Formula
Mean = sum of values ÷ number of values. Median = middle value after sorting, or the average of the two middle values for an even count. Mode = most frequent value. Range = maximum − minimum.
Percentage & Math
Mean Median Mode Calculator
Calculate the mean, median, mode and range for a small data set, with visible ordering, frequency checks and a printable classroom or data-review worksheet.
Calculator
Working calculator
Live resultMean 9 · median 8Sorted values: 4, 7, 7, 9, 12, 15 · mode 7 · range 11 · comparison value is +1 from the mean
Formula used
Mean = sum of values ÷ number of values. Median = middle value after sorting, or the average of the two middle values for an even count. Mode = most frequent value. Range = maximum − minimum.
This is the method behind the answer, so the result can be checked rather than simply trusted.Visual grid
This number is one point on a larger pattern
Mean Median Mode is not just a final answer. It is a step on a line: before and after, input and output, assumption and result.
Micro-timehours, minutes, shiftsHuman scaledays, weeks, projectsMacro-timemonths, years, calendars
InputFormulaResult
Mean 9 · median 8CalculationTime keeps the path visible: the input, the method and the final number belong together.
CalculationTime
Mean Median Mode Calculation Report
Mean 9 · median 8Sorted values: 4, 7, 7, 9, 12, 15 · mode 7 · range 11 · comparison value is +1 from the mean
Inputs
- Value 1
- 4
- Value 2
- 7
- Value 3
- 7
- Value 4
- 9
- Value 5
- 12
- Value 6
- 15
- Optional comparison value
- 10
Method
Mean = sum of values ÷ number of values. Median = middle value after sorting, or the average of the two middle values for an even count. Mode = most frequent value. Range = maximum − minimum.
- For 4, 7, 7, 9, 12 and 15, the sum is 54 and the mean is 54 ÷ 6 = 9. The sorted middle values are 7 and 9, so the median is 8. The mode is 7 because it appears twice. The range is 15 − 4 = 11.
Assumptions
- All six visible values are included in the calculation, including zeros and repeated values.
- The calculator treats the inputs as a simple numeric data set, not grouped or weighted data.
- If every value appears once, the data set is reported as having no repeated mode.
- Mean can be pulled by outliers, so median and range should be read beside it when the data is uneven.
Notes
Use this space on the printed report for client, supplier, classroom, job-location, measurement, quote or approval notes.
Worked example
For 4, 7, 7, 9, 12 and 15, the sum is 54 and the mean is 54 ÷ 6 = 9. The sorted middle values are 7 and 9, so the median is 8. The mode is 7 because it appears twice. The range is 15 − 4 = 11.
Professional note
Master’s Tip: do not pick one average word casually. Mean is best for balanced numeric data, median is often clearer when outliers exist, and mode is useful when repetition matters.
Regional and unit assumptions
Standard or basis: elementary descriptive statistics for an unweighted numeric list. The page uses direct arithmetic and does not infer sampling design, population claims, grouped classes or statistical significance.
Assumptions and limitations
- All six visible values are included in the calculation, including zeros and repeated values.
- The calculator treats the inputs as a simple numeric data set, not grouped or weighted data.
- If every value appears once, the data set is reported as having no repeated mode.
- Mean can be pulled by outliers, so median and range should be read beside it when the data is uneven.
Methodology & Accuracy
How this calculator is checked
CalculationTime pages are built around visible arithmetic: the formula, assumptions, worked example and practical limitations are shown so the result can be checked rather than simply trusted.
Formula used
Mean = sum of values ÷ number of values. Median = middle value after sorting, or the average of the two middle values for an even count. Mode = most frequent value. Range = maximum − minimum.
Standard or basis
Standard or basis: elementary descriptive statistics for an unweighted numeric list. The page uses direct arithmetic and does not infer sampling design, population claims, grouped classes or statistical significance.
Where a calculator follows a named legal, trade or industry standard, that standard is cited visibly. Otherwise the page uses transparent general arithmetic and states its limits.Master's Tip
Master’s Tip: do not pick one average word casually. Mean is best for balanced numeric data, median is often clearer when outliers exist, and mode is useful when repetition matters.
Related calculators
Questions
How do you find mean, median and mode?
Find the mean by adding all values and dividing by the count. Find the median by sorting the data and taking the middle. Find the mode by identifying the value that appears most often.
What is the mean of 4, 7, 7, 9, 12 and 15?
The sum is 54 and there are six values, so the mean is 54 ÷ 6 = 9.
What happens if there are two middle values?
When the data set has an even number of values, the median is the average of the two middle values after sorting.
Can a data set have no mode?
Yes. If every value appears the same number of times and no value repeats more than the others, the calculator reports no repeated mode.
What should I print for a mean median mode worksheet?
Print the original values, sorted values, sum, count, mean, median, mode, range, formula and notes area so the calculation can be checked or marked later.
Calculation note
Mean, median and mode are often taught together because “average” can mean different summaries. Keeping the sorted list, frequency check and range beside the answer helps readers see which summary fits the data.
Mean balances the total
The mean shares the total equally across all values. It is sensitive to every number, which makes it useful but also vulnerable to outliers.
Median starts by sorting
The median ignores the exact distance of extreme values and asks for the middle position. That makes it a useful companion when the data is skewed.
Mode looks for repetition
The mode is about frequency, not size. It is especially helpful for categories, common scores, repeated measurements and quick classroom examples.
Sources and further readingOpenStax Introductory Statistics — Measures of the Center of the DataKhan Academy — Mean, median and mode