Average calculator · Free · No sign-up
Average Calculator
An average calculator finds the mean by adding the numbers and dividing by how many there are, and the median, mode and range from the same list. This one also works from counts in a tally, from grouped classes such as 0 to 20, and from group averages that need weighting, and it shows the working.
12, 15, 9, 15, 22, 15, 11, 9 and 41: mean 16.56, median 15, mode 15, range 32.
Read 9 numbers.
- Count
- 9
- Sum
- 149
- Mean
- 16.56
- Median
- 15
- Mode
- 15
- Range
- 32
Type a target average to see what the next value must be.
| Value | Count | Value × count | Running count | Note |
|---|---|---|---|---|
| 9 | 2 | 18 | 2 | |
| 11 | 1 | 11 | 3 | |
| 12 | 1 | 12 | 4 | |
| 15 | 3 | 45 | 7 | median, mode |
| 22 | 1 | 22 | 8 | |
| 41 | 1 | 41 | 9 | |
| Total | 9 | 149 |
Median: the 5th of 9 values in order. Mode: 15 appears 3 times, more than any other value. The mean is 1.56 above the median. Without 41, the value furthest from the median, the mean would be 13.5.
The figures above are an example: replace them with yours. Worked out in this browser and kept there. To count first, use the tally counter, or the multi counter for several things at once.
Paste a list, type each value with how many times it was counted, enter grouped classes, or combine group averages. The mean, median, mode and range come back with the frequency table they are worked from.
An average is one number standing for a set of values. The mean is their total divided by how many there are, the median the middle value in order, and the mode the most frequent value; the range, largest minus smallest, says how spread out they are.
- No sign-up
- Nothing sent anywhere
- Shows its working
- Works offline
- Decimal commas
Key facts
| Detail | Answer |
|---|---|
| Price | Free, no sign-up, nothing to install |
| Input | A list; values with counts; grouped classes with counts; or group averages with counts |
| Gives | Count, sum, mean, median, mode and range, with a frequency table |
| Grouped data | Mean from midpoints, median by interpolation at n ÷ 2, modal class by density when widths differ |
| Combined averages | Weighted by each group’s count, shown beside the plain average |
| Mode | Every tied value listed; no mode when every value appears equally often |
| Decimal places | 0 to 4 |
| Where figures are kept | This browser only |
How to find the mean, median, mode and range
Choose what you have, enter it, and read the board and the table.
Choose what you have
A list of numbers, Values and counts for a tally, Grouped classes for banded data, or Combine averages for groups.
Enter the figures
Paste the list with commas, spaces or new lines between the numbers, or type a row for each value, class or group.
Read the board
The mean is at the top, with the median, mode and range under it and in the boxes below.
Check the working
The table shows value × count and the running count; the note names the median’s position and any value pulling the mean.
Set a target
Type a target average under a list to see the next value it needs.
Copy it out
Copy the table pastes into a spreadsheet as columns.
Who uses an average calculator
Anyone with a set of numbers, or a set of counts, who needs one figure for them.
Pupils and teachers
Mean, median and mode from a list, a frequency table or grouped data, with the columns a mark scheme wants.
Coaches and scorers
Goals, runs or points per match from a season’s tally, and the average across teams of different sizes.
Wildlife counts
Birds per walk or moths per trap night, with the one huge night named so it does not pass for typical.
Shops and stock
Sales per day across a week, and average order values combined across branches.
Events and venues
Attendance per session from door counts, and the median when one event was a sell-out.
Marks and grades
A combined class average, a weighted coursework and exam mark, and the score the next test needs.
Averages from a tally: the mean, median and mode of counted data
Most things worth averaging on this site arrive as a tally, not a list: goals per match, birds per walk, faults per batch. A tally is a frequency table, a value and how many times it came up, and the average calculators at the top of the search results want the list typed out in full instead: fifteen numbers for fifteen matches. Choose Values and counts and enter the tally as it is.
A team’s goals in 15 matches: no goals 3 times, one goal 5 times, two goals 4 times, three goals twice and five goals once.
| Goals (value) | Matches (count) | Value × count | Running count |
|---|---|---|---|
| 0 | 3 | 0 | 3 |
| 1 | 5 | 5 | 8 |
| 2 | 4 | 8 | 12 |
| 3 | 2 | 6 | 14 |
| 4 | 0 | 0 | 14 |
| 5 | 1 | 5 | 15 |
| Total | 15 | 24 |
Mean: the value × count column is the total number of goals, 24, and the count column is the number of matches, 15. 24 ÷ 15 = 1.6 goals a match.
