Mean, Median, Mode & Range Calculator

The mean is the arithmetic average — sum of all values divided by the count. The median is the middle value of a sorted dataset (or the average of the two middle values when n is even). The mode is the most frequently occurring value. The range is max − min. They measure different things: mean and median measure the center (location) of the data; mode measures the most common value; range measures the spread.

Step 1 — Sort the dataset (required for median; optional but helpful for mode). Step 2 — Mean: add all values, divide by count. Step 3 — Median: with n odd, take the middle value at position (n+1)/2; with n even, average the two values at positions n/2 and n/2+1. Step 4 — Mode: find the value(s) that appear most frequently (if all are unique, there is no mode). Step 5 — Range: subtract the minimum from the maximum. Example: for {4, 8, 6, 5, 3, 2, 8, 9, 2, 5}: sorted = {2,2,3,4,5,5,6,8,8,9}, mean = 5.2, median = (5+5)/2 = 5, modes = 2, 5, 8, range = 7.

Sort the values from smallest to largest. With n even, the median is the average of the values at positions n/2 and (n/2 + 1). For example, with {2, 4, 6, 8} (n = 4), the two middle values are 4 and 6, so the median is (4 + 6)/2 = 5. The median may not be a value that appears in the original dataset — this is normal. This is the convention used by Excel MEDIAN, Google Sheets MEDIAN, and Python's statistics.median.

Yes — a dataset can be bimodal (two modes), trimodal (three) or multimodal (multiple). This happens when two or more values are tied for the highest frequency. For example, {1, 2, 2, 3, 4, 4, 5} has modes 2 and 4 (each appears twice). A dataset has no mode when every value appears exactly once — there is no single most-frequent observation. Multimodality in real data often signals that the sample mixes two underlying populations (e.g., adult heights split by sex).

A single extreme outlier can shift the mean dramatically — e.g., {1, 2, 3, 4, 1000} has mean 202 but median 3. The median is robust to outliers as long as fewer than 50% of values are extreme (it has the highest breakdown point of any common statistic). The mode is usually unaffected by a single outlier unless that outlier repeats. The range is maximally affected — by definition it is controlled entirely by the two extremes. To detect outliers, use the IQR rule: flag values below Q1 − 1.5·IQR or above Q3 + 1.5·IQR.

The range is simply maximum − minimum, the total spread. It is easy to compute but not robust: a single outlier (data-entry error, sensor glitch) inflates it arbitrarily. For most serious analyses, prefer the interquartile range (IQR) = Q3 − Q1, which captures the middle 50% of the data, or the standard deviation, which weights every observation by distance from the mean. Use the range for quick exploratory summaries and engineering tolerance checks where the extremes are what matters.

In everyday speech, yes. When people say 'average' they almost always mean the arithmetic mean. In statistics, 'average' is more general and can refer to the geometric mean (used for growth rates), harmonic mean (used for averaging rates like speed), median, or mode. For formal writing, use the specific name. For most descriptive purposes 'arithmetic mean' and 'average' are interchangeable.

For the mean itself, no — the formula is the same: sum / count. The distinction matters for variability measures like variance and standard deviation, where the sample formula divides by (n − 1) (Bessel's correction) while the population formula divides by n. This calculator computes the arithmetic mean of whatever data you paste, treating it as the complete collection. If you are inferring properties of a larger population, the sample mean is an unbiased estimator of the population mean.

A large gap between mean and median is a strong signal of skewness or outliers. If the mean is much larger than the median, the distribution is right-skewed — a few large values pull the mean up (typical of income, wealth, response times). If the mean is much smaller than the median, the distribution is left-skewed — a few small values drag the mean down. When mean ≈ median, the distribution is roughly symmetric. As a rule of thumb, if |mean − median| > 0.2 × standard deviation, examine a histogram before reporting.

Results are identical — same formulas, same conventions. The equivalent spreadsheet functions are: =AVERAGE() for mean, =MEDIAN() for median, =MODE.SNGL() or =MODE.MULT() for mode, and =MAX()-MIN() for range. Use this calculator when you want a fast answer without opening a spreadsheet, or when teaching students who don't yet know spreadsheet functions. Use Excel/Sheets when you need to keep the data for further analysis or build charts.

This calculator expects numeric values separated by commas. Blanks and non-numeric tokens are silently skipped — they don't count toward n, mean, median, mode or range. In practice, decide on a missing-data policy before calculating: (1) list-wise deletion (skip the missing observations) is what this tool does by default; (2) mean imputation (replace missing with the dataset mean) is acceptable for exploratory work but biases inferential analyses. Never enter '0' as a placeholder for missing — it distorts every statistic.

Yes to both. Calculations use IEEE 754 double-precision floating point (~15–17 significant digits), matching what Excel, Google Sheets, R, and Python NumPy return. All calculations run client-side in your browser — your data never leaves your device, is not transmitted to any server, and is not logged or stored anywhere. You can safely use this tool with confidential data such as student grades, patient measurements, or financial figures.