What is the difference between mean, median and mode?

Mean is the sum divided by count (arithmetic average). Median is the middle value when sorted. Mode is the most frequently occurring value. For skewed data sets, median is often more representative than mean.

What is standard deviation?

Standard deviation measures how spread out numbers are from the mean. A low SD means values are close to the mean; a high SD means they are widely spread. Formula: SD = √(variance), where variance = average of squared differences from mean.

📊 Statistics Calculator

Average Calculator

Calculate mean, median, mode, range, standard deviation and more from any set of numbers. Enter numbers separated by commas, spaces or new lines.

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Quick examples

Mean (Average) --

--Median

--Mode

--Range

Sorted numbers — ■ median · ■ mode

Value distribution

Complete statistics

Understanding mean, median and mode

These three "measures of central tendency" each describe a dataset differently. Together with range and standard deviation, they give a complete picture of your data distribution.

📊 Mean vs Median

Mean is affected by outliers (extreme values). If 5 people earn ₹30,000 and 1 earns ₹10 crore, the mean salary is misleading. Median shows the "middle" salary better. Always check both.

📈 Standard deviation

Tells you how spread out the data is. Low SD = values are close to the mean. High SD = values vary widely. In a normal distribution, 68% of data falls within 1 SD of the mean.

🎯 Mode uses

Mode is used for categorical data and finding the most common value. A dataset can have no mode (all unique), one mode (unimodal), or multiple modes (bimodal/multimodal).

📐 Range

Range = Maximum − Minimum. It shows the spread of data. A large range indicates high variability. Range is simple but sensitive to extreme outliers — use SD for a more robust measure.

Frequently asked questions

How do I calculate the average of numbers?

Average (mean) = Sum of all numbers ÷ Count of numbers. Example: average of 4, 7, 13, 2, 1 = (4+7+13+2+1) ÷ 5 = 27 ÷ 5 = 5.4. This calculator does this instantly and also calculates median, mode, range and standard deviation.

What is the difference between population and sample standard deviation?

Population SD uses N (total count) in the denominator — used when you have all data. Sample SD uses N-1 — used when your data is a sample from a larger population (most practical cases). This calculator shows both. For most purposes, use sample SD.

How do I find the median of an even number of values?

Sort the numbers in order. With an even count, the median = average of the two middle values. Example: for 2, 4, 6, 8 → median = (4+6)/2 = 5. This calculator handles even and odd counts automatically.

What does geometric mean mean?

Geometric mean = n-th root of the product of all values. It is used for rates of change, investment returns (CAGR), and ratios. It is less affected by extreme high values than arithmetic mean. Example: geometric mean of 2, 8 = √(2×8) = √16 = 4.