Median: with 15 matches the middle one is the 8th. The running count passes 8 in the one-goal row (3, then 8), so the median is 1.
Mode: the largest count is 5, in the one-goal row, so the mode is 1. It is the value with the biggest count, never the biggest count itself.
Range: 5 − 0 = 5. The four-goal row has a count of 0, which changes nothing here; a 0 at either end of the table would not stretch the range either.
The two slips this table invites are both divisions by the wrong number. Dividing the 24 goals by the 6 rows gives 4; averaging the values column (0, 1, 2, 3, 4, 5) gives 2.5. Both describe the table, not the matches. The divisor is always the number of things counted, the total of the count column.
Grouped data: the estimated mean, median and modal class
When the values were collected in classes, minutes of homework in bands of 20 or heights in bands of 5 cm, the exact values are gone and the averages can only be estimated. The calculator’s Grouped classes setting works them out the way school courses such as GCSE teach it, and labels every figure an estimate.
| Minutes | Pupils | Midpoint | Midpoint × pupils | Running count |
|---|---|---|---|---|
| 0–20 | 4 | 10 | 40 | 4 |
| 20–40 | 9 | 30 | 270 | 13 |
| 40–60 | 12 | 50 | 600 | 25 |
| 60–80 | 7 | 70 | 490 | 32 |
| 80–100 | 3 | 90 | 270 | 35 |
| Total | 35 | 1,670 |
Estimated mean: every pupil in a class is taken to sit at its midpoint, so the midpoint × count column stands in for the total: 1,670 ÷ 35 ≈ 47.71 minutes.
Estimated median: half of 35 is 17.5. The running count reaches 13 by the end of 20–40 and 25 by the end of 40–60, so the median is in 40–60, 4.5 of its 12 pupils in. Spreading those 12 evenly across the 20 minutes gives 40 + 4.5 ÷ 12 × 20 = 47.5. That is linear interpolation, the method used to read a median off a cumulative frequency graph, which is why it uses n ÷ 2 rather than the (n + 1) ÷ 2 used for a list.
Modal class: 40–60, the class with the most pupils.
Range: unknown exactly. The shortest time is under 20 and the longest at least 80, so the range lies between 60 and 100, and the calculator gives it as those two bounds.
Classes of different widths. If the classes are 0–10 with 10 values and 10–30 with 16, the second has more values but is twice as wide: 1.0 value per unit of width against 0.8. The modal class is the one with the highest frequency density, the tallest bar of a histogram, so it is 0–10. The calculator switches to density whenever the widths differ, and says so.
Classes with gaps. Whole-number classes such as 10–19 and 20–29 leave a gap of 1. Their midpoints are 14.5 and 24.5, worked from the limits as written, and the median uses the class boundaries 9.5, 19.5 and 29.5, halfway across each gap. Enter the classes as printed and the calculator works out both.
Averaging averages: why 82 and 72 make 76, not 77
Two classes sat the same test. Class A, 20 pupils, averaged 82; Class B, 30 pupils, averaged 72. The average of 82 and 72 is 77, and it is wrong for the 50 pupils, because it counts the class of 20 as if it were as big as the class of 30. The right figure goes back to the totals: 82 × 20 = 1,640 marks and 72 × 30 = 2,160 marks, together 3,800 marks for 50 pupils, which is 76. Choose Combine averages, enter each average with its count, and the calculator gives the combined average with the plain average of the averages beside it, so the difference is visible.
| What is combined | Plain average | Weighted by count |
|---|---|---|
| Class A: 20 at 82; class B: 30 at 72 | 77 | 76 |
| 9 of 10 (90%) and 30 of 50 (60%) | 75% | 65% |
| Two shops: 40 sales at £12 and 10 at £30 | £21 | £15.60 |
| Two groups of 25 at 60 and at 70 | 65 | 65 |
Percentages are averages too. 90% of 10 is 9 and 60% of 50 is 30, so together they are 39 of 60, which is 65%. Averaging 90 and 60 gives 75 only when both percentages are of the same number. Enter each percentage as the average and its base as the count.
