Descriptive Statistics
Mean Median Mode Calculator
Mean, median, and mode are computed from the same list, and a one-line note appears when those three summaries do not land on one number.
Worksheet
Press Calculate to see the result.
Mean, median, and mode are computed from the same list, and a one-line note appears when those three summaries do not land on one number.
What this calculator answers
A short batch can tell three honest stories at once. The mean spends the total evenly, the median stands on the middle rank after sorting, and the mode is whichever value shows up most often. In 4, 7, 4, 9, 7, 4, 3 the crowd is 4, the middle rank is 4, and the mean is higher because 9 and the two 7s still sit in the sum. Reporting only one of them hides that split. This page prints all three and adds a note when they are not the same number.
The mean uses every magnitude once. The median uses Hyndman-Fan type 7 on the ordered list. The mode reports every value that ties for the highest frequency, or says there is no mode when nothing repeats. Supporting counts and intermediate terms sit under the headline so a reader can see what was divided by what. When a checkbox or a tail setting changes the divisor or the rejection region, that choice appears in the steps rather than vanishing into a silent default.
The formula, written out
Mean, median, and mode together uses this relationship.
mean = sum / n. median = type 7 middle. mode = every value with the highest frequency.
- mean. Sum divided by the count.
- median. Center of the ordered list.
- mode. Value or values with the greatest frequency.
- note. A line added when those three do not agree.
The three formulas answer different questions, so they are not required to match. A long right tail lifts the mean, leaves the median in place, and does nothing to the mode unless the tail value itself repeats. The algebra is the named textbook identity for this worksheet. Intermediate products and quotients appear in order so a calculator and a pencil can agree to the displayed rounding. If a neighbouring page uses a different divisor or a continuity correction, that page says so on its own ticket.
A full worked example
Example loaded in the worksheet
The form is prefilled with a small example so every arithmetic step can be checked by hand. Change one field after you finish the walkthrough and confirm the ticket moves the way the formula predicts.
The values are 4, 7, 4, 9, 7, 4, 3. The sum is 38 and the count is 7, so the mean is 5.4286. Ordered, the list is 3, 4, 4, 4, 7, 7, 9.
The median, using Hyndman-Fan type 7, is 4. The highest frequency is 3, so the mode is 4. The mean is 5.4286, the median is 4, and the mode is 4, so the three summaries do not agree.
The mean spends magnitudes, the median uses rank, and the mode uses repeats. None of the three is converted into one of the others.
| Mean | 5.4286 |
|---|---|
| Median | 4 |
| Mode | 4 |
| Count | 7 |
The mean is 5.4286, the median is 4, and the mode is 4, so the three summaries do not agree.
A second situation
A single 100 replaces the repeated values and pulls the mean
The values are 1, 2, 3, 4, 100. The sum is 110 and the count is 5, so the mean is 22. Ordered, the list is 1, 2, 3, 4, 100.
The median, using Hyndman-Fan type 7, is 3. Every distinct value appears once, so there is no mode. The mean is 22, the median is 3, and the mode is No mode, so the three summaries do not agree.
The mean spends magnitudes, the median uses rank, and the mode uses repeats. None of the three is converted into one of the others.
| Mean | 22 |
|---|---|
| Median | 3 |
| Mode | No mode |
| Count | 5 |
The mean is 22, the median is 3, and the mode is No mode, so the three summaries do not agree.
The alternate list 1, 2, 3, 4, 100 has a mean of 22 and a median of 3, and it has no mode because nothing repeats. The gap between 22 and 3 is the whole point of printing all three numbers. The second example changes the feature that this formula is sensitive to, and the ticket shows the new figure beside the same definition. That contrast is the fastest way to see which input owns the movement.
What moves when the input moves
An extra 9 was added, which changes the mean and creates a second candidate in the frequency tally. The headline result went from 5.4286 to 5.875.
The nudged inputs
The values are 4, 7, 4, 9, 7, 4, 3, 9. The sum is 47 and the count is 8, so the mean is 5.875. Ordered, the list is 3, 4, 4, 4, 7, 7, 9, 9.
The median, using Hyndman-Fan type 7, is 5.5. The highest frequency is 3, so the mode is 4. The mean is 5.875, the median is 5.5, and the mode is 4, so the three summaries do not agree.
The mean spends magnitudes, the median uses rank, and the mode uses repeats. None of the three is converted into one of the others.
| Mean | 5.875 |
|---|---|
| Median | 5.5 |
| Mode | 4 |
| Count | 8 |
The mean is 5.875, the median is 5.5, and the mode is 4, so the three summaries do not agree.
