Free mean, median and mode calculator. Paste any list of numbers to get all three averages instantly, with the mode explained when values tie or never repeat.
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The mean is the total of all numbers divided by how many there are. The median is the middle value once the list is sorted (the average of the two middle values for an even-sized list). The mode is the value that appears most often; when every value appears once there is no single mode. Paste any list of numbers and all three averages are computed instantly.
These are the three measures of central tendency — three different answers to "what's typical?" The mean formula is Σx ÷ n: add all values and divide by how many there are. To find the median, sort the values and take the middle one (for an even number of values, average the two middle values). To find the mode, pick the value that appears most often.
Take 2, 2, 4, 5, 7: the mean is 20 ÷ 5 = 4, the sorted middle (median) is 4, and the mode is 2 because it appears twice. The mean, median and mode can all differ — that difference is often the most informative thing about a dataset.
Find the mean, median and mode of 12, 15, 18, 18, 22, 24 — a mean median mode calculator with steps does exactly this:
Step 1 — order the data: 12, 15, 18, 18, 22, 24 (already sorted). Step 2 — the mean: (12 + 15 + 18 + 18 + 22 + 24) ÷ 6 = 109 ÷ 6 = 18.17. Step 3 — the median: with an even count of 6, average the 3rd and 4th values: (18 + 18) ÷ 2 = 18. Step 4 — the mode: 18 appears twice, more than any other value, so the mode is 18.
Decimals and negative numbers work the same way — the formulas don't care about the sign. Enter numbers separated by commas, spaces or line breaks; the calculator ignores non-numeric entries and shows the count of values it used.
Use this comparison to pick the right average for your data:
| Situation | Best average | Why | |---|---|---| | Symmetric data, no outliers | Mean | Uses every value; most efficient | | Skewed data or outliers present | Median | Ignores extremes — the $50k salaries and one $10M outlier give a honest middle | | Categorical data (favorite color) | Mode | Mean and median are meaningless for categories | | "Typical" customer, most common size | Mode | Directly answers "what's most popular" |
When should you use the median instead of the mean? Whenever extreme values would drag the mean away from the bulk of the data — house prices, incomes and response times are the classic cases. Which central tendency is affected by extreme values? The mean — one billionaire moves the mean, never the median. Which of the three should you report? Report the mean for well-behaved data, the median for skewed data, and the mode when frequency is the question.
The range is max − min — the full spread of the data. The midrange is (max + min) ÷ 2, which unlike the median only looks at the extremes, so a single outlier swings it wildly. Quartiles split sorted data into quarters; the interquartile range (IQR = Q3 − Q1) covers the middle 50% and resists outliers, which is why the IQR matters for box plots and the five-number summary (min, Q1, median, Q3, max).
Outlier detection uses the Tukey fence method: values beyond Q1 − 1.5×IQR or Q3 + 1.5×IQR are flagged as outliers. Standard deviation tells you the typical distance from the mean; variance is its square. What is the difference between variance and standard deviation? Variance is in squared units, standard deviation is in the original units — report the latter for readability. When should you use population variance instead of sample variance? Use population formulas (divide by n) when you have every member; use sample formulas (divide by n − 1, Bessel's correction) when estimating from a sample. Related averages: the weighted average gives values different importance (like GPA), the geometric mean suits growth rates, and the harmonic mean suits average speeds. Skewness measures which side the tail is on: right-skewed data pulls the mean above the median, left-skewed data pulls it below. A frequency table counts how often each value occurs; dividing each count by the total gives the relative frequency. Results table for the worked example: 12, 15, 18, 18, 22, 24 → mean 18.17, median 18, mode 18.
This statistics calculator focuses on the three core averages, and the accepted input format is flexible: commas, spaces or line breaks all work.
Paste or type numbers separated by commas, spaces or new lines — 2, 4, 6 / 2 4 6 / one per line all work. The order of the numbers doesn't matter; sorting happens internally before the median is found. Repeated values are kept (they define the mode); non-numeric entries are skipped and reported in the count.
How to calculate mean, median and mode in Excel: use =AVERAGE(range) for the mean, =MEDIAN(range) for the median, and =MODE.SNGL(range) for the mode. For grouped data (values with frequencies), expand the frequencies or use a weighted calculation — the same engine that powers weighted averages.
The mean is the arithmetic average (Σx ÷ n), the median is the middle value of sorted data, and the mode is the most frequent value. They are three measures of central tendency that can each be the right "typical" value in different situations.
The mean uses every value, so outliers pull it; the median is the sorted middle, so outliers don't move it. For 2, 3, 4, 100 the mean is 27.25 but the median is 3.5 — the median better represents the bulk of the data.
Yes. Two values tied for most frequent make it bimodal; three or more make it multimodal. This calculator lists every tied value.
It means every value appears exactly once, so no value is more frequent than the rest. With no repeats, there is no single mode.
Sort the values and average the two middle ones. For 12, 15, 18, 18, 22, 24, the middle pair is 18 and 18, so the median is 18.
The mean. Adding one huge outlier shifts the mean dramatically while the median and mode barely move — which is why median income is reported instead of mean income.
The range is max − min. The midrange is (max + min) ÷ 2 — it uses only the extremes, unlike the median which uses the sorted middle, so one outlier corrupts the midrange but not the median.
The interquartile range (Q3 − Q1) spans the middle 50% of the data. It measures spread without outlier influence and drives box plots, the five-number summary, and Tukey-fence outlier detection.
Divide by n for a full population; divide by n − 1 (Bessel's correction) when estimating population variance from a sample, because a sample underestimates spread on average.
Use =AVERAGE(range), =MODE.SNGL(range), and =MEDIAN(range). For standard deviation: =STDEV.P(range) for a population, =STDEV.S(range) for a sample.
No. The mean and mode ignore order entirely, and the median sorts the data first, so any input order gives the same results.
Repeated values are kept — they determine the mode. Non-numeric text is skipped, and the results show how many valid values were counted.
Sort the values and average the two middle ones. For 12, 15, 18, 18, 22, 24, the middle pair is 18 and 18, so the median is 18.
It tells you the typical distance of values from the mean — a small standard deviation means the data clusters tightly; a large one means it spreads widely.
Yes — free, online, no sign-up, and it runs entirely in your browser.