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Average Calculator

Compute mean, median, mode, range and standard deviation from a list of numbers.

Mean
30
n = 5

Parsed 5 values.

Mean (average)
30
mean = (10 + 20 + 30 + 40 + 50) ÷ 5 = 30
Median
30
Mode
none
Min / Max
10 / 50
Range
40
Sum
150
Std. dev (σ)
14.1421

n = 5, sum = 150, mean = 30, median = 30, range = 40, σ = 14.1421.

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How to use the Average Calculator

  1. 1

    Enter your numbers

    Paste or type your data values separated by commas, spaces or newlines. The calculator accepts any mix of separators — handy when copying directly from a spreadsheet column or a CSV row.

  2. 2

    Pick population or sample standard deviation

    Toggle population (divide by n) for summarising the data in hand, or sample (divide by n−1, Bessel-corrected) when inferring about a wider population from a sample. Sample is the default for inferential statistics.

  3. 3

    Read mean, median, mode, range and σ

    The result shows all six statistics at once: mean (sum/n), median (middle), mode (most frequent), range (max−min), variance and standard deviation. The gap between mean and median signals skewness.

  4. 4

    Spot outliers and skewness

    If mean and median diverge significantly, your data is skewed — typical for incomes, house prices and response times. In those cases the median is the more honest centre; report both for transparency.

  5. 5

    Copy or share the full breakdown

    Use the share link to send the exact dataset to a collaborator, or copy the formatted statistics block for paste into a report. Every input value is preserved in the URL so the recipient sees identical results.

What this calculator does

Statistics summarises a dataset with a few key numbers so you do not have to look at every value. Central tendency tells you where the data is centred: mean = sum / n (sensitive to outliers), median = middle value when sorted (robust to outliers), mode = most frequent value (useful for categorical or discrete data). Spread tells you how scattered the data is: range = max — min (simple but sensitive to extremes), variance = average squared deviation from the mean, standard deviation σ = √variance (in the same units as the data). This calculator returns the population standard deviation (dividing by n). For inferential statistics on a sample, divide by n−1 (Bessel correction) to get the sample standard deviation.

Formula

mean = Σx / n. median = middle of sorted x. mode = most-frequent x. range = max − min. variance = Σ(x − mean)² / n. σ = √variance.
x
Each data value in the list
n
Count of values in the list
Σ
Sum over all values
mean
Arithmetic average
σ
Population standard deviation

The mean treats every value equally. The median ignores magnitude and only cares about order. The mode counts occurrences. For a symmetric distribution, mean = median = mode. For a right-skewed distribution (like income), mean > median > mode. Standard deviation expresses spread in the original units: a dataset with σ = $5,000 has typical deviation $5K from the mean. For roughly normal data, ~68% of values fall within 1σ of the mean, ~95% within 2σ, ~99.7% within 3σ (the empirical rule).

Worked examples

Example: 5 test scores [72, 85, 90, 88, 95]

Sum = 430. Count n = 5. Mean = 430 ÷ 5 = 86. Sorted: [72, 85, 88, 90, 95]. Median (middle of 5) = 88. No value repeats — no mode. Range = 95 − 72 = 23. Deviations from mean: −14, −1, 2, 4, 9. Squared: 196, 1, 4, 16, 81 → sum 298. Variance = 298 ÷ 5 = 59.6. Standard deviation σ = √59.6 ≈ 7.72.

Interpretation: mean score 86 with typical deviation ±7.7 points; range 72-95.

Example: skewed data [40, 45, 50, 50, 200]

Mean = 385 ÷ 5 = 77. Median = 50. Mode = 50.

Notice how the single outlier (200) pulls the mean up to 77 while the median stays at 50. If this were household income in a 5-person town, "average income $77K" overstates how the typical resident lives. The median ($50K) is the more honest centre. Whenever you see a "mean vs median" mentioned in news, watch for outlier-driven distortion.

Example: bimodal data [1, 2, 2, 3, 3, 4]

Mean = 15 ÷ 6 = 2.5. Median (avg of middle two: (2+3)/2) = 2.5. Modes = [2, 3] (both appear twice).

