How to Calculate Mean, Median, and Other Statistics
Calculate mean, median, mode, standard deviation, and more for any data set with our free Statistics Calculator. Paste numbers for instant analysis.
Steps
Enter your data
Paste or type your numbers separated by commas, spaces, or line breaks. The tool accepts any reasonable number format including negative numbers and decimals. For example: 23, 45, 12, 67, 34, 45, 89.
View central tendency measures
Mean (average): sum of all values divided by count. Median: the middle value when sorted. Mode: the most frequently occurring value(s). These three measures describe where the data is centred.
Review dispersion measures
Range: max minus min. Variance: average of squared differences from the mean. Standard deviation: square root of variance — how spread out the data is from the mean. A low standard deviation means values are close to the mean; high means they are spread out.
Check the data distribution
The tool also shows quartiles (Q1, Q2/median, Q3), interquartile range (IQR = Q3-Q1), and a histogram of the data distribution. These reveal whether the data is symmetric, skewed, or has outliers.
Descriptive Statistics: Understanding Your Data
Descriptive statistics summarise and describe the main features of a data set without making inferences beyond the data. They are the first step in any data analysis: before modelling or drawing conclusions, you need to understand what your data looks like. Minimum and maximum tell you the range. Mean and median tell you the centre. Standard deviation and IQR tell you the spread. Skewness tells you whether the distribution has a long tail. Outliers (values more than 1.5×IQR from the quartiles, or more than 3 standard deviations from the mean) may represent data entry errors, genuine extreme cases, or interesting anomalies worth investigating separately. Always compute descriptive statistics before any further analysis — they prevent misinterpretation and reveal data quality issues.
Frequently Asked Questions
Use the mean when data is roughly normally distributed (symmetric bell curve) without significant outliers. Use the median when data is skewed or has outliers — the median is resistant to extreme values. Income data famously uses median because a small number of very high earners would inflate the mean significantly. If mean and median are very different, it signals skewed data or outliers worth investigating.
Standard deviation measures how spread out values are around the mean. In a normal distribution: 68% of data falls within 1 standard deviation of the mean, 95% within 2, and 99.7% within 3 (the 68-95-99.7 rule). A small standard deviation means values are tightly clustered; large means they are widely spread. Standard deviation is used in quality control, finance (portfolio risk), academic testing, and scientific measurement to characterise variability.