Weights instead of counts. A grade where coursework counts 40% and the exam 60% is the same sum with the percentages as the counts: coursework 70 and exam 58 give (70 × 40 + 58 × 60) ÷ 100 = 62.8. The count field takes any positive number for that reason.
When every average rises and the total falls. Last year Class A had 10 pupils averaging 80 and Class B 40 averaging 60: 64 overall. This year A has 5 pupils averaging 82 and B 45 averaging 61. Both classes improved, and the year group fell to 63.1, because more pupils are now in the lower-scoring class. This is Simpson’s paradox, and the only protection against it is to keep the counts beside the averages, as the calculator’s table does.
Mean, median or mode: which average to quote
The example on the calculator is nine counts of birds on nine walks: 12, 15, 9, 15, 22, 15, 11, 9 and 41. The mean is 16.56, the median 15 and the mode 15. One walk of 41 lifts the mean 1.56 above the median; without it the mean would be 13.5, and so would the median. Neither figure is wrong. They answer different questions, and the calculator’s note under the table names the value pulling the mean whenever the two disagree, so you can decide which one to quote.
| What you counted | Quote | Why |
|---|---|---|
| Scores, times or measurements with no extreme values | The mean | It uses every value, and mean × count gives the total back |
| Daily counts with an occasional huge day (visitors, birds, sales) | The median for a typical day; the mean for planning a total | One busy day moves the mean but not the median; a month’s stock needs the mean |
| Categories: shoe sizes sold, favourite colours, answers | The mode | Names have no mean or median; the tally to percentage calculator gives each one’s share |
| Whole things, such as children per family | The median or the mode for a typical case; the mean for totals | A mean of 2.4 children describes no family, but 2.4 × 100 families is still 240 children |
| Speeds over equal distances, growth rates | Not an arithmetic mean | These need the harmonic or geometric mean; see what this calculator does not do |
The mean has one property the others lack, and it is why it is the default: the mean times the count is the total. Fifteen matches at 1.6 goals is 24 goals; no median or mode can be multiplied back like that. When the total matters, quote the mean. When a typical case matters and a few values are extreme, quote the median, and say which you used.
No mode, two modes, zeros and decimal commas
| Case | Example | The calculator says |
|---|---|---|
| Every value appears once | 2, 5, 8, 11, 14 | No mode |
| Every value appears equally often | 1, 1, 4, 4 | No mode, noting that some courses call 1 and 4 joint modes |
| Two values tie for most often | 3, 3, 5, 7, 7 | Modes 3 and 7 |
| One value only | 6, 6, 6 | Mode 6 |
| An even number of values | 3, 6, 7, 9 | Median 6.5, halfway between the 2nd and 3rd |
| Negative values | −4, −1, 2 | Mean −1, range 6 |
| A zero | 0, 4, 5 | Counted: mean 3 |
| A word or a blank | 4, n/a, 5 | Left out and listed: mean 4.5 |
No mode. The mode is the value that appears more often than the others, so a list where nothing repeats has none. Courses agree on that. They differ when every value repeats equally, as in 1, 1, 4, 4: most say there is no mode, some call both values modes. The calculator says no mode and names the values a course of the second kind would accept. When some values tie and others do not, every tied value is a mode, and all of them are listed.
Zeros and blanks. A walk that found no birds is a value of 0 and belongs in the average; a day you did not go out is not a value at all. The calculator counts every 0 and skips anything that is not a number, then lists what it skipped, so a stray “n/a” never becomes a silent zero.
Decimal commas. In much of Europe, South America and Africa 3,5 is three and a half. Commas normally separate the numbers here, so tick My numbers use a decimal comma and separate them with spaces, semicolons or new lines instead. Without it, the calculator warns when it sees something like 1,234, which it would otherwise read as two numbers.
The range is one number. It is the largest value minus the smallest, 41 − 9 = 32, not “9 to 41”. Grouped data is the exception: only bounds are known, and the calculator gives them.