When two values tie for highest frequency, the dataset is bimodal — the calculator returns both. This is common in mixed populations (e.g. exam scores from two ability groups taught the same material).

Common use cases

  • Test grading — class mean and grade distribution
  • Sports — batting averages, points per game, running pace per km
  • Finance — average daily price, average return, drawdown statistics
  • Quality control — mean and standard deviation of manufactured part dimensions
  • Salary benchmarking — median wage (preferred over mean for skewed distributions)
  • Survey results — average rating and spread on a 1-5 or 1-10 scale
  • Climate data — monthly mean temperature and standard deviation
  • Medical data — vital signs trends, lab result averages
  • Marketing — average order value, average session duration, conversion rate
  • Sleep, fitness and habits — daily step counts, sleep hours per week

What affects the result

  • Outliers — a single extreme value can shift the mean substantially but barely move the median
  • Skewness — right-skewed distributions (income, house prices) have mean > median
  • Sample size — small samples are noisy; standard deviation estimates from <10 values are unreliable
  • Sample vs population — divide by n−1 (sample) when inferring about a larger population; divide by n (population) when summarising the data in hand
  • Distribution shape — for non-normal data the empirical rule (68/95/99.7) does not apply
  • Units — all values must be in the same units (don't mix cm and m, USD and INR, etc.)
  • Missing values — exclude or impute before averaging; including blanks as 0 corrupts the mean

Tips

  • Always report at least mean and median together — the gap signals skewness
  • For skewed data (incomes, house prices, response times), prefer median; for symmetric data, mean is fine
  • Always pair central tendency with a spread metric — "mean 86" alone is incomplete; "mean 86 ± 8" is informative
  • Visualise — a histogram beats any single statistic for understanding shape
  • For comparing two groups, compare means AND standard deviations; a t-test formalises the comparison
  • Beware "Simpson's paradox" — averages can reverse direction when groups are combined
  • For ratios and rates (mpg, prices), use the harmonic mean instead of arithmetic mean

Mistakes to avoid

  • Reporting the mean when the median is more honest (skewed distributions)
  • Including zero placeholders for missing data — distorts both mean and standard deviation
  • Computing standard deviation with n instead of n−1 when the data is a sample meant to infer a population
  • Confusing variance (squared units) with standard deviation (original units) — always report in original units
  • Averaging averages — the mean of group means is not the overall mean unless groups are the same size
  • Calling the "average" of percentages the simple mean — for rates and ratios, the weighted average or geometric mean may be needed

Frequently asked questions

What is the difference between mean, median and mode?

Mean is the arithmetic average (sum divided by count). Median is the middle value when the list is sorted. Mode is the most-frequent value. For symmetric data they roughly agree; for skewed data they can be very different. Use median for skewed data.

How do I calculate standard deviation?

Compute the mean. Subtract the mean from each value to get deviations. Square each deviation. Average the squared deviations (divide by n for population, n−1 for sample). Take the square root. σ is in the same units as the original data, making it easier to interpret than variance.

When should I use the median instead of the mean?

Whenever your data is skewed or has outliers. Examples: incomes (a few millionaires drag the mean up), house prices, response times in software, time-on-page. For test scores or measurements that follow roughly a normal distribution, the mean is fine.

Why divide by n−1 for sample standard deviation?

Bessel's correction. When you compute a sample mean from data and then compute deviations from THAT mean, you underestimate the true population variance because the sample mean is already centred on this specific sample. Dividing by n−1 corrects for that bias when inferring about the wider population.

What does "range" tell me?

The simplest spread metric: max − min. Useful for quick comparison and for showing extremes, but unreliable as a stand-alone summary because it depends entirely on the two extreme points. Standard deviation is more robust.

How do I compute a weighted average?

Multiply each value by its weight, sum those products, then divide by the sum of weights: weighted mean = Σ(x × w) / Σw. This is the math behind GPA (weights = credit hours), portfolio returns (weights = portfolio fraction) and exam grading (weights = section scores).

Can the average be a value not in the original list?

Yes — the mean rarely matches any single data point. The median can also be a non-data value (the average of the two middle values when n is even). Only the mode is guaranteed to be a data point.

Last reviewed:

Sources & references

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