The Average & Statistics Calculator computes all descriptive statistical measures from a data set.
Displays mean, median, mode, standard deviation, variance, quartiles, IQR, and coefficient of variation. Supports weighted averages and frequency tables.
Calculator information
📋 How to use this calculator
- Enter numeric data separated by commas or spaces, e.g. 7, 8, 9, 6, 7, 10.
- Choose the mode: single dataset, weighted data (requires a weight column), or frequency table (value + frequency).
- For weighted averages, pair each value with its corresponding weight.
- Press Calculate to obtain the mean, median, mode, variance, standard deviation, Q1, Q3, IQR, and coefficient of variation.
- Review the box plot visualization to see data spread and outliers.
- Copy results in a table format ready to paste into Excel or Word. Tip: if the coefficient of variation exceeds 30%, the data is heterogeneous and the mean is less representative.
🧮 Basic Descriptive Statistics
Mean = Sum(x_i) / n; Variance = Sum((x_i - mean)^2) / (n-1); SD = sqrt(Variance); Median = middle value after sorting; Mode = most frequently occurring value; CV = (SD / Mean) * 100%
- x_i = the i-th data value
- n = sample size or N (population)
- Divisor (n-1) for sample variance (Bessel's correction); N for population
- Q1 = 25th percentile, Q3 = 75th percentile, IQR = Q3 - Q1
For weighted data: Mean = Sum(x_i * w_i) / Sum(w_i), where w_i is the weight.
💡 Worked example: Exam scores of 10 students: 70, 75, 80, 85, 90, 70, 75, 80, 85, 90
Given:- Data: 70, 75, 80, 85, 90, 70, 75, 80, 85, 90
- n = 10
Steps:- Mean = (70+75+80+85+90+70+75+80+85+90)/10 = 800/10 = 80
- Sorted data: 70,70,75,75,80,80,85,85,90,90
- Median = (80+80)/2 = 80
- Mode = 70, 75, 80, 85, 90 (multimodal, each appears twice)
- Sample variance = Sum((x-80)^2)/(10-1) = 500/9 = 55.56
- SD = sqrt(55.56) = 7.45
- CV = (7.45/80)*100% = 9.3%
Result: Mean and median both equal 80, SD 7.45, CV 9.3% (low, homogeneous data). Student scores are relatively uniform with tight spread around the mean.
❓ Frequently asked questions
When should I use mean, median, or mode?
Use the mean for symmetric, continuous data (temperatures, exam scores). Use the median for skewed data or when outliers are present (income, home prices, where outliers pull the mean). Use the mode for nominal or categorical data (favorite color, car brand). U.S. Census Bureau household income reports use the median, since income distributions are heavily right-skewed.
What is the difference between sample and population standard deviation?
Sample SD divides by (n-1) as Bessel's correction to be an unbiased estimator of the population SD. Population SD divides by N. Use sample SD when the data is a subset of a larger population (most common). Use population SD only when the data covers the entire population (e.g., all students in a specific class treated as the full population).
How do I detect outliers?
Tukey's IQR rule: outliers are values outside [Q1 - 1.5*IQR, Q3 + 1.5*IQR]. Z-score method: outliers have |Z| > 3 (z = (x-mean)/SD). For non-normal distributions, the IQR method is more robust. Box plots automatically flag outliers using the 1.5*IQR rule.
What does the coefficient of variation (CV) mean?
CV is the ratio of SD to mean, expressed as a percentage. It measures relative variability: CV <10% is low/homogeneous, 10-30% moderate, >30% high/heterogeneous. CV is useful for comparing variability across datasets with different units. Example: stock price CV 25%, employee salary CV 8%; the stock is relatively more variable.
Why is the median more robust than the mean?
The median is unaffected by extreme values because it only depends on the middle position. Example: data 1, 2, 3, 4, 1000 has mean = 202 (pulled by the outlier 1000) but median = 3 (still representative). This is why the U.S. Census Bureau reports median income rather than mean in welfare statistics, since income distributions are highly asymmetric.
📚 Sources & references
Last updated: May 11, 2026