How to Find the Median in Statistics — A Step-by-Step Guide

By Pankaj Kumar|Last Updated: July 12, 2026|

Key Takeaways

The median is the middle value of a data set arranged in order of magnitude.
For odd n, the median position is (n+1)/2; for even n, average the two middle values.
The median equals the 50th percentile and is resistant to outliers and skewed data.
Grouped data uses the formula: Median = l + [(n/2−c)/f] × h.
Excel’s native MEDIAN function calculates the median directly from a selected range.

What Is the Median in Statistics?

The median is the data point that falls in the middle of a data set arranged in ascending or descending order. These numbers either belong to a sample data set or a population. There is no universal symbol for the median, but x͂ or Mdn generally represent it. Students working through statistics tutoring often encounter the median as one of the first core concepts in descriptive analysis.

Median as a Measure of Central Tendency

Median is one of the main measures of the central tendency of a data set, and the other two popular ones are mean and mode. Measures of central location and summary statistics are some synonyms for measures of central tendency.

We use measures of central tendency to get more insights into the nature of the data set. The median may not represent the average value or the data points with the highest frequencies. Still, it captures the value of the data points representing the center of the spread of the sample or population.

In many cases, there is no single suitable measure of central tendency to reveal everything about the nature of the data. In many cases, the mean or mode represents the sample or population more accurately. However, the median has the advantage that it is less affected by outliers and skewed data as it is the middle value of the data set.

Is the Median the Same as the 50th Percentile?

Yes! The Median and the 50th percentile value are the same things. The Median represents the middle value of the given data points, and so does the 50th percentile value of a data set with 50% values smaller and 50% values larger than itself.

Refer to the blog posts ‘How to find mean’ and ‘How to find mode‘ to learn how to calculate mean and mode. These concepts also appear frequently in AP Statistics tutoring, where understanding central tendency is foundational.

How to Find the Median in Statistics

How to Find the Median of a Data Set

As mentioned above, the median is nothing but the value of the data points that occur in the middle of a data set sorted in order of magnitude.

Step 1

We must arrange the given data in ascending or descending order before calculating the median. Let us take n to represent the total number of data points.

Step 2

If n is odd, the middle value is the median. We calculate its position by the formula (n + 1)/2.
If n is even, the average of the two middle values is the median with positions n/2 and (n/2) + 1.

How to Find the Median from a Histogram

A histogram represents a frequency table visually as a bar chart. It usually has ordered data representing the class intervals on one axis. We can calculate the median by locating the central class intervals in the histogram. If we have grouped data, we must follow the method illustrated in example 3.

How to Find the Median Using Excel

The native ‘MEDIAN’ function returns the median value in Excel. We can select MEDIAN from the formula dropdown menu containing formulas or type MEDIAN in the formula bar. Then, we select the cells containing the data. For example, if we want to calculate the median for column K, rows three through 23, the formula will be ‘MEDIAN(K3:K23).’

Understanding how software handles statistical functions is also a key skill in R programming tutoring, where median calculations are performed programmatically on large data sets.

Sample Problems on Median

Example 1: Median of an Odd-Numbered Ungrouped Data Set

What is the median of the ungrouped sample data set containing 3, 5, 9, 2, 16, 14, 3, 15, 5, 17, 26, 2, and 21?

The data points arranged in increasing order = 2, 2, 3, 3, 5, 5, 9, 14, 15, 16, 17, 21, 26

The data set has 13 values. Hence, n = 13. Here, n is an odd number.

The position of the median value = (n+1)/2 = (13+1)/2 = 7

Median = 9

Example 2: Median of an Even-Numbered Ungrouped Data Set

What is the median of the ungrouped sample data set containing 9, 4, 7, 13, 5, 15, 23, 18, 4, 35, 46, 51, 13, and 22?

The data points in increasing order = 4, 4, 5, 7, 9, 13, 13, 15, 18, 22, 23, 35, 46, 51

n = 14

The positions of the data points occurring in the middle of the data set = n/2 and (n/2) + 1 = 7 and 8

Median = (13 + 15)/2 = 14

The data can be ungrouped or grouped. In the case of grouped data, we may not know the exact values of the data points in the sample or the population. However, we know the frequency of the data points occurring in the groups or intervals. For such data, we calculate the median differently.

Grouped data problems like these also appear in precalculus tutoring when students begin working with frequency distributions and data interpretation.

Example 3: How to Find the Median for Grouped Data

The time (in minutes) taken by participants of a group to finish a task is shown below.

Frequency distribution table of the time taken by the participants to finish a task

Time taken (in minutes)	Frequency (f_i)	Cumulative frequency (c)
1 ≤ t < 10	1	1
10 ≤ t < 15	4	5
15 ≤ t < 20	4	9
20 ≤ t < 25	6	15
25 ≤ t < 30	2	17
30 ≤ t < 35	2	19
35 ≤ t < 40	1	20

Median = l + [(n/2−c)/f] × h

In the given data, the 4th class interval (20 ≤ t < 25) is the median class interval as it is the middle value of the data set.

l = lower limit of the median class interval = 20

n = number of observations = 20

c = cumulative frequency of the class interval before the median class interval = 9

f = frequency of the median class interval = 6

h = class interval size = 5

Hence, median = 20 + [(20/2−9)/6] × 5 = 20.83

Still not sure how to find the median in statistics? You are not alone. Working through problems like these is exactly the kind of material covered in psychological statistics tutoring, where grouped frequency data appears regularly in research contexts.

If you find yourself struggling with the broader concepts behind data analysis, this guide on how to choose an algebra tutor using a verification checklist offers useful advice on finding qualified academic support. Students preparing for standardized exams may also find this post on struggling with AP Calculus and how to find the right tutor to score a 5 helpful for understanding how to approach difficult quantitative subjects. For those interested in how technology intersects with academic work, the article on Photomath and academic integrity is worth reading. And for engineering students who rely on strong math foundations, this post on AP Calculus tutors and engineering success explores the connection between early math preparation and long-term outcomes.