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Median Calculator

Find the median, sorted values, count, minimum, and maximum from a list of numbers.

  • median
  • middle value
  • statistics median
  • sorted values
  • mean median mode

Supports decimals, negative numbers, commas, spaces, and line breaks.

Status: initial

Results

Awaiting calculation

Explore your result

Five-number summary

Explore the median calculator result visually while keeping this page's detailed guidance and examples.

Five-number summary
Minimum4
Q112
Median20
Q331
Maximum48

Use this result well

  1. 1Verify the calculator inputs.
  2. 2Compare the key result relationships.
  3. 3Review the page guidance before acting.

Median and IQR are more resistant to extreme values than mean and range.

Calculator guide

Introduction

The Median Calculator finds the middle value in a sorted list of numbers and shows related descriptive statistics, including mean, mode, range, quartiles, IQR, five-number summary, frequency table, and possible outliers.

What is the median?

The median is the central value after numbers are sorted from smallest to largest. It is often useful when unusually high or low values would distort the mean.

How this median calculator works

Sort the numbers first. If there is an odd number of values, the median is the middle value. If there is an even number of values, the median is the average of the two middle values. The calculator also splits the sorted list into lower and upper halves to estimate Q1, Q3, and IQR.

Variable explanations

Understand what each input and result means before calculating.

Numbers

The list of values used to find the median and summary statistics.

Sorted values

The same numbers arranged from smallest to largest.

Count

The number of values in the list.

Median

The middle value or average of the two middle values.

Mean

The arithmetic average of all values.

Mode

The most frequent value or values.

Q1 and Q3

The lower and upper quartiles.

IQR

The spread between Q1 and Q3.

Reviewed by the Calculator.org.in Editorial Team

Formula behavior, validation cases, explanatory examples, and cited sources are checked before publication. This review supports educational accuracy and is not a substitute for qualified professional advice.

Last reviewed: 2026-08-03

Review process

Formula guide

See the calculation logic, variable definitions, and practical meaning.

Odd count median

Median = middle sorted value

  • Sort values in ascending order.
  • Use the value at the center position.

Use this when the list has 1, 3, 5, 7, or another odd number of values.

Even count median

Median = (lower middle + upper middle) / 2

  • Sort values first.
  • Average the two center values.

Use this when the list has 2, 4, 6, 8, or another even number of values.

Mean

Mean = sum(values) / count

  • The mean uses every value in the list.

Compare mean and median to see whether outliers or skew may affect the average.

Mode

Mode = most frequent value

  • A data set can have no mode, one mode, or multiple modes.

Use this to identify repeated values.

Quartiles

Q1 = median of lower half; Q3 = median of upper half

  • The median is excluded from the halves when count is odd.

Quartiles divide the sorted data into four parts.

Interquartile range

IQR = Q3 - Q1

  • IQR measures the spread of the middle 50%.

IQR is commonly used with box plots and outlier checks.

Outlier fences

Lower fence = Q1 - 1.5 x IQR; Upper fence = Q3 + 1.5 x IQR

  • Values outside these fences are possible outliers.

This is a common exploratory-data rule, not proof that a value is wrong.

Worked examples

Follow realistic inputs through the calculation step by step.

1

Worked example

Odd number of values

  1. 1Values 8, 3, 12, 7, 9 sort to 3, 7, 8, 9, 12.
  2. 2The median is 8.
2

Worked example

Even number of values

  1. 1Values 4, 10, 2, 8 sort to 2, 4, 8, 10.
  2. 2Median = (4 + 8) / 2 = 6.
3

Worked example

Median with an outlier

  1. 1Values 10, 11, 12, 13, 100 have a median of 12.
  2. 2The mean is pulled upward more than the median.
4

Worked example

Five-number summary

  1. 1Sort the data.
  2. 2Find minimum, Q1, median, Q3, and maximum.
  3. 3Use those five values to understand center and spread.
5

Worked example

Outlier check

  1. 1Calculate Q1 and Q3.
  2. 2Find IQR = Q3 - Q1.
  3. 3Check values outside Q1 - 1.5 x IQR and Q3 + 1.5 x IQR.

Common mistakes

Avoid these common input and interpretation errors.

Forgetting to sort first

The median is based on sorted order, not the order values were entered.

Using the mean instead of the median

The mean adds values and divides by count. The median finds the center of the sorted list.

Choosing one middle value for an even count

When the count is even, average the two middle values.

Dropping repeated values

Repeated values still count as separate data points unless your data-cleaning process says otherwise.

Treating possible outliers as automatic errors

Outlier fences flag unusual values; they do not prove a value should be removed.

Expecting one universal quartile method

Different textbooks and software tools can use different quartile conventions.

Using grouped data as raw data

This calculator expects raw values, not frequency-class intervals or grouped data tables.

Frequently asked questions

Quick answers to the questions users ask most often.

What does this Median Calculator do?
It sorts a list of numbers and returns median, mean, mode, count, sum, minimum, maximum, range, quartiles, IQR, outlier fences, and frequency counts.
What is the median?
The median is the middle value of a sorted data set.
How do I find the median with an odd number of values?
Sort the values and choose the one in the middle.
How do I find the median with an even number of values?
Sort the values and average the two middle values.
Can this calculator handle decimals?
Yes. Decimal values are supported.
Can this calculator handle negative numbers?
Yes. Negative values are sorted and included normally.
Do repeated values count?
Yes. Every entered number counts, including duplicates.
Is median the same as average?
No. Average usually means arithmetic mean, while median is the center of sorted values.
When is median useful?
Median is useful when outliers would make the mean less representative.
What is Q1?
Q1 is the median of the lower half of the sorted data.
What is Q3?
Q3 is the median of the upper half of the sorted data.
What is IQR?
IQR is Q3 minus Q1. It measures the spread of the middle 50% of values.
What is a five-number summary?
It is minimum, Q1, median, Q3, and maximum.
How are possible outliers found?
The calculator uses the common 1.5 x IQR rule: values below Q1 - 1.5 x IQR or above Q3 + 1.5 x IQR are flagged.
Can I paste numbers from a spreadsheet?
Yes. Commas, spaces, and line breaks are supported.
What happens if I enter one number?
The median is that number.
Does order matter?
No. The calculator sorts values before finding the median.
Can the median be a number not in the list?
Yes. For even counts, averaging the two middle values can produce a value not directly entered.
What is the middle position formula?
For an odd count n, the middle position is (n + 1) / 2 after sorting.
How is this different from a mode calculator?
Median finds the center value. Mode finds the most frequent value.
Does this calculate grouped-data median?
No. It expects raw values rather than grouped frequency intervals.

References

Sources used to support the calculator guidance.

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Version history

A transparent record of calculator content updates.

Updated 2026-08-03
  • 1.0.0 · 2026-07-06

    Initial median calculator release.

  • 1.1.0 · 2026-08-03

    Added mean, mode, sum, range, quartiles, IQR, outlier fences, five-number summary, frequency table, and mean-vs-median comparison.