Calculate The Median of The Following Frequency Distribution Table

The median is the middle value in a frequency distribution table. It's a measure of central tendency that helps identify the central point of a dataset. This guide explains how to calculate the median from a frequency distribution table and provides an interactive calculator to perform the calculation.

What is the Median?

The median is the middle value in a dataset when it's ordered from smallest to largest. For a frequency distribution table, the median represents the value that separates the higher half of the data from the lower half. Unlike the mean, the median isn't affected by extreme values, making it a robust measure of central tendency.

The median is particularly useful when dealing with skewed distributions or when outliers might distort the mean. It provides a better representation of the "typical" value in such cases.

How to Calculate the Median

Calculating the median from a frequency distribution table involves these steps:

List all values in ascending order
Calculate the cumulative frequency for each value
Find the middle position (N/2 for even, (N+1)/2 for odd)
Identify the value where the cumulative frequency first exceeds the middle position

Formula for Median:

For a frequency distribution table with N total observations, the median is the value where the cumulative frequency first reaches or exceeds N/2.

When the total number of observations is even, the median is the average of the two middle values. When it's odd, it's the middle value itself.

Worked Example

Consider the following frequency distribution table:

Class Interval	Frequency
10-20	5
20-30	8
30-40	12
40-50	7

To find the median:

Calculate total observations: 5 + 8 + 12 + 7 = 32
Find the middle position: 32/2 = 16
Create a cumulative frequency table:

Class Interval	Frequency	Cumulative Frequency
10-20	5	5
20-30	8	13
30-40	12	25
40-50	7	32

The cumulative frequency first exceeds 16 in the 30-40 interval. Therefore, the median is the lower bound of this interval, which is 30.

FAQ

What if the median falls in the middle of a class interval?

If the cumulative frequency reaches the middle position within a class interval, use the lower bound of that interval as the median.

Can the median be the same as the mean?

Yes, the median can equal the mean in symmetric distributions, but they often differ in skewed distributions.

How does the median compare to the mode?

The median represents the middle value, while the mode represents the most frequent value. They can be the same in some distributions but differ in others.