Formula
Sort the included values from lowest to highest. If n is odd, median = value at position (n + 1) ÷ 2. If n is even, median = average of values at positions n ÷ 2 and n ÷ 2 + 1.
Math & Percentages
Median Calculator
Find the middle value of a small number set, with the sorted order, count and even-number averaging rule kept visible.
Calculator
Working calculator
Live result24 median7 values sorted: 12, 18, 21, 24, 30, 34, 39 · middle position 4: 24
Formula used
Sort the included values from lowest to highest. If n is odd, median = value at position (n + 1) ÷ 2. If n is even, median = average of values at positions n ÷ 2 and n ÷ 2 + 1.
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
Median 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
24 medianCalculationTime keeps the path visible: the input, the method and the final number belong together.
CalculationTime
Median Calculation Report
24 median7 values sorted: 12, 18, 21, 24, 30, 34, 39 · middle position 4: 24
Inputs
- Value 1
- 12
- Value 2
- 18
- Value 3
- 21
- Value 4
- 24
- Value 5
- 30
- Value 6
- 34
- Value 7
- 39
- How many values to include
- 7 2 to 7
Method
Sort the included values from lowest to highest. If n is odd, median = value at position (n + 1) ÷ 2. If n is even, median = average of values at positions n ÷ 2 and n ÷ 2 + 1.
- For 12, 18, 21, 24, 30, 34 and 39, the sorted list is already in order. There are 7 values, so the median position is (7 + 1) ÷ 2 = 4. The 4th value is 24.
Assumptions
- The active count is rounded to a whole number from 2 to 7.
- Only Value 1 through the active count are included; later boxes are ignored.
- Negative values, decimals and repeated values are allowed because the median depends on order, not on positive-only quantities.
- This page calculates the simple median of the entered list; grouped frequency tables and weighted medians need a separate method.
Notes
Use this space on the printed report for client, supplier, classroom, job-location, measurement, quote or approval notes.
Worked example
For 12, 18, 21, 24, 30, 34 and 39, the sorted list is already in order. There are 7 values, so the median position is (7 + 1) ÷ 2 = 4. The 4th value is 24.
Professional note
Master’s Tip: print the sorted list beside the answer. The median is robust against very high or very low outliers, but only if the values being included are clear and the count is not accidentally wrong.
Regional and unit assumptions
The calculator uses the standard descriptive-statistics median rule taught in school mathematics and used in basic data summaries. It does not apply weighting, sampling correction or frequency-table shortcuts.
Assumptions and limitations
- The active count is rounded to a whole number from 2 to 7.
- Only Value 1 through the active count are included; later boxes are ignored.
- Negative values, decimals and repeated values are allowed because the median depends on order, not on positive-only quantities.
- This page calculates the simple median of the entered list; grouped frequency tables and weighted medians need a separate method.
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
Sort the included values from lowest to highest. If n is odd, median = value at position (n + 1) ÷ 2. If n is even, median = average of values at positions n ÷ 2 and n ÷ 2 + 1.
Standard or basis
The calculator uses the standard descriptive-statistics median rule taught in school mathematics and used in basic data summaries. It does not apply weighting, sampling correction or frequency-table shortcuts.
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: print the sorted list beside the answer. The median is robust against very high or very low outliers, but only if the values being included are clear and the count is not accidentally wrong.
Related calculators
Questions
How do you calculate the median?
Sort the values from lowest to highest. If there is one middle value, that value is the median. If there are two middle values, add them and divide by two.
What is the median of an even number of values?
For an even count, the median is the average of the two middle values after sorting. For example, the median of 4, 8, 10 and 20 is (8 + 10) ÷ 2 = 9.
Is the median the same as the average?
No. The average adds all values and divides by the count. The median only uses position after sorting, so it is less affected by extreme outliers.
Can repeated numbers be used?
Yes. Repeated numbers stay in the sorted list and can be the middle value or one of the two middle values.
Why does the calculator ask for an active count?
The active count makes the printable worksheet clear by showing exactly how many of the value boxes were included in the median.
Calculation note
Median is a positional measure of centre. It is useful when a single unusually large or small value would pull an arithmetic mean away from the typical middle of the list.
The median is about position, not total
An average uses the total of all values. A median uses the order of values. That difference matters in wages, house prices, classroom scores and response times, where one extreme value can make the average feel unlike the middle of the group.
Sorting is the audit trail
The most common median mistake is choosing a value before the list has been sorted. A useful worksheet keeps the sorted order beside the answer so the middle position can be checked by eye.
Even counts need two middle values
When the count is even, there is no single centre item. The standard rule averages the two middle values, which is why a median can be a number that was not one of the original entries.