What this calculator does not do
The calculator finds the four averages taught in school, the mean, median, mode and range, from a list, a tally, grouped classes or group averages. It does not:
| It does | It does not |
|---|---|
| The arithmetic mean, median, mode and range | The geometric mean for growth rates (10% up then 10% down is a 1% loss, not 0%) or the harmonic mean for speeds (out at 40 km/h and back at 60 averages 48, not 50) |
| Combine group averages, or values with weights | Drop the lowest score, or apply a school’s grading categories for you |
| Estimate averages from grouped classes | Recover the exact values the classes hid |
| Show the range | Give the standard deviation, variance or quartiles |
| Count while you go: no, use the tally counter or the multi counter, then bring the counts here | Send your figures anywhere: they stay in this browser |
Calculator, typical average tool, spreadsheet or by hand
Four ways to find an average, and where each one stops.
| This calculator | A typical average calculator | A spreadsheet | By hand | |
|---|---|---|---|---|
| Cost | Free, no sign-up | Free | Free or paid | Free |
| A pasted list | Up to 10,000 numbers | Yes | Yes | Slow |
| Values and counts from a tally | Yes, with the working | Type every value out | With SUMPRODUCT | Yes |
| Grouped classes | Estimated mean, median and modal class | No | Only if you build it | Yes |
| Combining group averages | Weighted, beside the plain average | Usually not | With formulas | Yes |
| Every tied mode, or no mode | Listed and explained | Often one mode or none shown | MODE gives only the first | Yes |
| Decimal commas | Yes | Rarely | By locale | Yes |
| Next value for a target average | Yes | No | With a formula | Yes |
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Frequently asked questions
How do you calculate the average of a set of numbers?
Add the numbers and divide by how many there are. For 12, 15, 9, 15, 22, 15, 11, 9 and 41 the total is 149 and there are 9 numbers, so the average, the mean, is 149 ÷ 9 = 16.56. Paste the numbers into the calculator, separated by commas, spaces or new lines, and it shows the median, mode and range as well.
What is the difference between mean, median, and mode?
The mean is the total divided by how many values there are. The median is the middle value once they are sorted, or halfway between the two middle ones. The mode is the value that appears most often. For 9, 9, 11, 12, 15, 15, 15, 22 and 41 they are 16.56, 15 and 15: one large value lifts the mean but not the other two.
How do you find the mean from a frequency table?
Multiply each value by its frequency, add those products, and divide by the total frequency. For goals per match of 0 three times, 1 five times, 2 four times, 3 twice and 5 once, that is 24 ÷ 15 = 1.6 goals. Dividing by the number of rows instead is the usual slip. Choose Values and counts and the calculator builds the table with every column.
Is there a mode if every number appears once?
No. The mode is the value that appears more often than the others, so when every value appears once there is no mode, and the calculator says so. It says the same when every value appears equally often, such as 1, 1, 4, 4, although some courses call those joint modes. When two or more values tie for most often, every one of them is a mode.
How do I calculate the median with an even number of values?
Sort the values, take the two in the middle and go halfway between them. For 3, 6, 7 and 9 the middle pair is 6 and 7, so the median is 6.5, which is not one of the values. With n values the middle pair sits at positions n ÷ 2 and n ÷ 2 + 1. The calculator names both positions and both values in its working.
Which central tendency is affected by extreme values?
The mean. Every value goes into the total, so one very large or very small value moves it, while the median and mode barely notice. Eight bird counts between 9 and 22 plus one walk of 41 give a mean of 16.56 against a median of 15; without the 41 the mean drops to 13.5. The range is set entirely by the extremes.
How do I calculate weighted average?
Multiply each value by its weight, add the results, and divide by the total of the weights. A test average of 82 for 20 pupils and 72 for 30 pupils gives (82 × 20 + 72 × 30) ÷ 50 = 76. Choose Combine averages, enter each average with its count or weight, and the calculator shows the weighted result beside the plain average of the averages.
Can you average averages?
Only if every group is the same size. Otherwise weight each average by the number of values behind it: classes averaging 82 and 72 with 20 and 30 pupils combine to 76, not the 77 a plain average gives. Percentages work the same way: 9 of 10 and 30 of 50 are 90% and 60%, but together they are 39 of 60, which is 65%, not 75%.
What score do I need on my next test to get an average of 80?
Multiply the target by the number of tests including the next one, then subtract the total so far. Scores of 70, 74, 87 and 85 total 316; an 80 average over five tests needs 400, so the next score must be 84. Paste your scores, type the target average under the list, and the calculator works it out. It assumes every test counts equally.
Is the average the same as the mean?
Usually. In everyday use and in most calculators, the average is the arithmetic mean: the total divided by the count. Statistics uses average more loosely for any typical value, including the median and the mode, so a question asking for the average of a lopsided set may want the median. When in doubt, quote the mean and the median together.
Related guides
Longer answers to the questions behind the numbers.