How to read the result
If the note says the summaries disagree, do not pick the one that flatters the decision and ignore the others. Say which center you are using and why the others differ. Say the unit, the sample size or contract terms, and the formula name in the same sentence as the figure. A number without those three pieces invites a later reader to invent a definition that this page never used.
Write the result with its unit, the inputs that produced it, and the name of the formula. Write the result with its unit, the inputs that produced it, and the name of the formula. If the ticket shows a decision sentence, quote the alpha and the tail with it. If the ticket shows a money or dose figure, quote the rate and the schedule that produced it.
Assumptions that have to stay true
- The values can be added, ordered, and tallied as the same kind of observation.
- Equal numbers are truly ties, not an artifact of rounding you did not intend.
- You want all three centers, not a blended compromise.
- A missing observation is omitted rather than coded as zero.
If an assumption above is false, do not average the discomfort away. Change the worksheet or change the question. A correct arithmetic step on the wrong model is still the wrong answer for the decision you are trying to make.
Mistakes that change the answer
- Averaging the mean and the median into a fourth number nobody defined.
- Declaring a mode when every frequency is 1.
- Using the mean as the typical value after the note has said the tail pulled it.
- Sorting for the median and then forgetting that the mode does not care about order.
Where a different calculator is the honest choice
Use the mean, median, or mode calculator when only one of those definitions is the job. Use the descriptive statistics calculator when you also need the spread on the same ticket. Related links under the essay open pages that keep their own formulas instead of hiding a mode switch inside this ticket.
When the job changes, move to a page built for that job: Mean Calculator, Median Calculator, Mode Calculator.
Check yourself
Values are 4, 7, 4, 9, 7, 4, and 3. What are the mean, the median, and the mode?
The mean is 5.4286, the median is 4, and the mode is 4.
Using the result in a sentence
Class sets, small surveys, and defect codes are easier to brief when the equal share, the middle rank, and the crowd are visible together. Keep the count, the unit, and the assumption list beside any copy of the number that leaves this browser tab.
Agreement among the three is not proof that the list is symmetric in every tail. Disagreement is a signal to plot the values, not a license to hide two of the three numbers. Pair the headline with the steps before you staff a route, set a grade boundary, or compare two contracts from a single number.
Questions people ask next
01What definition does the Mean Median Mode Calculator commit to?
This page uses Mean, median, and mode together: mean = sum / n. median = type 7 middle. mode = every value with the highest frequency.. The three formulas answer different questions, so they are not required to match. A long right tail lifts the mean, leaves the median in place, and does nothing to the mode unless the tail value itself repeats. If a textbook uses a different divisor, a different continuity correction, or a different rounding rule, the last digits can move, so the definition is printed above the result. The worksheet asks for Numbers, and it refuses a blank that the formula cannot interpret. Keep that printed definition in the sentence you write next to the figure so a later reader can rebuild the arithmetic without guessing which convention you chose.
02How should the worked example be read out loud?
In the loaded example the mean is 5.4286. If the note says the summaries disagree, do not pick the one that flatters the decision and ignore the others. Say which center you are using and why the others differ. Say the unit and the count before you say whether the number is large or small. Read the steps in order rather than jumping to the headline, because the intermediate terms are where a swapped percent and proportion usually hide. If the ticket shows both a primary figure and a comparison figure, name which one you are quoting.
03What is the fastest way to get a misleading result?
Averaging the mean and the median into a fourth number nobody defined. Agreement among the three is not proof that the list is symmetric in every tail. Disagreement is a signal to plot the values, not a license to hide two of the three numbers. A second common failure is leaving a checkbox or tail setting in the wrong state and then treating the number as if the default had matched your plan. Reset the example, change one input, and confirm the ticket moves in the direction the formula predicts before you trust a live run.
04When should I leave this page for a different calculator?
Use the mean, median, or mode calculator when only one of those definitions is the job. Use the descriptive statistics calculator when you also need the spread on the same ticket. The related links under the essay go to those worksheets, which keep their own formulas instead of hiding them in a mode switch. If the question changed from a summary to a test, from a payment to a refinance, or from a raw score to a percentile, switch pages rather than forcing this ticket to answer a job it was not built for.
05What belongs in the sentence next to the number?
The mean is 5.4286, the median is 4, and the mode is 4. Name the formula, the sample size or the inputs, and the unit before you compare the figure with someone else's. A bare number without those three pieces cannot be audited when a score, a rate, or a lab value is challenged later. Store the inputs beside the result whenever the figure will travel into a report.