Free Mean Median Mode Calculator
Calculate mean, median, and mode — the three measures of central tendency — for any dataset. Also computes variance, standard deviation, range, IQR, and frequency distribution. Free, private — all calculations run in your browser.
Mean Median Mode Calculator — All Central Tendency Measures
Calculate the mean, median, mode, geometric mean, harmonic mean, midrange, standard deviation, variance, quartiles, and IQR for any dataset. Enter numbers separated by commas, spaces, or semicolons. Used in statistics, education and data analysis.
How to Use This Calculator
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Type or paste numbers separated by commas, spaces, or semicolons.
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Mean, median, and mode appear instantly.
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Scroll down for standard deviation, quartiles, and IQR.
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The frequency distribution shows how often each value appears.
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Export a PDF with the complete statistical summary.
📐 How This Is Calculated
Mean = Σxᵢ/n | Median = middle value | Mode = most frequent | σ = √[Σ(xᵢ−μ)²/n]
Mean (x̄)—Arithmetic average — sum of all values divided by countMedian—Middle value when sorted. For even n: average of two middle valuesMode—The value(s) that appear most frequently. A dataset can have multiple modes or noneσ—Population standard deviation — uses divisor n (not n−1 as in sample SD)Reference: Descriptive statistics — R.A. Fisher (1925); NIST/SEMATECH Statistical Methods §1.3
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Disclaimer
Results are provided for informational and educational purposes only. They should not be used as a substitute for professional financial, engineering, medical, or legal advice. Always verify outputs with a qualified professional before making important decisions. Roughtools makes no warranties regarding accuracy or completeness for your specific situation.
About This Mean Median Mode Calculator
The Mean Median Mode Calculator computes all three classical measures of central tendency for any list of numbers you provide. Central tendency measures answer the question: "what is a typical value in this dataset?" Each of the three answers that question differently, and together they provide a complete picture of where data is centred and how that centre should be interpreted.
The Formulas
Median = middle value of sorted data
Mode = most frequently occurring value(s)
Where Σx is the sum of all values and n is the count. For the median with an even number of values: average the two middle values after sorting. For example, in [3, 5, 7, 9], the median = (5 + 7) / 2 = 6.
When Each Average Is Appropriate
The mean is best for symmetric distributions without extreme outliers — exam scores, heights, temperatures. It uses every data point and is the foundation for many further statistical calculations (variance, standard deviation, correlation). The median is best when the data is skewed or contains outliers — income, home prices, reaction times. It is resistant to extremes because it only considers the position of values, not their magnitude. The mode is best for categorical or discrete data — the most common shoe size, the most popular choice in a survey, the most frequent defect type in a quality report. It is the only one of the three that works for non-numeric data.
Resistance to Outliers — A Real Example
Consider seven workers' annual salaries: $30k, $31k, $29k, $32k, $30k, $31k, $500k (the owner). Mean = $97.6k — higher than six out of seven people earn. Median = $31k — the value that splits the group in half and accurately reflects what a typical worker earns. Mode = $30k — the most common salary. This example illustrates why government income statistics always quote median household income: the mean would be misleading.
What the Calculator Also Computes
Beyond the three averages, the calculator provides additional statistics to give a complete summary of your data:
- •Standard deviation — how spread out values are around the mean
- •Variance — the squared average deviation (SD²)
- •Range — the difference between the maximum and minimum values
- •IQR (Interquartile Range) — the spread of the middle 50% of data (Q3 − Q1)
- •Frequency distribution — a count of how often each value appears
Privacy Notice
All calculations run entirely in your browser. No data you enter is transmitted to any server, stored in any database, or shared with third parties. Your dataset stays completely private on your device. See our Privacy Policy for full details.
When to Use This Calculator
Find the class average (mean), the middle score (median), and the most common score (mode). Compare mean and median to spot whether a few very high or low scores are skewing the average.
Analyse compensation data with median (resistant to outliers from executive salaries), mode (most common salary band), and mean for comparison. Understand the full distribution.
Calculate a player's average score, most frequent performance level (mode), and median game score across a season. Identify outlier performances that inflate the mean.
Compare median vs. mean home prices in a neighbourhood. The median gives the price a typical buyer encounters; the mean is pulled up by luxury properties. Both are useful together.
Analyse product measurements from a production run. Mean and standard deviation tell you if the process is centred and consistent; mode reveals the most common defect size.
💡 Pro Tips
Use the median for right-skewed data — especially income, home prices, wealth, and any measure where a small number of very large values exist. The mean will be pulled high by these extremes, making the median a more honest description of the typical value. A quick check: if mean > median, the data is right-skewed.
Mode is the only appropriate average for nominal (categorical) data — data that has no natural numeric order. For example, the most common eye colour, favourite music genre, or preferred payment method can only have a mode, never a meaningful mean or median. Applying mean or median to categorical data produces a meaningless result.
A dataset with no mode and one with multiple modes are very different situations. No mode means all values are equally frequent (uniform distribution). Multiple modes suggest distinct subgroups or clusters in the data. Before reporting "no mode" or "bimodal", verify whether the data should be split into separate categories.
Always check for outliers before reporting the mean. Sort the data and visually inspect the minimum and maximum. If the largest value is more than 3 standard deviations from the mean (a z-score > 3), investigate whether it is a real data point or a data entry error. Outliers can be legitimate (record-breaking events) or errors (a typo adding an extra zero).
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