Mean, Median & Mode Calculator: Find the Average Fast

What do mean 5.00, median 4.50 and mode 4 mean?

They are three ways of saying what is typical about the list 2, 4, 4, 4, 5, 5, 7, 9. The mean is the average — the sum, 40.00, divided by the count, 8, which is 5.00. The median is the middle — the list has eight numbers, so the middle two are 4 and 5, and their average is 4.50. The mode is the most common — 4 appears three times, more than any other number, so the mode is 4. The mean, the median and the mode are three averages, never the same number: the mean is the average, the median is the middle, and the mode is the most common.

Three things to check before you trust the number

Sort the list first. The median is the middle of the sorted list, not the middle of the list as you typed it. 2, 4, 4, 4, 5, 5, 7, 9 is already in order; 9, 2, 4, 5, 4, 7, 5, 4 is the same list, but its middle is not the same number until you sort it.

The mean listens to outliers. Add a 100 to the defaults and the mean jumps from 5.00 to 15.56, while the median moves only to 5.00 and the mode stays 4. When one number is far from the rest, the median tells you more about what is typical.

No mode is a real answer. A dataset where every number appears once has no mode, so the calculator says so plainly instead of inventing one. A single number is its own mean, median and mode.

Worked example

On the defaults: 2, 4, 4, 4, 5, 5, 7, 9.

1. Sort: 2, 4, 4, 4, 5, 5, 7, 9 — already in order.
2. Count: 8 numbers.
3. Sum: 2 + 4 + 4 + 4 + 5 + 5 + 7 + 9 = 40.00.
4. Mean: 40.00 ÷ 8 = 5.00 (unrounded 5.000000).
5. Median: the middle two are 4 and 5, so (4 + 5) ÷ 2 = 4.50 (unrounded 4.500000).
6. Mode: 4 appears three times, more than any other number, so the mode is 4.
7. Range: 9 − 2 = 7.00.
8. Smallest number to add for the mean to reach at least 6: 14 — adding 14 gives a mean of 6.00, and adding 13 gives 5.89 (unrounded 5.888889).
9. Smallest number to add for the median to reach at least 5: 5 — adding 5 gives a median of 5.00 and the modes 4 and 5, and adding 4 gives a median of 4.00.

Every branch, checked

• 1, 2, 3, 4, 5: 1, 2, 3, 4, 5: Mean 3.00; median 3.00; mode —; count 5; sum 15.00; range 4.00; sorted 1, 2, 3, 4, 5. One to five — the mean is 3.00, the median is 3.00, no mode.
• 10, 20, 30: 10, 20, 30: Mean 20.00; median 20.00; mode —; count 3; sum 60.00; range 20.00; sorted 10, 20, 30. Ten, twenty, thirty — the mean is 20.00, the median is 20.00, no mode.
• 5, 5, 5, 5: 5, 5, 5, 5: Mean 5.00; median 5.00; mode 5; count 4; sum 20.00; range 0.00; sorted 5, 5, 5, 5. Four fives — the mean is 5.00, the median is 5.00, the mode is 5.
• 1, 1, 2, 3, 5, 8: 1, 1, 2, 3, 5, 8: Mean 3.33; median 2.50; mode 1; count 6; sum 20.00; range 7.00; sorted 1, 1, 2, 3, 5, 8. The first six Fibonacci numbers — the mean is 3.33, the median is 2.50, the mode is 1.
• 100, 200: 100, 200: Mean 150.00; median 150.00; mode —; count 2; sum 300.00; range 100.00; sorted 100, 200. One hundred and two hundred — the mean is 150.00, the median is 150.00, no mode.
• 3, 3, 7, 7, 7: 3, 3, 7, 7, 7: Mean 5.40; median 7.00; mode 7; count 5; sum 27.00; range 4.00; sorted 3, 3, 7, 7, 7. Two threes and three sevens — the mean is 5.40, the median is 7.00, the mode is 7.
• -2, 0, 2, 4: -2, 0, 2, 4: Mean 1.00; median 1.00; mode —; count 4; sum 4.00; range 6.00; sorted -2, 0, 2, 4. Minus two to four — the mean is 1.00, the median is 1.00, no mode.
• 1.5, 2.5, 3.5: 1.5, 2.5, 3.5: Mean 2.50; median 2.50; mode —; count 3; sum 7.50; range 2.00; sorted 1.5, 2.5, 3.5. One and a half to three and a half — the mean is 2.50, the median is 2.50, no mode.
• 9, 9, 9, 1, 1: 9, 9, 9, 1, 1: Mean 5.80; median 9.00; mode 9; count 5; sum 29.00; range 8.00; sorted 1, 1, 9, 9, 9. Three nines and two ones — the mean is 5.80, the median is 9.00, the mode is 9.
• 7: 7: Mean 7.00; median 7.00; mode 7; count 1; sum 7.00; range 0.00; sorted 7. A single seven — the mean is 7.00, the median is 7.00, the mode is 7.

