation | Square root of variance | Most common spread measure |
| IQR | Q3 - Q1 | Robust spread, outlier detection |
| CV | (SD / Mean) x 100% | Comparing variability across datasets |
| SEM | SD / sqrt(n) | Precision of sample mean estimate |
Quartiles, IQR and Outlier Detection
Quartiles divide sorted data into four equal parts. Q1 (25th percentile) marks the point below which 25% of data falls. Furthermore, Q2 is the median (50th percentile) and Q3 is the 75th percentile. Additionally, the interquartile range (IQR) equals Q3 minus Q1 and represents the spread of the middle 50% of values.
The IQR method detects outliers by defining fences. Values below Q1 minus 1.5 times IQR or above Q3 plus 1.5 times IQR are flagged as potential outliers. Furthermore, this method is resistant to the outliers themselves, unlike methods based on the mean and standard deviation. Additionally, the calculator highlights outliers in red in the sorted data display.
Skewness and Kurtosis
Skewness measures the asymmetry of a distribution. Positive skewness means the right tail is longer. Furthermore, negative skewness indicates a longer left tail. Additionally, values between -0.5 and 0.5 indicate approximate symmetry, while values beyond 1 or below -1 indicate significant skewness.
Kurtosis measures the heaviness of distribution tails. Excess kurtosis above zero indicates heavier tails than a normal distribution. Furthermore, a distribution with high kurtosis has more extreme values. Additionally, this calculator reports excess kurtosis, where zero corresponds to a normal distribution.
Sample vs Population Statistics
Choose population when your data includes every member of the group you are studying. Furthermore, choose sample when your data is a subset of a larger population. Additionally, the key difference is the denominator in the variance formula: population divides by N while sample divides by N minus 1.
Bessel correction (dividing by n-1 for samples) produces an unbiased estimate of the population variance. Furthermore, without this correction, sample variance systematically underestimates the true population variance. Additionally, for large samples (n greater than 30), the difference between n and n-1 becomes negligible.
Statistics in Different Fields
Education professionals use descriptive statistics to analyse test scores, grade distributions and student performance trends. Furthermore, the mean and standard deviation help identify whether a class is performing consistently or showing high variability. Additionally, outlier detection reveals students who may need additional support or advanced challenges.
Business analysts use these measures for sales analysis, quality control and financial reporting. Furthermore, the coefficient of variation allows comparison of variability across products with different price ranges. Additionally, skewness in revenue data reveals whether a few large transactions dominate total revenue.
How to Interpret Your Results
Start with the mean and median. If they are close, the data is roughly symmetric. Furthermore, if the mean exceeds the median, the data is likely right-skewed by high values. Additionally, if the mean is below the median, left skew from low values is pulling the average down.
Next, examine the standard deviation relative to the mean. A CV below 15% indicates low variability. Furthermore, a CV between 15% and 30% shows moderate variability, and above 30% indicates high variability. Additionally, always check for outliers before drawing conclusions, as they can distort both the mean and standard deviation significantly.