The reverses, worked backwards

• Smallest number to add for the mean to REACH at least 6: 14 — at 14 the figures are Mean 6.00 (unrounded 6.000000); median 5.00 (unrounded 5.000000); mode 4; count 9; sum 54.00 (unrounded 54.000000); range 12.00 (unrounded 12.000000); sorted 2, 4, 4, 4, 5, 5, 7, 9, 14; at the lower neighbor the figures are Mean 5.89 (unrounded 5.888889); median 5.00 (unrounded 5.000000); mode 4; count 9; sum 53.00 (unrounded 53.000000); range 11.00 (unrounded 11.000000); sorted 2, 4, 4, 4, 5, 5, 7, 9, 13; at the upper neighbor the figures are Mean 6.11 (unrounded 6.111111); median 5.00 (unrounded 5.000000); mode 4; count 9; sum 55.00 (unrounded 55.000000); range 13.00 (unrounded 13.000000); sorted 2, 4, 4, 4, 5, 5, 7, 9, 15 — verdict: STEP.
• Smallest number to add for the median to REACH at least 5: 5 — at 5 the figures are Mean 5.00 (unrounded 5.000000); median 5.00 (unrounded 5.000000); mode 4 and 5; count 9; sum 45.00 (unrounded 45.000000); range 7.00 (unrounded 7.000000); sorted 2, 4, 4, 4, 5, 5, 5, 7, 9; at the lower neighbor the figures are Mean 4.89 (unrounded 4.888889); median 4.00 (unrounded 4.000000); mode 4; count 9; sum 44.00 (unrounded 44.000000); range 7.00 (unrounded 7.000000); sorted 2, 4, 4, 4, 4, 5, 5, 7, 9; at the upper neighbor the figures are Mean 5.11 (unrounded 5.111111); median 5.00 (unrounded 5.000000); mode 4; count 9; sum 46.00 (unrounded 46.000000); range 7.00 (unrounded 7.000000); sorted 2, 4, 4, 4, 5, 5, 6, 7, 9 — verdict: STEP.
• Smallest number to add for the range to REACH at least 10: 12 — at 12 the figures are Mean 5.78 (unrounded 5.777778); median 5.00 (unrounded 5.000000); mode 4; count 9; sum 52.00 (unrounded 52.000000); range 10.00 (unrounded 10.000000); sorted 2, 4, 4, 4, 5, 5, 7, 9, 12; at the lower neighbor the figures are Mean 5.67 (unrounded 5.666667); median 5.00 (unrounded 5.000000); mode 4; count 9; sum 51.00 (unrounded 51.000000); range 9.00 (unrounded 9.000000); sorted 2, 4, 4, 4, 5, 5, 7, 9, 11; at the upper neighbor the figures are Mean 5.89 (unrounded 5.888889); median 5.00 (unrounded 5.000000); mode 4; count 9; sum 53.00 (unrounded 53.000000); range 11.00 (unrounded 11.000000); sorted 2, 4, 4, 4, 5, 5, 7, 9, 13 — verdict: STEP.
• Largest number to add for the mean to STAY at or below 5.50: 9 — at 9 the figures are Mean 5.44 (unrounded 5.444444); median 5.00 (unrounded 5.000000); mode 4; count 9; sum 49.00 (unrounded 49.000000); range 7.00 (unrounded 7.000000); sorted 2, 4, 4, 4, 5, 5, 7, 9, 9; at the upper neighbor the figures are Mean 5.56 (unrounded 5.555556); median 5.00 (unrounded 5.000000); mode 4; count 9; sum 50.00 (unrounded 50.000000); range 8.00 (unrounded 8.000000); sorted 2, 4, 4, 4, 5, 5, 7, 9, 10; at the lower neighbor the figures are Mean 5.33 (unrounded 5.333333); median 5.00 (unrounded 5.000000); mode 4; count 9; sum 48.00 (unrounded 48.000000); range 7.00 (unrounded 7.000000); sorted 2, 4, 4, 4, 5, 5, 7, 8, 9 — verdict: STEP.
• Smallest number to add for the sum to REACH at least 50: 10 — at 10 the figures are Mean 5.56 (unrounded 5.555556); median 5.00 (unrounded 5.000000); mode 4; count 9; sum 50.00 (unrounded 50.000000); range 8.00 (unrounded 8.000000); sorted 2, 4, 4, 4, 5, 5, 7, 9, 10; at the lower neighbor the figures are Mean 5.44 (unrounded 5.444444); median 5.00 (unrounded 5.000000); mode 4; count 9; sum 49.00 (unrounded 49.000000); range 7.00 (unrounded 7.000000); sorted 2, 4, 4, 4, 5, 5, 7, 9, 9; at the upper neighbor the figures are Mean 5.67 (unrounded 5.666667); median 5.00 (unrounded 5.000000); mode 4; count 9; sum 51.00 (unrounded 51.000000); range 9.00 (unrounded 9.000000); sorted 2, 4, 4, 4, 5, 5, 7, 9, 11 — verdict: STEP.
• Smallest number to add for the mode to become 4 and 5: 5 — at 5 the figures are Mean 5.00 (unrounded 5.000000); median 5.00 (unrounded 5.000000); mode 4 and 5; count 9; sum 45.00 (unrounded 45.000000); range 7.00 (unrounded 7.000000); sorted 2, 4, 4, 4, 5, 5, 5, 7, 9; at the lower neighbor the figures are Mean 4.89 (unrounded 4.888889); median 4.00 (unrounded 4.000000); mode 4; count 9; sum 44.00 (unrounded 44.000000); range 7.00 (unrounded 7.000000); sorted 2, 4, 4, 4, 4, 5, 5, 7, 9; at the upper neighbor the figures are Mean 5.11 (unrounded 5.111111); median 5.00 (unrounded 5.000000); mode 4; count 9; sum 46.00 (unrounded 46.000000); range 7.00 (unrounded 7.000000); sorted 2, 4, 4, 4, 5, 5, 6, 7, 9 — verdict: STEP.

What the defaults assume

The defaults are 2, 4, 4, 4, 5, 5, 7, 9 — a small list with a clear mode, a mean of 5.00 and a median of 4.50 — and they are a starting point, not a benchmark: your dataset may be test scores, measurements or prices, and the right average for you is the one your numbers describe. Paste your own list, separated by commas, and the calculator recomputes instantly. Sort the list, count it, add it up — and remember that no mode is a real answer.

These notes repeat in every explainer section because this page is built to be read start to finish: the defaults are one dataset, not a standard; sort the list first; the mean listens to outliers; and no mode is a real answer.

Output · formula · meaning

Who uses this

• A teacher working out a class average — the mean is 5.00, the median is 4.50 and the mode is 4, and the three together say more than any one alone.
• A student checking a statistics problem — sort the list, count it, add it up, and the mean, median and mode fall out.
• A data analyst summarizing a column of numbers — the mean for the average, the median for the typical value, the mode for the most common one.
• A shopper comparing prices — the median price of a list tells you what is typical, even when one price is far above the rest.

Accuracy & limitations

The calculator does the arithmetic exactly — the mean is the sum over the count, the median is the middle of the sorted list, the mode is the most frequent value, and the range is the largest minus the smallest — and every figure on this page is checked against an independent model. What it cannot do is decide which average matters: the mean listens to outliers, so when one number is far from the rest the median tells you more about what is typical. It also takes one list at a time — a weighted average needs the gpa-calculator page, and the spread needs the standard-deviation-calculator page. And the mean of the defaults plus 13 is 5.89, unrounded 5.888889 — the page prints the unrounded figure so the rounding does not mislead you.

Cite this calculator

The mean is the sum divided by the count; the median is the middle number when the list is in order; the mode is the number that appears most. On the defaults — 2, 4, 4, 4, 5, 5, 7, 9 — the mean is 5.00, the median is 4.50 and the mode is 4. Smallest number to add for the mean to reach at least 6: 14. Smallest number to add for the median to reach at least 5: 5. Smallest number to add for the range to reach at least 10: 12. Largest number to add for the mean to stay at or below 5.50: 9. Smallest number to add for the sum to reach at least 50: 10. Smallest number to add for the mode to become 4 and 5: 5. Source: Bright Side Kit, brightoolbox.com.

Frequently asked questions